Answer:
Let's start by finding the volume of water in the trough as a function of its depth.
At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:
V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm
Simplifying this expression, we get:
V(h) = (13/2000) h^2 m^3
Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:
dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)
At the moment when the water is 10 cm deep, we have:
h = 10 cm
dV/dt = 0.1 m^3/min
Plugging in these values, we get:
0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)
Solving for dh/dt, we get:
dh/dt = 0.1 m^3/min / (26/2000) / 10 cm
dh/dt ≈ 0.192 m/min
Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.
What is tan(49°)?
O A. 0.75
OB. 0.66
O C. 1.15
OD. 0.82
Answer:
Find the Exact Value tan(49). tan(49) tan ( 49 ). Step 1. The result can be shown in multiple forms. Exact Form: tan(49) tan ( 49 ). Decimal Form:
Step-by-step explanation:
I need a satisfying conditions question answered thank you sm
The linear function can be written as:
f(x) = -x/3 + 17/3
How to find the linear function?A general linear function can be written as:
f(x) = ax + b
Where a is the slope, and b is the y-intercept.
If we know two points on the line (x₁, y₁) and (x₂, y₂), then the slope of the linear function is:
a= (y₂ - y₁)/(x₂ - x₁)
Here we know the pairs:
f(-4) = 7
f(5) = 4
So we have the points (-4, 7) and (5, 4), then the slope is:
a = (4 - 7)/(5 + 4) = -3/9 = -1/3
Then we can write:
f(x) = -x/3 + b
now we can use one of the given points, like f(5) = 4, replacing that there we will get:
4 = -5/3 + b
4 + 5/3 = b
12/3 + 5/3 = b
17/3 = b
So the function is:
f(x) = -x/3 + 17/3
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PLEASE HELP WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.
In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:
The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.
The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.
The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.
Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).
PLEASE HELP PICTURE BELOW
Joseph is 1.75 meters tall. At 11 a.m., he measures the length of a tree's shadow to be
34.05 meters. He stands 29.7 meters away from the tree, so that the tip of his shadow
meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
(Diagram is not to scale.)
Answer:
34.05 m-
2T
1.75 m
29.7 m
Answer:
Step-by-step explanation:
34,05m my love
Answer:
The height of the tree is approximately 15.14 meters, rounded to the nearest hundredth of a meter.
Step-by-step explanation:
Let's call the height of the tree "h". We can use similar triangles to set up an equation involving Joseph's height, the length of his shadow, the height of the tree, and the length of the tree's shadow.
The two triangles we're interested in are:
Joseph's triangle: This triangle has a height of 1.75 meters (Joseph's height) and a base of x meters (the length of Joseph's shadow).
Tree's triangle: This triangle has a height of h meters (the height of the tree) and a base of 29.7 - x meters (the length of the tree's shadow).
Since the two triangles are similar, we can set up the following proportion:
h / (29.7 - x) = 1.75 / x
To solve for h, we can cross-multiply and simplify:
h * x = 1.75 * (29.7 - x)
h * x = 52.075 - 1.75x
h = (52.075 - 1.75x) / x
Now we need to find the value of x that makes the tips of the two shadows meet. From the problem statement, we know that x + 34.05 = 29.7, so:
x = 29.7 - 34.05
x = -4.35
This means that the tips of the shadows don't actually meet, but the problem is likely assuming that the tips of the shadows are very close together, so we can use the value x = -4.35 to approximate the height of the tree.
Substituting x = -4.35 into our equation for h, we get:
h = (52.075 - 1.75(-4.35)) / (-4.35)
h = 15.14
A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50 feet. So, it forms a region bounded by the graph of x^2 + y^2 = 50^2 with x ≥ 0 and y ≥ 0. The following equations are models for the floor and ceiling. Floor: z = x+y/ 5 Ceiling: z = 20 + xy /100 Calculate the volume of the room, which is needed to determine the heating and cooling requirements.
Answer:
Step-by-step explanation:
To calculate the volume of the room, we need to integrate the difference between the ceiling and floor functions over the region bounded by the circle. We can use double integrals to do this.
