To begin with, let us define the system of ordinary differential equations for the benzene ring:
[tex]d^2θj/dt^2 + αdθj/dt + ω^2(θj−1−2θj+θj+1) = F cos(γt)[/tex]
Verification of time-independent particular solution:
When α = 0, the system becomes time-independent, and the equation reduces to:
[tex]θj'' + ω^2(θj−1−2θj+θj+1) = F cos(γt)[/tex]
We can assume a time-independent solution of the form θj = Aj, where A is a constant. Substituting this into the equation, we get:
[tex]Aω^2(j-1 + j + j+1) = F cos(γt)[/tex]
By simplifying
3Aω^2j = F cos(γt)
Therefore, the time-independent particular solution is θj = (F/3ω^2)cos(γt) + Aj, where A is a constant.
Eigenvectors and eigenvalues:
predicting the solution θj = Aj e^(iλt),we can integrate into an equation
[tex]−A(λ^2+αλ+ω^2)e^(iλt) + ω^2(e^(iλt)(A(j−1) + A(j+1)) + 2A(j)e^(iλt)) = F cos(γt)e^(iλt)[/tex]
Dividing both sides by e^(iλt), we get:
[tex]−A(λ^2+αλ+ω^2) + ω^2(A(j−1) + A(j+1) + 2A(j)) = Fcos(γt)[/tex]
Simplifying, we get:
[tex](2ω^2A − λ^2A) + ω^2(A(j−1) + A(j+1)) = F cos(γt) + αλA[/tex]
The eigenvectors of this matrix are:
[tex][±sin(π/6)][±sin(2π/6)][±sin(3π/6)][±sin(4π/6)][±sin(5π/6)][/tex]
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what is the fraction of players on the field that are midfielders
a soccer team has 11 players on the fields . of those players , 2 are forwards , 4 are midfeilders, 4 are defenders , and 1 is a goalie
After addressing the issue at hand, we can state that As a result, decimal midfielders make up around 36.36% of the players on the pitch
what is decimal?The decimal number system is frequently used to express both integer and non-integer quantities. Non-integer values have been added to the Hindu-Arabic numeral system. The technique used to represent numbers in the decimal system is known as decimal notation. A decimal number consists of both a whole number and a fractional number. The numerical value of complete and partially whole amounts is expressed using decimal numbers, which are in between integers. The full number and the fractional part of a decimal number are separated by a decimal point. The decimal point is the little dot that appears between whole numbers and fractions. An example of a decimal number is 25.5. In this case, 25 is the total number, and 5 is the minimum.
The following formula can be used to determine the percentage of midfielders on the field:
Overall number of players on the field / Total number of midfielders
In this situation, the total number of midfielders is 4, and the total number of players on the pitch is 11.
As a result, the percentage of midfielders on the field is:
4 / 11
This can be expressed in decimal or percentage form as follows:
0.3636 (rounded to four decimal places) (rounded to four decimal places)
36.36% (rounded to two decimal places) (rounded to two decimal places)
As a result, midfielders make up around 36.36% of the players on the pitch.
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A company has two manufacturing plants with daily production levels of 8x+15 items and 3x-7 items, respectively. The first plant produces how many more items daily than the second plant?
Therefore , the solution of the given problem of equation comes out to be the first plant makes 5x + 22 more items per day.
How do equations work?
Mathematical formulas frequently employ same variable word to guarantee agreement between two claims. Many academic numbers are shown to be equal using mathematical expression, also known as assertions. In this case, the normalise method adds b + 6 to employ the example of y + 6 rather than splitting 12 into two parts. It is possible to determine the length of the line and the quantity of connections between each sign's constituents. The significance of a symbol usually contradicts itself.
