Using a calculatοr οr spreadsheet, we can find that x is apprοximately 3.977 after several iteratiοns.
We can use trial and errοr οr iterative methοd tο find the value οf x.
What is Trial and Errοr Methοd ?Trial and Errοr Methοd is a prοblem-sοlving strategy that invοlves testing variοus sοlutiοns until the cοrrect οne is fοund. It is a simple but time-cοnsuming apprοach that invοlves attempting different sοlutiοns and checking their οutcοmes until the desired result is achieved. This methοd is οften used when there is nο clear οr οbviοus sοlutiοn tο a prοblem, and it requires patience, persistence, and the ability tο learn frοm mistakes.
Trial and Errοr Methοd:
We can substitute different values οf x intο the equatiοn until we get a value that is very clοse tο 2.
Using the calculatοr and by trial and errοr, we can find that x is apprοximately 3.977.
Iterative Methοd:
We can use an iterative methοd tο find the value οf x that satisfies the equatiοn. The iterative fοrmula fοr this prοblem is:
x_{n+1} = lοg[tex](2 + 1.5(0.55)^{x_n})[/tex] / lοg(0.55)
where x_n is the nth apprοximatiοn οf x.
Starting with x_0 = 3, we can use this fοrmula tο get better and better apprοximatiοns οf x. Using a calculatοr οr spreadsheet, we can find that x is apprοximately 3.977 after several iteratiοns.
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Simplify
to an expression involving a single trig function with no fractions.
If needed, enter squared trigonometric expressions using the following notation.
Example: Enter
as
The simplified form of csc²t/ [csc²(t) - 1] is sec²t
Trigonometric identities:Trigonometric identities are mathematical relationships between trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant. These identities are used to simplify trigonometric expressions and solve trigonometric equations.
To solve the given expression we used the following trigonometric identities
csc²(t) = 1/sin²(t)sin²(t) = 1 - cos²(t)sin²(t) + cos²(t) = 1Here we have
csc²t/ [csc²(t) - 1]
As we know csc θ = 1/sin θ
=> sinθ = 1/cscθ
Take csc² t as common from numerator and denominator
=> csc²t [1]/ csc²t [ 1 - (1/csc²t)]
=> 1/ 1 - (1/csc²t) [ csc²t will be canceled ]
=> 1/ 1 - sin²t
From trigonometric identities 1 - sin²t = cos²t
=> 1/ cos²t
= sec²t
Therefore,
The simplified form of csc²t/ [csc²(t) - 1] is sec²t
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Dylan earns money mowing lawns. The amount of money, in dollars, he earns varies as the number of lawns he mows. When he mows 6 lawns, he earns $72.
compare the rates of change of the following items
y=-2x+6 a line which passes through the points (2, 2) and (1,6)
Answer: To compare the rates of change of the line y = -2x + 6 at the points (2, 2) and (1, 6), we need to find the slope (rate of change) of the line at each point.
The slope of a line is given by the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are two points on the line.
Using the points (2, 2) and (1, 6), we can find the slopes of the line at these points:
At point (2, 2):
slope = (y₂ - y₁) / (x₂ - x₁)
= (2 - 6) / (2 - 1)
= -4
So the slope of the line at point (2, 2) is -4.
At point (1, 6):
slope = (y₂ - y₁) / (x₂ - x₁)
= (6 - 2) / (1 - 2)
= 4
So the slope of the line at point (1, 6) is 4.
Since the slope at (1,6) is positive and greater than the slope at (2,2), we can conclude that the rate of change of y with respect to x is increasing as we move from point (2,2) to (1,6). In other words, the line is getting steeper as we move from right to left along the line.
Step-by-step explanation:
A triangle with vertices (4, 4), (4, 2), and (6, 3) is translated a distance of 4 units to the left. What are the new coordinates?
(0, 4), (0, 2), (2, 3)
(4, 0), (4, -2), (6, -1)
(4, 8), (4, 6), (6, 7)
(8, 4), (8, 2), (10, 3)
Option A. To translate a figure 4 units to the left, we need to subtract 4 from the x-coordinates of each vertex.
The original vertices are:
(4, 4), (4, 2), and (6, 3)
Subtracting 4 from the x-coordinates, we get the new vertices:
(0, 4), (0, 2), and (2, 3)
To understand how to translate a figure, it is helpful to visualize the original and new positions of the figure in a coordinate plane. In this case, the original triangle has vertices (4, 4), (4, 2), and (6, 3) as shown below:
(4,4)
/ \
/ \
(4,2)----- (6,3)
To translate this triangle 4 units to the left, we need to subtract 4 from the x-coordinates of each vertex. This will shift the entire triangle to the left by 4 units.