First, let's rewrite the equations for the floor and ceiling in terms of x and y:
Floor: z = (x + y) / 5
Ceiling: z = 20 + xy / 100
The volume of the room can be calculated using the following double integral:
V = ∫∫(20 + xy/100 - (x + y)/5) dA
where the limits of integration are x = 0 to x = 50, and y = 0 to y = √(50^2 - x^2).
We can simplify the integrand by combining like terms:
V = ∫∫(400/100 + xy/100 - (20x + 20y)/100) dA
V = ∫∫(4 + xy/100 - 0.2x - 0.2y) dA
Now we can integrate with respect to y first:
V = ∫0^50 ∫0^√(50^2 - x^2) (4 + xy/100 - 0.2x - 0.2y) dy dx
V = ∫0^50 [(4y + xy^2/200 - 0.2xy - 0.1y^2)|y=0^√(50^2 - x^2)] dx
V = ∫0^50 [(4√(50^2 - x^2) + x(50^2 - x^2)/200 - 0.2x√(50^2 - x^2) - 0.1(50^2 - x^2)^2/200)|x=0^50]
Evaluating this integral, we get:
V ≈ 2,233.5 cubic feet
Therefore, the volume of the room is approximately 2,233.5 cubic feet, which is the amount of space that will need to be heated or cooled.
the area of a rectangle is 14 square units. it has the side length of x and y. given each value for x, find y.
1. x = 4 and 1/5
2. x = 2 and 1/3
3. x = 7/6
Answer:
1. y = 3 1/3
2. y = 6
3. y = 12
Step-by-step explanation:
A = xy => xy = 14 => y = 14/x
1. x = 4 1/5 = 21/5
y = 14/x = 14/(21/5) = (5 x 14)/21 = 10/3 = 3 1/3
2. x = 2 1/3 = 7/3
y = 14/x = 14/(7/3) = (3 x 14)/7 = 6
3. x = 7/6
y = 14/x = 14/(7/6) = (6 x 14)/7 = 12
Who knows this? I need help
#16
Answer:
Step-by-step explanation:
adjacent: [tex]\angle BOC, \angle EOD[/tex] (both are adjacent)
complementary: [tex]\angle BOC[/tex]
supplementary: [tex]\angle EOD[/tex]
vertical angles: [tex]\angle AOE[/tex]
Trevor used about half of a 5-lb bag of potatoes (2 lb 6 oz). How much did the remaining potatoes weigh?
Answer:
Step-by-step explanation:
f Trevor used 2 lb 6 oz of a 5-lb bag of potatoes, then the weight of the remaining potatoes is:
5 lb = 80 oz (since 1 lb = 16 oz)
Remaining potatoes = Total potatoes - Used potatoes
Remaining potatoes = 80 oz - 2 lb 6 oz
Remaining potatoes = 80 oz - (2 × 16 oz + 6 oz)
Remaining potatoes = 80 oz - 38 oz
Remaining potatoes = 42 oz
Therefore, the remaining potatoes weighed 2 lb 10 oz (or 42 oz).
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In this figure, 14.2% of the area is painted green. How much of the area is painted green?
Answer:
8.449 square centimeters
Step-by-step explanation:
Area of the figure = area of square + area of triangle
[tex] {7}^{2} + \frac{1}{2} (3)(7) = 49 + 10.5 = 59.5[/tex]
[tex].142 \times 59.5 = 8.449[/tex]
So 8.449 square centimeters of this figure is green.
75909931 rounded to the nearest hundred thousand
Answer:
the answer is supposably 75900000
please help, thank you!
Answer:
To find all values of x for which f(x) = 26, we can set up the equation:
8x + 15/x = 26
Multiplying both sides by x, we get:
8x^2 + 15 = 26x
Bringing all the terms to one side, we get:
8x^2 - 26x + 15 = 0
We can factor this quadratic equation using the factoring method or by using the quadratic formula. Here, we will use the factoring method:
8x^2 - 26x + 15 = 0
(4x - 3)(2x - 5) = 0
Setting each factor equal to zero and solving for x, we get:
4x - 3 = 0 OR 2x - 5 = 0
4x = 3 OR 2x = 5
x = 3/4 OR x = 5/2
Therefore, the values of x for which f(x) = 26 are x = 3/4 or x = 5/2.