Here,
The first plant cranks out 8x + 15 items every day, while the second cranks out 3x - 7 items every day. By deducting the daily output of the second plant from the daily output of the first plant, we can determine how many more items the first plant creates than the second plant:
=> (8x + 15) - (3x - 7) (3x - 7)
If we condense this phrase, we get:
=> 8x + 15 - 3x + 7
Combining related words gives us:
=> 5x + 22
Therefore, compared to the second plant, the first plant makes 5x + 22 more items per day.
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What is the quotient of (x³ + 3x² + 5x + 3) = (x + 1)?
O x² + 4x +9
O x² + 2x
Ox²+2x+3
O x² + 3x + 8
Using the remainder theorem, the quotient of (x³ + 3x² + 5x + 3) divided by (x + 1) is Ox²+2x+3
What exactly is the remainder theorem?
The Remainder Theorem is an approach to Euclidean polynomial division. According to this theorem, dividing a polynomial P(x) by a factor (x - a), which is not an element of the polynomial, yields a smaller polynomial and a remainder.
Given Data
x³ +3x² +5x +3 / x+1 = x² +2x +3
x³ +x²
------------
0 2x² +5x
2x² +2x
----------------
0 3x +3
3x+3
----------------
0 0
The quotient of (x³ + 3x² + 5x + 3) divided by (x + 1) is x² +2x+3 using remainder theorem.
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Calculate the area of the region defined by the simultaneous inequalities y ≥ x-4,
y ≤ 10, and 5 ≤ x+y.
Answer: To solve this problem, we need to graph the three inequalities and find the overlapping region.
First, let's graph the inequality y ≥ x - 4. We can start by graphing the line y = x - 4, which has a y-intercept of -4 and a slope of 1.
|
10| + +
| + +
| +
|+
|
|
| +
| +
| +
| +
0|-----------------
0 1 2 3 4 5
Since we want the region where y is greater than or equal to x - 4, we shade the area above the line.
Next, let's graph the inequality y ≤ 10. This is a horizontal line passing through y = 10.
|
10| +----+
| + +
| +
|+
|
|
|
|
|
|
0|-----------------
0 1 2 3 4 5
Since we want the region where y is less than or equal to 10, we shade the area below the line.
Finally, let's graph the inequality 5 ≤ x + y. This is a line with a y-intercept of 5 and a slope of -1.
|
10| +----+
| + | +
| + |
|+ |
| |
| |
| |
| |
| |
| +
0|-----------------
0 1 2 3 4 5
Since we want the region where x + y is greater than or equal to 5, we shade the area above the line.
Now we can find the overlapping region of the three shaded areas:
|
10| +----+
| + | +
| + |
|+ |
| |
| |
| +
| +
| +
|+
0|-----------------
0 1 2 3 4 5
The region is a triangle with vertices at (0, 4), (1, 5), and (5, 0).
To find the area of the triangle, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
The base of the triangle is the distance between the points (0, 4) and (5, 0), which is 5.
The height of the triangle is the distance between the point (1, 5) and the line 5 = x + y. We can find the equation of the line perpendicular to 5 = x + y and passing through (1, 5). This line has a slope of 1 and passes through (1, 5), so its equation is y = x + 4. We can find the intersection of this line and the line 5 = x + y by solving the system of equations:
y = x + 4
y = 5 - x
Substituting y = x + 4 into the second equation, we get:
x + 4 = 5 - x
Solving for x, we get:
x = 1
Step-by-step explanation:
5. Jack has a 35-foot ladder leaning against the side of his house. If the bottom of the ladder is 21 feet away from his house, how many feet above the ground does the ladder touch the house?
Therefore, the ladder touches the house at a height of 28 feet above the ground.
What is triangle?A triangle is a geometric shape that consists of three straight sides and three angles. It is a polygon with three sides. The sides of a triangle are connected by its vertices or corners. The triangle is one of the simplest and most fundamental shapes in geometry, and it has many important properties and applications. Triangles have many practical applications in everyday life and in various fields, such as architecture, engineering, and physics. The study of triangles and their properties is an important part of mathematics and geometry.