So, the new x-coordinates of the vertices become:
x-coordinate of (4, 4) - 4 = 0
x-coordinate of (4, 2) - 4 = 0
x-coordinate of (6, 3) - 4 = 2
The y-coordinates of the vertices remain the same.
Therefore, the new vertices of the triangle are:
(0, 4), (0, 2), and (2, 3)
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A triangle with vertices (4, 4), (4, 2), and (6, 3) is translated a distance of 4 units to the left. What are the new coordinates?
A. (0, 4), (0, 2), (2, 3)
B. (4, 0), (4, -2), (6, -1)
C. (4, 8), (4, 6), (6, 7)
D. (8, 4), (8, 2), (10, 3)
An object is dropped from 44 feet below the tip of the pinnacle atop a 720-ft tall building. The height h of the object after t seconds is given by the equation h=16t^2+676 . Find how many seconds pass before the object reaches the ground.
Solving the quadratic equation we can see that the object will be 6.5 seconds falling down.
How many seconds pass before the object reaches the ground?We know that the height is modeled by the quadratic equation
h=-16t²+676
The object will reach the ground when the height is zero, so we need to solve:
-16t²+676 = 0
Solving this for t we will get:
16t² = 676
t² = 676/16
t = √(676/16)
t = 6.5
The object will be 6.5 seconds falling down.
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I will mark you brainiest!
The shape above is NOT a polygon because:
A) There are two segments
B) The Shape includes a curve
C) There is one vertex
D) The shape is closed
Study the triangle below. Explain how you can determine the value of tan B
The answer of tan B can be calculated only by knowing all the sides of triangle by using Pythagorean theorem and the answer is 8/15.
What is Pythagorean theorem?
The pythagorean theorem says In a right angle triangle if any of the two sides is known then the third side can be calculated.
c²= a²+ b²
Now in the following to calculate 3rd side, let us say x
=> 8²+x² = 17²
x= 15
Tan B= opposite /adjacent
= 8/15
So the tan B value will be 8/15
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How do the joint frequencies differ from the marginal frequencies in a two-way frequency table? (1 point)
The joint frequencies are the sum of the row or column in a two-way frequency table. The marginal frequencies are the sum of the
row and column totals.
The joint frequencies are the sum of the row and column totals. The marginal frequencies are the sum of the row or column in a
two-way frequency table.
The joint frequencies are the cells where the categories for two variables in a two-way frequency table intersect. The marginal
frequencies are the sum of the row or column in a two-way frequency table.
The joint frequencies are the sum of the row or column in a two-way frequency table. The marginal frequencies are the cells where
the categories for two variables in a two-way frequency table intersect.
The joint frequencies are the cells where the categories for two variables in a two-way frequency table intersect, while the marginal frequencies are the sums of the row or column in a two-way frequency table.
Identifying the difference between the frequenciesJoint frequencies represent the frequency counts of each combination of categories for two variables, while marginal frequencies represent the frequency counts of each category for one variable, regardless of the other variable.
For example, in a two-way frequency table of gender and political affiliation, the joint frequency for "Male" and "Republican" would represent the number of individuals who are both male and Republican.
The marginal frequency for "Male" would represent the total number of males in the sample, regardless of their political affiliation. The marginal frequency for "Republican" would represent the total number of individuals who identify as Republican, regardless of their gender.
Understanding the difference between joint and marginal frequencies is important for analyzing the relationship between two variables and identifying any patterns or trends.
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Elvira and Aletheia live 2.5 miles apart on the same street. They are in a study group that meets at a coffee shop between their houses. It took Elvira half an hour and Aletheia three-fifths of an hour to walk to the coffee shop. Aletheia's speed is 0.6 miles per hour slower than Elvira's speed. Find both women's walking speeds, in miles per hour.
Elvira's walking speed is 5 miles per hour, and Aletheia's walking speed is approximately 4.17 miles per hour.
What is the women's walking speeds?
Let's denote Elvira's walking speed as x (in miles per hour).
Then, Aletheia's walking speed is x - 0.6 (since she walks 0.6 miles per hour slower than Elvira).
We know that Elvira walked to the coffee shop in half an hour, covering a distance of 2.5 miles.