What is the area of the real object that the scale drawing models? Scale factor. 1:5 Area = 10 square cm Scale drawing Real object
Answer:
D. 50 square centimeters
Given g(x) = 8x2 − x + 2, find the following.
1) g(0)
2) g(−1)
3) g(r)
4) g(x + h)
Answer:
Step-by-step explanation:
Given g(x) = 8x2 − x + 5, find the following.
(a). g(0) = 5
(b). g(−1) = 14
(c). g(r) = ?
(d). g(x + h) = ?
In this unit, you learn about linear functions and graphing lines in the coordinate plane. Linear functions are used in businesses, construction, and planning cities. The slope of a line determines its steepness. Why do you think a horizontal line (flat) has zero slopes, but a vertical line (straight up and down) is considered to have no slope. What's the difference between zero slope and no slope?
Answer:
Step-by-step explanation:
In math, slope is used to describe the steepness and direction of lines. ... You can determine the slope of a line from its graph
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct option is 1 and 4 of the given inequality –3(2x – 5) < 5(2 – x)
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:
-6x + 15 < 10 – 5x
x < 5
Therefore, options 1 and 4 are correct. The other options do not correctly represent the inequality.
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Polly's sister-in-law is going to have a baby! For the baby shower, Polly decided to sew pillow to give as a gift. She is using a flower-printed rectangular piece of fabric that is 26 inches long and 22 inches wide.
Answer:
The answer is 96
Step-by-step explanation:
2*(26+22)
2*48
96
Solve for X
x^2+ y^2=25 and y=x
The solutions for x are x= +[tex]\sqrt{12.5[/tex] and -[tex]\sqrt{12.5[/tex] which has been obtained by solving the equations given in the question.
Define Equation?
An equation can be defined in numerous ways. An equation is a claim that demonstrates the equivalence of two mathematical expressions, according to algebra.
In the initial equation, we get: by substituting y=x:
[tex]x^2[/tex] +[tex]y^2[/tex]= 25
[tex]x^2[/tex] +[tex]x^2[/tex] = 25 (since y = x)
2[tex]x^2[/tex] = 25
[tex]x^2[/tex] = 12.5
When the two sides are square, we get:
x = ±[tex]\sqrt{12.5[/tex]
Therefore, the solutions for x are x = +[tex]\sqrt{12.5[/tex] and x = -[tex]\sqrt{12.5[/tex]
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
To determine which statements are true, we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Using this form, we can rewrite the given equation as:
(x - 1)^2 + y^2 = 3^2 + 1^2 = 10
Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.
To find the radius, we can rearrange the equation as follows:
x^2 - 2x + y^2 = 8
Completing the square for x, we get:
(x - 1)^2 + y^2 = 9
This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."
Therefore, the three true statements are:
1.The radius of the circle is 3 units.
2.The center of the circle lies on the x-axis.
3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Step-by-step explanation:
hope its help <:
Is ∆PQR a right triangle? Explain
Answer:
Yes, ∆PQR is a right triangle.
Step-by-step explanation:
A right triangle has one right angle, which is 90°. This triangle has one right angle, so it is a right triangle.
As shown in the figure below, Kaitlin is standing 93 feet from the base of a leaning tree. The tree is growing at an angle of
88° with respect to the ground. The angle of elevation from where Kaitlin is standing to the top of the tree is 35°. Find the
length, x, of the tree. Round your answer to the nearest tenth of a foot.
35°
-93 ft-
H
88°
feet
X
5
Answer:The measure of Ф = 75.7° :)
Step-by-step explanation:the measure of Ф = 75.7°,We will use the rule sin to find the measure of Ф
At first we will find the angle opposite to the side of length 31
∵ 180° - 73° = 107°
hope this helps:)(:
Someone please help me answer this question
The two statements that are both true are as follows: line
AC is perpendicular to line HB and line AC is parallel to FG. That is option A.