Here,
We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs (the two shorter sides) is equal to the square of the length of the hypotenuse (the longest side, which is opposite the right angle). In this problem, the ladder, the side of the house, and the ground form a right triangle. The ladder is the hypotenuse, the distance from the house to the ladder is one leg, and the height we want to find is the other leg.
Let x be the height above the ground where the ladder touches the house. Then, using the Pythagorean theorem, we have:
x² + 21² = 35²
Simplifying and solving for x, we get:
x² + 441 = 1225
x² = 784
x = 28
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nobody had the right awnser last time so What is the sum of (x−5x^2−12)
and (4+11x−3x^2)
−2x^2−10x−16
−8x^2+12x−8
8x^2+12x−8
4x^2+6x−15
Answer:
12x - 8x^2 - 8.
Step-by-step explanation:
To find the sum of the two expressions, we add the corresponding coefficients of each term:
(x - 5x^2 - 12) + (4 + 11x - 3x^2)
= x + 11x - 5x^2 - 3x^2 - 12 + 4
= 12x - 8x^2 - 8
Rewrite cos (x+5π/4) in terms of sin x and/or cos x
Find the work done by a person weighing195lbwalking exactly one revolution(s) up a circular, spiral staircase of radius4ftif the person rises18ftafter one revolution (which can be parameterized asr(t)=⟨4cos(2πt),4sin(2πt),18t⟩where0≤t≤1) Work=∣∣ft−lbQuestion Help:□Message instructor
The correct work done by the person walking up the spiral staircase is -3,325.89 ft-lb, indicating that the person did work against gravity while climbing up the stairs.
The force required to lift a person of weight 195 lb against gravity is F = mg,
where g is the acceleration due to gravity and
m is the mass of the person.
We can convert the weight in pounds to mass in pounds by dividing by the gravitational acceleration, g = 32.2 ft/s²:
m = 195 lb / 32.2 ft/s²= 6.05 slugs
The work done by a force F over a distance d is given by the dot product of the force and displacement vectors:
W = F · d
In this case, the force is the weight of the person, F = mg, and the displacement vector is the difference between the initial and final positions, d = r(1) - r(0),
where r(t) is the position vector parameterized by t.
We can compute the displacement vector as follows:
r(1) = ⟨4cos(2π), 4sin(2π), 18⟩ = ⟨4, 0, 18⟩
r(0) = ⟨4cos(0), 4sin(0), 0⟩ = ⟨4, 0, 0⟩
d = r(1) - r(0) = ⟨0, 0, 18⟩
The work done is therefore:
W = F · d = (6.05 slugs) · (32.2 ft/s^2) · ⟨0, 0, 18⟩
= 0 · 0 + 0 · 0 + (6.05 slugs) · (32.2 ft/s^2) · 18 ft
= 3,325.89 ft-lb
Therefore, the work done by the person walking one revolution up the spiral staircase is 3,325.89 ft-lb.
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Patricio deposit $500 in a savings account theat pays 1. 5% simple interest. He does not withdraw any money from the account, and he makes no other deposit. How much money does Patricio have in the savings account after 5 years? The formula for simple interest is I=prt
According to simple interest, Patricio will have $537.50 in his savings account after 5 years.
To calculate the amount of money Patricio will have in his savings account after 5 years, we can use the formula for simple interest, which is I = prt. "I" stands for the amount of interest earned, "p" stands for the principal amount deposited, "r" stands for the interest rate per year (as a decimal), and "t" stands for the time period in years.
In this case, the principal amount (p) is $500, the interest rate (r) is 1.5% or 0.015 as a decimal, and the time period (t) is 5 years. Using the formula I = prt, we can calculate the amount of interest earned over 5 years:
I = prt
I = $500 x 0.015 x 5
I = $37.50
So, Patricio will earn $37.50 in simple interest over 5 years. To find out the total amount of money he will have in his savings account after 5 years, we simply add the interest earned to the principal amount:
Total amount = Principal amount + Interest earned
Total amount = $500 + $37.50
Total amount = $537.50
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Which is an example of a suggestive survey question?