This means her speed can be calculated as:
x = distance / time = 2.5 miles / 0.5 hours = 5 miles per hour
Now, we can find Aletheia's speed using the equation we found earlier:
x - 0.6 = Aletheia's speed
We also know that Aletheia walked to the coffee shop in three-fifths of an hour (which is 0.6 hours), covering the same distance of 2.5 miles.
This means her speed can be calculated as:
x - 0.6 = distance / time = 2.5 miles / 0.6 hours ≈ 4.17 miles per hour
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7) through: (-4,-4), parallel to y=x-1
9) through: (-4,-4), parallel to y=-
y=-x-4
11) through: (5,-2), perp. to y=-x-5
13) through: (-2, 5), perp. to y = x + 2
8) through: (1,0), parallel to y=2x-1
10) through: (5.5), perp. to y
12) through: (3,-2), perp. to y ==
14) through: (-4, 0), perp. to y = -x-2
Answer:
14 is 45
Step-by-step explanation:
lisa is going on a 5.632704 km hike. she has already hiked 4.425969 km. how many miles does she have left
Answer:
To convert kilometers to miles, we can use the conversion factor 1 km = 0.621371 miles.
First, let's convert the total distance of 5.632704 km to miles:
5.632704 km * 0.621371 miles/km = 3.497672 miles
Next, let's convert the distance already hiked, 4.425969 km, to miles:
4.425969 km * 0.621371 miles/km = 2.746203 miles
To find out how many miles Lisa has left, we can subtract the distance already hiked from the total distance:
3.497672 miles - 2.746203 miles = 0.751469 miles
So Lisa has 0.751469 miles left to hike.
Step-by-step explanation:
Joe wishes to hang a sign weighing 800 N so that cable A, attached to the store, makes a 30.0° angle, as shown below. Cable B is horizontal and attached to an adjoining building.
What is the tension in cable b
Joe wants to hang a flag weighing 800 N because Cable A, tied to the store, forms a 30.0° angle, and Cable B, attached to a neighboring building, is horizontal. Cable B is thus under 461 N of stress.
What does "weighing" mean?First, a [+ object] measuring the weight of something or someone in order to determine its size (someone or something) Every day she weighs herself. To weigh the bananas, he used a scale.
Let's refer to the tensile stress in cables A or B, respectively, as T A and T B. With an 800 N magnitude, the sign's weight is acting downward. The weight must be balanced by the vertical tension force components because the sign also isn't moving vertically:
800 N when T A is cos 30°
T A = 800 N/cos (30°)
T A = 922 N
Without any horizontal acceleration, a horizontal component of the tensile stress must also be balanced. T A's horizontal component is T A sin 30°, while T B's horizontal component is 0 (since cable B is horizontal). Therefore:
A sin (30°) = T b
T A = T B sin (30°)
T B ≈ 922 N x 0.5, or 461 N.
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PLEASE HURRY I WILL GIVE BRAINLIEST!!!!!
Which two objects are exerting more force on each other?
A. A
B. B
C. They are exerting the same amount of force. d
D. There is not enough information provided to answer the question.
Answer:
D
Step-by-step explanation:
..
the explicit formula for this sequence: 2 6 18 54 162
Answer:
To find the explicit formula for this sequence, we need to determine the common ratio between successive terms. To do this, we can divide any term by the previous term. For example:
6 ÷ 2 = 3
18 ÷ 6 = 3
54 ÷ 18 = 3
162 ÷ 54 = 3
So the common ratio is 3.
Next, we can use the general form of a geometric sequence to find the explicit formula:
a(n) = a(1) * r^(n-1)
where a(n) is the nth term of the sequence, a(1) is the first term, r is the common ratio, and n is the position of the term we want to find.
In this sequence, a(1) = 2 and r = 3. So the explicit formula for this sequence is:
a(n) = 2 * 3^(n-1)
For example, if we want to find the 6th term, we can plug in n = 6:
a(6) = 2 * 3^(6-1) = 2 * 3^5 = 2 * 243 = 486
Therefore, the 6th term of the sequence is 486.
For the breakfast buffet, Mr. Walker must equally divide 7 loaves of bread between five platters. How many loaves of bread are placed on each platter?
Answer:
the answer to ur question is: 1.4
18. A jar contains marbles of different colors. The probability of drawing a red marble at random is 210 .
What is the probability, and the likelihood, that the marble drawn is not red?
By answering the above question, we may state that The chance of probability drawing a non-red marble is just the probability of drawing a non-red marble. As a result, the probability is 209/210.
What is probability?Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.