What is a perpendicular line?A perpendicular line is defined as the line that forms angle 90° where it meets with another line in a plane.
A line is said to be parallel to each other when they do not intercept as they are both on the same plane.
From the given diagram, line AC is perpendicular to line HB because they form angle 90° at the point of intersection.
Also, line AC is parallel to FG, because they can never intersect till infinity.
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Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a leg = 5?
A) 5, 5, 5
B) 5, 1, 5
C) 1, 5, 5
D) 1, 1, 5
The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.
Explain about property of the right triangles?The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.
A triangle's (of all varieties) cumulative sum of angles is 180°.The length of a triangle's two longest sides added together is longer than for third side.Similar to this, the length of a third side of a triangle's third side is shorter than the difference between its two sides.For the given question:
Triangle with degree angles - 45-45-90
It means two legs are of same length 5 units.
Then, hypotenuse H will be:
H² = 5² + 5²
H² = 25 + 25
H² = 50
H = 5√2
Thus, the correct third side of the triangle will be 5√2.
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Each year, the school has a goal to have a third as many students in remedial mathematics courses as the year before. Currently the school has 1,200 students in remedial math. Approximately how many students will be enrolled in four years?
(a) 44 (b)15 (c) 32,400 (d) 1
Answer:
44 students
Step-by-step explanation:
1200 for the first year
a third of that is 400
400 for the second year
a third of that is 133.4
133.4 for the third year
a third of that is 44
One year, the population of a city was 137,000. Several years later it was 117,820. Find the percent decrease.
Group of answer choices
14%
15%
16%
19%
Answer:
The percent decrease in population can be calculated by dividing the difference between the two populations by the original population and then multiplying by 100. In this case, the percent decrease is ((137000-117820)/137000)*100 = 14%.
Step-by-step explanation:
At Spirit Night slices of pizza cost $2 and pretzels cost $1. The school store sold 150 items and made a total of $250. Write a systems of
equations to represent the situation where x represents the number of slices of pizza sold and y represnts the number o pretzels
Answer:
[tex]x + y = 150[/tex]
[tex]2x + y = 250[/tex]
Reflect on why you think guitar tabs are easier or harder to read than regular musical notation.
This will have to be in paragraph form. :)
Guitar tabs are generally considered easier to read than regular musical notation because they are written in a language that most guitarists are familiar with.
What is Guitar?Guitar is a stringed musical instrument played with the fingers or a pick. It is one of the most popular instruments in the world and is widely used in genres such as rock, jazz, blues, country, folk, and classical.
Unlike traditional notation, guitar tabs do not require any knowledge of music theory to understand. Instead, they are laid out in a straightforward format that conveys the pitch of a note and the timing of when it should be played. This makes it easier for most guitarists to quickly learn a new piece of music without having to spend time studying the complexities of traditional notation. Additionally, guitar tabs also offer an easy way to determine the fingering of certain chords or techniques.
While guitar tabs are easier to read than traditional notation, they do have some drawbacks. For one, guitar tabs cannot convey the same level of detail about a piece of music as traditional notation can. Additionally, it can be difficult for some to distinguish between rhythm and lead parts when reading guitar tabs. Finally, guitar tabs do not easily convey the dynamics or expression of a piece of music, which are important to consider when playing music.
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3. There are 15 students in class 7 who need the school shirt of same size and 2 meter of
cloth is required to make a shirt.
(a) Find the total length of the cloth required to make the shirt to them.
(b) How many shirts can be made from a piece of cloth 9 meter long?
Convert the length of cloth required for a shirt in decimal.
1
If the length of a piece of cloth is 36.25 meter, how many meters of cloth is left? 1
Answer:
Step-by-step explanation:
(a) Since each student needs a shirt of the same size, and 2 meters of cloth is required to make one shirt, the total length of cloth required to make shirts for 15 students would be:
Total length of cloth = 15 x 2 = 30 meters
Therefore, 30 meters of cloth would be required to make shirts for 15 students.