What do you like and don’t like about the CEO?
Do you own a car or a truck?
What is your favorite brand of soda?
How much credit card debt do you owe?
The survey questiοn is What is yοur favοrite brand οf sοda?
What is a survey?In mathematics, a survey is a technique fοr gathering data that invοlves pοsing a series οf questiοns tο participants in οrder tο learn mοre abοut their attitudes and behaviοrs. It is the mοst typical and affοrdable methοd οf data cοllectiοn. A sample size can change depending οn the situatiοn.
What dο yοu like and dοn’t like abοut the CEO? It is nοt a survey questiοn. In a survey questiοn, there shοuld be an οbject, nοt a persοn.
Dο yοu οwn a car οr a truck? It is nοt a survey questiοn. The survey is dοne οn a particular prοduct. But in the questiοn, nο band is mentiοned.
Hοw much credit card debt dο yοu οwe? It is nοt a survey questiοn. It is a persοnal questiοn.
What is yοur favοrite brand οf sοda? It is a survey questiοn. The survey is dοne οn a sοda brand.
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what is the value of the expression
m+(7*9)/n
when m = 2.5 and n= 5
a 6.3
b 9.5
c 11.9
d 13.1
Answer:
We can substitute m = 2.5 and n = 5 into the expression:
m + (7*9)/n = 2.5 + (7*9)/5
We can simplify the second term:
(7*9)/5 = 63/5
Substituting back into the expression:
m + (7*9)/n = 2.5 + 63/5
We can find a common denominator and add the terms:
2.5 + 63/5 = 12.5/5 + 63/5 = 75/5 = 15
Therefore, the value of the expression is 15, which corresponds to option (b) as the correct answer.
The diameter of two circle are 3. 5 and 4. 2. Find the ratio of their area
Answer:The ratio of the area of the small circle to that of the bigger circle is 25:36.
Step-by-step explanation:
as in the previous problems, consider the model problem (4.3) with a real constant a < 0. show that the solution of the trapezoidal method i
The solution yn+1 is always less than or equal to yn, which means that the solution is stable for a < 0. Therefore the solution is of trapezoidal method.
The model problem (4.3) with a real constant a < 0 is given by:
[tex]y' = ay, y(0) = 1[/tex]
The trapezoidal method is given by:
[tex]yn+1 = yn + (h/2)(f(tn, yn) + f(tn+1, yn+1))[/tex]
where h is the step size, tn and yn are the current time and solution values, and [tex]f(t, y) = ay[/tex] is the right-hand side of the model problem.
To show that the solution of the trapezoidal method is stable for a < 0, we can substitute the right-hand side into the trapezoidal method and solve for yn+1:
[tex]yn+1 = yn + (h/2)(ayn + ayn+1)yn+1 - (h/2)ayn+1 = yn + (h/2)aynyn+1(1 - (h/2)a) = yn(1 + (h/2)a)yn+1 = yn(1 + (h/2)a)/(1 - (h/2)a)[/tex]
Since a < 0, the denominator [tex](1 - (h/2)a)[/tex] is always positive, and the numerator [tex](1 + (h/2)a)[/tex] is always less than or equal to 1. Therefore, the solution yn+1 is always less than or equal to yn, which means that the solution is stable for a < 0.
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Tony's Glass Factory makes crystal bowls and has a daily production cost C(x) in dollars given by
C(x) = 0.2x² - 10x + 650, where x is the number of bowls made.
Determine how many bowls should
be made to minimize the production cost? What is the cost when this many bowls are made?