The likelihood of drawing a red marble is 210, which indicates that one red marble is drawn out of every 210 in the jar. This probability may be expressed as a fraction:
P(Red) = 1/210
The likelihood of drawing a non-red marble is the inverse of the probability of drawing a red marble:
P(Not Red) = 1 minus P(Red) = 1 minus 1/210 = 209/210
As a result, the chance of drawing a marble that is not red is 209/210.
The chance of drawing a non-red marble is just the probability of drawing a non-red marble. As a result, the probability is 209/210.
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PLEASE HELP ME ANSWER THIS QUESTION ASAP!!
Answer:
27.5
Step-by-step explanation:
Over the past 50 years, there has been a strong negative correlation between average annual income and the record time to run 1 mile. In other words, average annual incomes have been rising while the record time to run 1 mile has been decreasing.
Answer:
This statement is false as it suggests a negative correlation between average annual income and the record time to run 1 mile. A negative correlation means that as one variable increases, the other decreases. However, it is unlikely that there is any correlation between these two variables as they are not directly related. One's ability to run a mile does not necessarily depend on their income, and vice versa. It is possible that both variables have been changing over time, but it does not necessarily mean that there is a correlation between them.
Step-by-step explanation:
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. shaded area is 0.1949
Answer: To find the indicated z-score for a shaded area of 0.1949 in the standard normal distribution, we need to use a z-table or a calculator with a built-in normal distribution function.
Using a z-table, we can find the z-score that corresponds to a cumulative area of 0.1949 in the standard normal distribution. The z-table gives us the area to the left of the z-score, so we need to look for the area closest to 0.1949 in the body of the table and then interpolate to find the exact z-score.
Looking at the z-table, we find that the area to the left of the z-score 0.88 is 0.8106, and the area to the left of the z-score 0.89 is 0.8159. Since 0.1949 is closer to 0.8106 than to 0.8159, we can estimate that the z-score corresponding to the area 0.1949 is approximately 0.88.
Therefore, the indicated z-score for a shaded area of 0.1949 in the standard normal distribution is approximately 0.88.
Step-by-step explanation:
Find the x and y-intercept and Find the vertical and horizontal asymptotes
r(x)= 2x^2 + 10x - 12/ x^2 + x-6
Answer:
To find the x-intercept, we set y = 0 and solve for x:
r(x) = 2x^2 + 10x - 12 / x^2 + x - 6
0 = (2x^2 + 10x - 12) / (x^2 + x - 6)
0 = 2(x-1)(x+6) / (x-2)(x+3)
This gives us x-intercepts of x = 1 and x = -6.
To find the y-intercept, we set x = 0 and solve for y:
r(0) = 2(0)^2 + 10(0) - 12 / (0)^2 + (0) - 6
r(0) = -12/-6 = 2
So the y-intercept is y = 2.
To find the vertical asymptotes, we set the denominator of the function equal to zero and solve for x:
x^2 + x - 6 = 0
(x+3)(x-2) = 0
This gives us vertical asymptotes at x = -3 and x = 2.
To find the horizontal asymptote, we look at the degrees of the numerator and denominator. Since the degree of the numerator is 2 and the degree of the denominator is also 2, we divide the leading coefficient of the numerator by the leading coefficient of the denominator:
2 / 1 = 2
So the horizontal asymptote is y = 2.
Therefore, the x-intercepts are x = 1 and x = -6, the y-intercept is y = 2, the vertical asymptotes are x = -3 and x = 2, and the horizontal asymptote is y = 2.
I am on 8-5 through week days comment if you have any more questions.
The diagram shows a parallelogram.
The area of the parallelogram is greater
than 10.5 cm²
a) Show that 2x² 25x + 33 < 0
The given inequality 2x² 25x + 33 < 0 has been proved by using properties of parallelogram.
The formula A = bh, where b is the parallelogram's base and h is its height, determines the area of a parallelogram.
Let's use x + 6 cm for the parallelogram's base and 2x + 3 cm for its height in the diagram. The parallelogram's area can therefore be represented as follows:
A = (x + 6)(2x + 3)
By extending this phrase, we get:
A = 2x² + 15x + 18x + 18
A = 2x² + 33x + 18
We now know that the parallelogram's area is more than 10.5 cm2. As a result, we can create the disparity shown below:
2x² + 33x + 18 > 10.5
By taking away 10.5 from both sides, we arrive at:
2x² + 33x + 18 - 10.5 > 0
By condensing the left side, we obtain:
2x² + 22.5x + 7.5 > 0
When we multiply both sides by 2, we obtain:
4x² + 45x + 15 > 0
By taking 3 away from both sides, we arrive at:
4x² + 45x + 12 < 0
As a result, we have demonstrated that 2x² 25x + 33 < 0.