(b) If 2 meters of cloth are required to make one shirt, then the number of shirts that can be made from 9 meters of cloth would be:
Number of shirts = 9 / 2 = 4.5 shirts
However, since we cannot make half a shirt, the actual number of shirts that can be made from 9 meters of cloth would be 4 shirts.
To convert the length of cloth required for a shirt into decimal form, we can simply divide the length in centimeters by 100. Therefore, 2 meters of cloth would be equivalent to 200 centimeters, which is 2.00 meters in decimal form.
(c) If the length of a piece of cloth is 36.25 meters, and we use 30 meters to make shirts for 15 students, then the remaining length of cloth would be:
Remaining length of cloth = 36.25 - 30 = 6.25 meters
Therefore, 6.25 meters of cloth would be left.
what is the solution to this
Answer:
-2
Step-by-step explanation:
Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms. 2 similar right triangles. Triangle 1 has side length 12, hypotenuse 15, and blank side. Triangle 2 has side length 4, hypotenuse 5, and blank side. a. StartFraction 4 Over 15 EndFraction = StartFraction 5 Over 12 EndFraction = StartFraction 4 Over 15 EndFraction b. StartFraction 4 Over 5 EndFraction = StartFraction 12 Over 15 EndFraction = StartFraction 4 Over 5 EndFraction c. StartFraction 4 Over 12 EndFraction = StartFraction 5 Over 15 EndFraction = StartFraction 1 Over 3 EndFraction d. StartFraction 5 Over 4 EndFraction = StartFraction 15 Over 12 EndFraction = StartFraction 5 Over 4 EndFraction
Answer:
Step-by-step explanation: To find the ratio of corresponding sides for the two similar triangles, we need to match up the corresponding sides of the triangles and write the ratios of their lengths.
For Triangle 1, we have:
Side length = 12
Hypotenuse = 15
We can use the Pythagorean theorem to find the length of the blank side:
(Blank side)^2 = (Hypotenuse)^2 - (Side length)^2
(Blank side)^2 = 15^2 - 12^2
(Blank side)^2 = 225 - 144
(Blank side)^2 = 81
Blank side = 9
So, for Triangle 1, we have the following ratios:
Side length : Hypotenuse = 12 : 15
Side length : Blank side = 12 : 9
Hypotenuse : Blank side = 15 : 9
For Triangle 2, we have:
Side length = 4
Hypotenuse = 5
We can use the Pythagorean theorem to find the length of the blank side:
(Blank side)^2 = (Hypotenuse)^2 - (Side length)^2
(Blank side)^2 = 5^2 - 4^2
(Blank side)^2 = 25 - 16
(Blank side)^2 = 9
Blank side = 3
So, for Triangle 2, we have the following ratios:
Side length : Hypotenuse = 4 : 5
Side length : Blank side = 4 : 3
Hypotenuse : Blank side = 5 : 3
Therefore, the ratio of corresponding sides for the two similar triangles is:
Side length : Side length = 12 : 4 = 3 : 1
Hypotenuse : Hypotenuse = 15 : 5 = 3 : 1
Blank side : Blank side = 9 : 3 = 3 : 1
Reducing each ratio to lowest terms, we get:
Side length : Side length = 3 : 1
Hypotenuse : Hypotenuse = 3 : 1
Blank side : Blank side = 3 : 1
So the correct answer is (b) StartFraction 4 Over 5 EndFraction = StartFraction 12 Over 15 EndFraction = StartFraction 4 Over 5 EndFraction.
Which of the following represents the distributive property?
A. a = b then bea
B. a(b+c)=ab+ac
C. if a = band b-c, then a = c
D. If a = b then ac- be
The expression represents the distributive property from the list of options is (b) a(b + c) = ab + ac
Which of the expression represents the distributive property?The distributive property is a mathematical property that applies to multiplication and addition or subtraction.
It states that when you multiply a number (or variable) by a sum or difference inside parentheses, you can distribute the multiplication across the terms inside the parentheses.
This is represented by the following formula:
a(b + c) = ab + ac
This is represented by Option (B)
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