Answer:
Step-by-step explanation:
To find this answer you need to find the vertex of the parabola. Do this by using the formulas for h and k as follows:
[tex]h=\frac{-b}{a}[/tex] and [tex]k=c-\frac{b^2}{4a}[/tex], where a, b, and c come from the quadratic equation.
Filling in for h:
[tex]h=\frac{10}{2(.2)}=25[/tex]
Filling in for k:
[tex]k=650-\frac{100}{4(.2)} =525[/tex]
Thus, the coordinates for the vertex are (25, 525). The h value interprets the number of bowls that should be produced to minimize the cost of production (25) and the minimum production cost is the k value (525).
The planetarium is remodeling and want to know the surface area of the building, including the skyview. Calculate the surface area and SHOW WORK.
The surface area of building with the skyview is found as 331.625 sq. yd.
Explain about the curved surface area?A solid shape having six square faces is called a cube. Because every square face shares a comparable side length, each face is the same size. A cube has 8 vertices and 12 edges. An intersection of three cube edges is referred to as a vertex.
The quantity of space enclosing a three-dimensional shape's exterior is its surface area.The area of just the curved portion of the shape, omitting its base, is referred to as the curved surface area (s).Total area = TSA of cuboid + CSA of hemisphere - area of circle
Total area = 2(lb + bh + hl) + 2πr² - πr²
Total area = 2(6*10 + 10*6 + 6*6) + 2*3.14*2.5² - 3.14*2.5²
On simplification:
Total area = 331.625
Thus, surface area of the building with the skyview is found as 331.625 sq. yd.
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An athletic field is a 44yd-by-88yd rectangle, with a semicircle at each of the short sides. A running track 10 yd wide surrounds the field. If the track is divided into eight lanes of equal width, with lane 1 being the inner-most and lane 8 being the outer-most lane, what is the distance around the track along the inside edge of each lane?
The distance around the track along the inside edge of each lane is 614.44 yd for lane 1, 634.88 yd for lane 2, 655.32 yd for lane 3, 675.76 yd for lane 4, 696.20 yd for lane 5, 716.64 yd for lane 6, 737.08 yd for lane 7 and 757.52 yd for lane 8.
The distance around the track along the inside edge of each lane can be calculated using the following formula:
Distance = (2 × 44 yd) + (2 × π × radius)
where the radius is equal to 44 yd + (lane number × 10 yd).
For lane 1, the radius is equal to 44 yd + (1 × 10 yd) = 54 yd. Therefore, the distance around the track along the inside edge of lane 1 is (2 × 44 yd) + (2 × π × 54 yd) = 614.44 yd.
The same calculation can be done for the other lanes, with the radius increasing by 10 yd for each lane. The radius for lane 2 is 64 yd, for lane 3 is 74 yd, for lane 4 is 84 yd, for lane 5 is 94 yd, for lane 6 is 104 yd, for lane 7 is 114 yd and for lane 8 is 124 yd.
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Which fraction looks same even if you turn it upside?
Answer:
The fraction that looks the same even if you turn it upside down is 6/9 or six-ninths.
Step-by-step explanation:
Determine the average rate of change of f(x) = x² - 10x + 5 over the interval [-4, 4].
The average rate of change is the slope of the line between the points
( -4, f(-4) ) and ( 4, f(4) )
f(-4) = 16 + 40 + 5 = 61
f(4) = 16 - 40 + 5 = 19
The slope (AKA average rate of change) is then
[tex]m =\dfrac{19-61}{4-(-4)}=\dfrac{-42}{8} = -\dfrac{21}{4}[/tex]
at a pizza parlor, the lunch special comes with your choice of a pizza slice, a salad and a drink. there are pizza slice options, salad options, and soda options. how many different ways are there to choose a lunch special combination?
There are 27 different ways to choose a lunch special combination.
To determine how many different ways there are to choose a lunch special combination:
At a pizza parlor, the lunch special comes with your choice of a pizza slice, a salad and a drink.
There are pizza slice options, salad options, and soda options.