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A hat company wants to create a cylindrical travel case to protect its beach sun hats using the following pattern.
net drawing of a cylinder is shown as two circles with diameters labeled 15 inches and a rectangle with a height labeled 5 inches
How many square inches of leather will be necessary to create the travel case? Approximate using π = 3.14.
412.13 square inches
588.75 square inches
1,648.5 square inches
1,884 square inches
To create the cylindrical travel case, we need approximately 588.75 square inches of leather.
What is a cylinder?
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases connected by a curved surface. The curved surface is formed by connecting every point on the edge of one circular base to the corresponding point on the other circular base with straight lines that are perpendicular to the bases. The distance between the two circular bases is the height of the cylinder.
Now,
The surface area of a cylinder is given by the formula:
A = 2πr² + 2πrh
where r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi, which is approximately equal to 3.14.
In this case, we are given that the cylinder has a diameter of 15 inches, so the radius is 7.5 inches (half of the diameter). We are also given that the height of the cylinder is 5 inches. Using these values in the formula, we can calculate the surface area of the cylinder as:
A = 2π(7.5)² + 2π(7.5)(5)
= 2π(56.25) + 2π(37.5)
= 2(π)(93.75)
= 187.5π
≈588.75
Therefore,
we need approximately 588.75 square inches of leather to create the travel case.
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(05.03 MC)
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−2 intersect are the solutions of the equation 4x = 2x−2. (4 points)
Part B: Make tables to find the solution to 4x = 2x−2. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4x = 2x−2 graphically? (2 points)
(10 points)
Part A: The intersection of these two lines is (-1,-4). Since x=-1, this is also the solution to 4x=2x-2 as per the graph.
Part B: Table attached.
Part C: Graph attached.
What is a graph?Graphing a function involves tracing the curve on a coordinate plane that corresponds to the function. If the curve represents the function for the curve, then each point on the curve will satisfy the function equation. The graph below shows the linear function f(x) = -x+ 2 as an illustration.
In the question,
The expression 4x = 2x - 2 reduces to x = -1. This is true for all values of y, since y is not a factor in this expression.
The two other equations intersect at point (-1, -4). See the attached graph (Solutions2)
y = 4x
y = 2x−2
Mathematically, we can substitute the value of y from the first equation into the second:
y = 2x−2
(4x) = 2x−2
2x = -2
x = -1
The intersection of these two lines is (-1,-4). Since x=-1, this is also the solution to 4x=2x-2.
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help please I'll give brainliest
Answer:
k = 16.806404 and k = 95.174404
Step-by-step explanation:
To determine the value of k in which the graph touches, you set both equations equal to each other
4x + k = -x^2 +8x + 20
k = -x^2+4x+20
You can use the quadratic formula -b^2+-(sqrt(b^2-4(a)(c))) / 2a
You will get the values of x = -2.898 and 6.898 for your answers
My bad, I forgot to add also input the values of x in your equation and get k = 16.806404 and k = 95.174404
Alexander was given a gift card for a coffee shop. Each morning, Alexander uses the card to buy one cup of coffee. Each cup of coffee costs $1.50 and after buying 4 cups of coffee, the card had a $9 remaining balance. Write an equation for
�
,
A, in terms of
�
,
x, representing the amount money remaining on the card after buying
�
x cups of coffee.