Therefore, there are three options for each category, which are pizza slice, salad, and drink.
Then, we can use the multiplication principle to determine how many different ways there are to choose a lunch special combination:
3 options for pizza × 3 options for salad × 3 options for drink
= 27 different ways to choose a lunch special combination.
Therefore, there are 27 different ways to choose a lunch special combination.
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What percent of 64 is 4?
Responses
116%
1 over 16 end fraction percent
614%
6 and 1 over 4 end fraction percent
6212%
62 and 1 half percent
625%
The percentage value that represents what percent of 64 is 4? is (b) 6 1/4%
How to determine the percentage valueA percentage is a way to express a fraction or portion of a whole as a number out of 100.
From the question, we have the following parameters that can be used in our computation:
What percent of 64 is 4?
Represent the percentage with x
So, we have
x percent of 64 is 4
Express as product expression
x% * 64 = 4
Multiply through by 100
x * 64 = 400
Divide by 64
x = 6.25 or 6 1/4
Hence, the percentage is 6 1/4%
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نے
A pilot is preparing to land her plane and is descending at a rate of 750 feet for every 3 miles
that she flies horizontally. If the she begins her descent at an altitude of 32,000 ft., how many
miles will she have travelled (m) when she is 16,000 ft. above the ground?
A. 21-1/2
B. 48
C. 52
D. 64
Answer:
the answer is (A) 21-1/2.
Step-by-step explanation:
First, we need to calculate the rate of descent in feet per mile:
750 ft / 3 miles = 250 ft/mile
Next, we can set up a proportion to solve for the distance traveled:
(distance traveled) / (total altitude change) = (distance traveled) / (altitude change due to descent) + (altitude at which descent begins)
Let m be the distance traveled:
m / (32000 ft - 16000 ft) = m / (250 ft/mile * x miles) + 16000 ft
where x is the number of miles traveled when the pilot is 16000 ft above the ground.
Simplifying:
m / 16000 ft = m / (250 ft/mile * x miles) + 1
Multiplying both sides by 16000 ft:
m = m / (250 ft/mile * x miles) * 16000 ft + 16000 ft * 16000 ft
Multiplying both sides by (250 ft/mile * x miles):
m * (250 ft/mile * x miles) = m * 16000 ft + 16000 ft * (250 ft/mile * x miles)
Simplifying:
250 * x * m = 16000 * m + 4000 * x * m
Dividing both sides by m:
250 * x = 16000 + 4000 * x
Subtracting 4000 * x from both sides:
-3750 * x = -16000
Dividing both sides by -3750:
x = 4.266666... miles
Rounding to the nearest half mile gives us:
x ≈ 4.5 miles
Therefore, the answer is (A) 21-1/2.
Make x the subject of the formula a/b = 2x/x+5
When x is the subject of the formula a/b = 2x/x+5, the value of x = 5a/(2b - a).
What are variables?The alphabetic letter that conveys a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.
Any alphabet from a to z can be used for these variables. Most frequently, the variables "a," "b," "c," "x," "y," and "z" are utilised in equations. By performing mathematical operations on variables as if they were express numbers, one is able to handle a variety of problems in a single computation. A quadratic recipe is a common example that demonstrates how to explain each quadratic condition by simply substituting the numerical estimates of the condition's coefficients for the variables that correspond to it.
The given formula is:
a/b = 2x/x+5
To make x the subject of the formula we have to isolate the value of x.
Using cross multiplication we have:
a(x + 5) = b(2x)
ax + 5a = 2bx
5a = 2bx - ax
5a = x (2b - a)
5a/(2b - a) = x
Hence, when x is the subject of the formula a/b = 2x/x+5, the value of x = 5a/(2b - a).
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Create two dot plots so that:
• They have at least 5 points each.
• Their centers are around 7.
• Dot Plot A has a larger spread than Dot Plot B.
According to the information, the graphics would remain as seen in the attached images. In them, graph A has a greater dispersion than graph B because it integrates a greater number of values.
What is a dot plot?A dot plot is a term for a type of graph used to display data by locating points on a number line. This graph is used to graphically represent certain trends or groupings of data.
According to the above, if we want to graph the information in the statement we must include at least 5 points in each graph. Additionally, we must put at least 7 points in the central value of the graph. Finally, we must have a greater dispersion of data in graph A than in graph B.
According to the above, the graphics would remain as shown in the image.
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5 large jars of coffee have a total weight of 1250 grams.
2 large jars of coffee and 7 small jars of coffee have a total weight of 1200 grams.
Work out the total weight of 4 small jars of coffee.
The total weight of the 4 small jars of coffee is W = 400 grams
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the weight of large jar be x
Let the weight of small jar be y
5 large jars of coffee have a total weight of 1250 grams.
So , 5x = 1250
Divide by 5 on both sides , we get
x = 250 grams
And , 2 large jars of coffee and 7 small jars of coffee have a total weight of 1200 grams.
So , 2x + 7y = 1200
2 ( 250 ) + 7y = 1200
Subtracting 500 on both sides , we get
7y = 1200 - 500
7y = 700
Divide by 7 on both sides , we get
y = 100 grams
On simplifying the equation , we get
So , the weight of 4 small jars is 4y = 400 grams
Hence , the weight of 4 small jars is y = 400 grams
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Score on last try: 0 of 1 pts. See Details for more. Find the derivative of the function \[ f(x)=\sqrt[2]{\left(x^{2}-3\right)^{7}} \text { at } x=-2 \] \[ f^{\prime}(-2)= \] Question Help: B video B
To find the derivative of the function, we can use the chain rule and the power rule of differentiation.
What is chain rule?
The chain rule is a formula used to find the derivative of a composite function. If y = f(g(x)), then as per chain rule the instantaneous rate of change of function ‘f’ relative to ‘g’ and ‘g’ relative to x results in an instantaneous rate of change of ‘f’ with respect to ‘x’
Let u = x² - 3, then we can rewrite the function as:
f(x) = [tex](u^{7})^\frac{1}{2}[/tex]
Using the chain rule and the power rule, we have:
f'(x) = (1/2) x (u^7)^(-1/2) x 7u^6 x 2x
Simplifying this expression, we get:
f'(x) = 7x(u^6) / (2(u^7)^(1/2))
Now, we can substitute x = -2 into this expression to find f'(-2):
f'(-2) = 7(-2)((-2)^2 - 3)^6 / (2(((-2)^2 - 3)^7)^(1/2))
Simplifying this expression, we get:
f'(-2) = -168/(2sqrt(19)^7) = -12.77 (rounded to two decimal places)
Therefore, f'(-2) = -12.77.
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Given the point (5,8) and y intercept of -2, calculate the slope
The slope of the line is 2, which was calculated using the slope-intercept form of a linear equation and the given point (5,8) and y-intercept of -2.
To calculate the slope, we need to use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept.
We are given that the point (5, 8) lies on the line, so we can substitute x = 5 and y = 8 into the equation:
8 = 5m + b
We are also given that the y-intercept is -2, which means that when x = 0, y = -2. We can use this information to find b:
-2 = 0m + b
b = -2
Substituting this value into the equation above, we have:
8 = 5m - 2
Solving for m, we get:
5m = 10
m = 2
Therefore, the slope of the line is 2.
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What is the measure of <TRS in the triangle shown?
A. 63°
B. 54°
C. 126°
D. 117°
Answer:
A. 63
Step-by-step explanation:
in triangle TRS, it is an isosceles triangle with TS congruent to RS. So, angle T congruent to angle r. So, the angle is 63.