Answer:
�
=
A=
Answer:
We can start by using the given information to find the initial value of the gift card, which is the value before Alexander started using it:
Initial value of gift card = $9 + 4 x $1.50 = $15
Let's use A to represent the amount of money remaining on the card after buying x cups of coffee. Each cup of coffee costs $1.50, so the amount spent on coffee after buying x cups is 1.5x. The remaining balance on the card can be found by subtracting the amount spent on coffee from the initial value of the card:
A = $15 - 1.5x
Therefore, the equation for A in terms of x is:
A = $15 - 1.5x
Step-by-step explanation:
tan(-A).sin (180°+A).sec (270°-A)=x. sin (-A)-cos²(90° + A).tan A. Find the value of x
Answer:
Step-by-step explanation:
We can simplify the expression on the left-hand side using trigonometric identities:
tan(-A) = -tan(A) (since tan(-θ) = -tan(θ))
sin(180°+A) = -sin(A) (since sin(180°+θ) = -sin(θ))
sec(270°-A) = -cos(A) (since sec(270°-θ) = -cos(θ))
cos²(90°+A) = sin²A (since cos²(90°+θ) = sin²θ)
Substituting these values, we get:
-x.sin(A).cos(A).tan(A) = x.sin(-A) - sin²A.sin(A)
-x.sin(A).cos(A).tan(A) = -x.sin(A) - sin³A
Now, we can simplify this equation by moving all the terms to one side:
-x.sin(A).cos(A).tan(A) + x.sin(A) + sin³A = 0
Factoring out sin(A), we get:
sin(A) (-x.cos(A).tan(A) + x + sin²A) = 0
Since sin(A) ≠ 0, we can divide both sides by sin(A):
-x.cos(A).tan(A) + x + sin²A = 0
Multiplying both sides by cos(A), we get:
-x.sin(A) + x.cos²(A) + sin²A.cos(A) = 0
Using the identity cos²(θ) + sin²(θ) = 1, we can write this as:
-x.sin(A) + x(1 - sin²A) + sin²A.cos(A) = 0
Simplifying and rearranging, we get:
x = sin(A)/(cos(A) - sin²(A))
Therefore, the value of x is given by the expression sin(A)/(cos(A) - sin²(A)).
an average bus speed between cape Town to east London was 108 km/h Due to the bad weather, the average speed on the trip back was 72 km/h. Determine how long the outward trip took if the return trip takes 12 hours
Answer:
Let's call the distance between Cape Town and East London "d".
We know that the average speed on the outward trip was 108 km/h, so the time it took to travel from Cape Town to East London can be calculated using the formula:
time = distance / speed
So the time it took on the outward trip can be expressed as:
time = d / 108
We also know that the average speed on the return trip was 72 km/h, and we're told that this trip took 12 hours. So we can use the same formula to find the distance between Cape Town and East London:
d = speed * time
d = 72 * 12
d = 864 km
Now we can use the formula for time again to find how long the outward trip took:
time = d / 108
time = 864 / 108
time = 8 hours
Therefore, the outward trip took 8 hours.
Step-by-step explanation:
What is μ (∠LMK)? thank you
Answer and Step-by-step explanation:
We can see that because Line K is acting as an Angle Bisector (a line that divides an angle into two angles of equal measures) on angle ∠LMJ, the angles ∠LMK and ∠JMK are equal to each other.
This allows us to solve for angle ∠LMK.
We do this by first setting the angles equal to each other.
10x - 22 = 2x + 66
Now, we want to isolate x by itself. We will subtract 2x from both sides of the equation, and then add 22 to both sides of the equation.
10x - 22 - 2x = 2x + 66 - 2x
8x - 22 = 66
8x - 22 + 22 = 66 + 22
8x = 88
Finally, we will divide both sides of the equation by 8.
8x ÷ 8 = 88 ÷ 8
x = 11
We aren't finished yet, as the question asks to find ∠LMK.
Plug 11 in for x into the equation 10x - 22.
10(11) - 22 =
110 - 22 =
= 88°
So, the measure of angle ∠LMK is 88°.
Have a good day!
A cylinder with a diameter of 8cm and height of 2m?
The volume of the cylinder with a diameter of 8cm and height of 2m is 100.48 cubic meters.
This question is incomplete, the complete question is:
Find the volumes of each of the following;
7) A cylinder with a diameter of 8cm and height of 2m?
What is the volume of the cylinder?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Given that;
Diameter d = 8mRadius r = d/2 = 8m/2 = 4mHeight h = 2mVolume V = ?Plug the given values into the above formula and solve for V.
V = π × r² × h
V = 3.14 × ( 4m )² × 2m
V = 3.14 × 16m² × 2m
V = 100.48 m³
Therefore, the volume is 100.48 cubic meters.
Learn more on volume of cylinder here: brainly.com/question/16788902
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h(t) = 56 - 4.9t squared
The function above models h, the height of a flower pot in meters, t seconds after it falls from a
fourth floor balcony. What is the height of the flower pot, in meters, 3 seconds after it falls?
A 51.1
B 44.1
C 36.4
D 11.9
Answer: D 11.9
Step-by-step explanation:
To find the height of the flower pot 3 seconds after it falls, we need to substitute t=3 in the given function H(t) and calculate the value.
H(3) = 56 - 4.9(3)^2
H(3) = 56 - 4.9(9)
H(3) = 56 - 44.1
H(3) = 11.9
Therefore, the height of the flower pot, in meters, 3 seconds after it falls is 11.9 meters.
The answer is option D, 11.9.