A population that is uniformly distributed between a=0 and b=10
is given in sample sizes 50(□)100(0),250(0), and 500(∅). Find the sample mean and the sample standard deviations for the given data. Compare your results to the average of means for a sample of size 10 , and use the empincal rules to analyze the sampling enrok. For each sample, also frid the standard entor of the mean using formula given below. Standard Error of the Mean =n0 Complele the following table with the results from the sampling experiment. (Round to four decimal places as needed.)
The standard error of the mean is smaller due to the better accuracy of the data.
What is standard deviations?Standard deviations are a measure of how spread out a dataset is. It is calculated by taking the square root of the variance of the data. The standard deviation is calculated by subtracting the mean of the dataset from each individual value, squaring the differences, and then adding them all together and dividing by the number of values in the dataset. The result is a measure of how much the individual values vary from the mean.
The average of means for a sample of size 10 is 5.0. Comparing the sample mean to the average of means, we can see that the sample mean for all sample sizes is close to the average of means for a sample of size 10. The sample standard deviation for the 50 sample size is the greatest, whereas the sample standard deviation for the 500 sample size is the least. Additionally, the standard error of the mean decreases as the sample size increases. This is an expected result, as the larger the sample size, the more accurate the data will be. Therefore, the standard error of the mean is smaller due to the better accuracy of the data.
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Ahmed buys a new monitor, keyboard and computer. He is given a 15% discount of the total price. The discounted price that ahmed pays is $1134. 75
If Ahmed is given a 15% discount of the total price, discounted price that ahmed pays is $1134. 75, the price of the computer before the discount was $335.14.
To calculate the price of the computer before the discount, we need to use the information given in the problem and some algebraic manipulation.
Let's start by setting up an equation. We can let x be the price of the computer before the discount. We know that Ahmed received a 15% discount off the total price, so the total price would be:
Total price = x + 375 + 70
Then, we can use the fact that the discounted price that Ahmed paid was $1134.75 to set up an equation:
Discounted price = Total price - 15% of Total price
$1134.75 = (x + 375 + 70) - 0.15(x + 375 + 70)
Simplifying this equation by combining like terms, we get:
$1134.75 = 1.85x + 513.75
To solve for x, we can subtract 513.75 from both sides of the equation:
$621 = 1.85x
Finally, we can divide both sides of the equation by 1.85 to get the price of the computer before the discount:
x = $335.14
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Complete question is:
Ahmed buys a new monitor, keyboard and computer.
He is given a 15% discount off the total price.
The discounted price that Ahmed pays is $1134.75.
The price of the monitor before the discount was $375.
The price of the keyboard before the discount was $70.
Calculate the price of the computer before the discount?
Simplify: 2x^3+3y^3+5x^3+4y
The simplified fοrm οf the expressiοn [tex]2x^3 + 3y^3 + 5x^3 + 4y is 7x^3 + 3y^3 + 4y.[/tex]
What is an expressiοn?Mathematical statements knοwn as expressiοns in mathematics are thοse with at least twο terms cοnnected by a separatοr and cοntaining either numbers, variables, οr bοth. It is pοssible tο add, subtract, multiply, οr divide using the mathematical οperatοrs.
Fοr instance, the expressiοn "x + y" is οne where "x" and "y" are terms with a separatοr added between them. There are twο different types οf expressiοns in mathematics: numerical and algebraic. Numerical expressiοns οnly cοntain numbers, while algebraic expressiοns alsο include variables.
Tο simplify the expressiοn [tex]2x^3 + 3y^3 + 5x^3 + 4y,[/tex] we can cοmbine the like terms:
[tex]2x^3 + 5x^3 + 3y^3 + 4y[/tex]
[tex]= (2 + 5)x^3 + (3)y^3 + (4)y[/tex]
[tex]= 7x^3 + 3y^3 + 4y[/tex]
Therefοre, the simplified fοrm οf the expressiοn
[tex]2x^3 + 3y^3 + 5x^3 + 4y is 7x^3 + 3y^3 + 4y[/tex].
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