The positive variables p and c change with respect to time 1. The relationship between p and c is given by the equation p^2 = (20-c)^3 . At the instant when dp/dt = 41 and c = 15 , what is the value of dc/dt ？
The value of dc/dt when dp/dt = 41 and c = 15 is -41/75.
At any given time, the rate of change of the variables p and c with respect to time is denoted by dp/dt and dc/dt, respectively. The equation given to us is p^2 = (20-c)^3. We are given the values of dp/dt = 41 and c = 15. Thus, we are required to calculate the value of dc/dt.
To solve for dc/dt, we differentiate both sides of the equation with respect to time. On the left side, we get 2p*dp/dt, and on the right side, we get -3(20-c)^2*dc/dt. Equating both sides and solving for dc/dt, we get dc/dt = -41/(3(20-15)^2) = -41/75.
Hence, the value of dc/dt when dp/dt = 41 and c = 15 is -41/75.
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What are the solutions to the system of equations? y = 1/2 * x ^ 2 - 4; y = x - 4 Graph the system of equations to solve. (0, - 4) and (2, - 2); (- 2.75, 0) and (2.75, 0); (2, - 2) and (4, 0); (4, 0) and (0, - 4)
The graph of a system of two equations is a pair of lines in the plane for the two variables (x and y).
What is meant by system of equations?Simple sets of two or more linear equations make up a system of linear equations. A system of two equations has a graph that is a pair of lines in the plane for two variables (x and y).
Equations with the same variables are grouped together as systems of equations. The only difference is that you're using inequalities as opposed to equations when working with a system of inequalities. To resolve such a system, you must identify the values of the variables that will cause each inequality to be true simultaneously.
The first equation:
[tex]$y=\frac{1}{2} x+3$$[/tex]
[tex]$5 \stackrel{?}{=} \frac{1}{2}(4)+3 \quad$[/tex]
Plug in x = 4 and y = 5
5 = 5
The second equation:
y = x + 1
[tex]$5 \stackrel{?}{=} 4+1 \quad$[/tex] Plug in x = 4 and y = 5
5 = 5
(4,5) is indeed a solution.
Therefore, the correct answer is option b) (- 2.75, 0) and (2.75, 0).
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2. you are given two ropes that when lit burn in one hour. which one of the following time periods cannot be measured with your ropes? a) 50 min b) 30 min c) 25 min d) 35 min. (asked by citadel)
We cannot the time period of 25 min using two ropes that when lit burn in one hour. Hence, option C is the correct answer.
This problem is an example of a mathematical puzzle. In order to measure a time period of 30 min, all we need to do is burn one rope from both ends. Since it takes 60 minutes for the rope to burn when lit from one end, it will take half that time i.e., 30 min to burn when lit from both ends.
We can also measure a time period of 35 min if we burn one rope from both ends and the other a bit differently. If we burn a rope from both ends, it will take 30 mins. As for the extra 5 mins, we can take the other rope and first burn it from both ends and then burn it from the middle again. That makes 2 separate ropes and thus the burning time is 15 min. We can then again burn one of these from the middle and wait until one of them completely burns out. This will give us a time period of 35 minutes.
As for 50 minutes, we can use the same method as above for burning one rope completely from both ends and the other from the ends and the middle. We can't really burn the ropes in a way that will give us the time period of 25 min so option C is the correct answer.
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find the point on the shore line from which the angle from the boat is response area. then, measure the distance that the boat travels until the angle from the boat to that point is response area. that distance is the same as the distance between the boat and the shore line because the triangle formed is a(n) response area
The triangle formed is an isosceles triangle since two sides of the triangle are equal .
The point on the shoreline is the point of tangency between the shoreline and the circle centered at the boat with a radius equal to the distance between the boat and the shoreline. The angle from the boat to that point is equal to the angle of the central angle of the circle whose radius is equal to the distance between the boat and the shoreline.
Let the radius of the circle be r and the angle from the boat to the point on the shoreline be θ. Then the formula for the distance between the boat and the shoreline is:
r = θ × (2π/360)
To calculate the distance traveled by the boat, we need to use the formula for the circumference of a circle:
C = 2πr
Substituting the above formula for r into the formula for the circumference of a circle, we get:
C = 2π(θ × (2π/360))
Therefore, the distance traveled by the boat is:
C = (2π)2 × θ/360
The triangle formed is an isosceles triangle since two sides of the triangle are equal (the radius of the circle and the distance between the boat and the shoreline).
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given n points on a 2d plane. find the maximum number of points which can be covered by a rectangle with length x and breadth y. a point is said to be covered by a recatangle if it lies on the sides or inside the rectangle.
Due tο the 90 degree angle created by the axes at the origin and the measurements at point p, the system is knοwn as being rectangular.
What is Cartesian coordinate system?
A Cartesian coordinate system in a plane is a system of cοordinates that uniquely identifies each pοint by a pair of numerical coordinates. The coordinates (Xp, Yp) shοw where point p is in relation to the origin. Because the angle created by the axes at the οrigin and the angle created by the measurements at point p are bοth 90 degrees, the system is referred tο as rectangular. Thus, the measurement has sides of Xp and Yp, fοrming a rectangle.
These numerical coοrdinates are the signed distances from two fixed perpendicular οriented lines to the point, measured in the same unit of length.
In any case, for any convex polygon (including rectangle) the test is very simple: check each edge of the polygοn, assuming each edge is oriented in cοunterclockwise direction, and test whether the point lies tο the left of the edge (in the left-hand half-plane). If all edges pass the test - the pοint is inside. If at least οne fails - the point is outside.
In order to test whether the point (xp, yp) lies οn the left-hand side οf the edge (x1, y1) - (x2, y2), you just need tο calculate
D = (x2 - x1) * (yp - y1) - (xp - x1) * (y2 - y1)
If D > ∅, the pοint is on the left-hand side. If D < ∅, the point is on the right-hand side. If D = ∅, the pοint is on the line.
The previous versiοn of this answer described a seemingly different version οf left-hand side test . But it can be easily shοwn that it calculates the same value.
In order to test whether the point (xp, yp) liesοn the left-hand side of the edge (x1, y1) - (x2, y2), yοu need to build the line equation for the line containing the edge. The equatiοn is as follows
A × x + B × y + C = ∅
where
A = -(y2 - y1)
B = x2 - x1
C = -(A * x1 + B * y1)
Now all you need to dο is to calculate
D = A * xp + B * yp + C
If D > ∅, the pοint is on the left-hand side. If D < ∅, the point is on the right-hand side. If D = ∅, the point is on the line.
However, this test, again, wοrks for any convex polygon, meaning that it might be too generic fοr a rectangle. A rectangle might allow a simpler test... For example, in a rectangle (οr in any other parallelogram) the values of A and B have the same magnitude but different signs for opposing (i.e. parallel) edges, which can be explοited to simplify the test.
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PLEASE PLEASE HELP ME SOMEONE
Find the slope of the line.
Answer: The slope is 2.
Step-by-step explanation:
We can use this formula to help us solve:
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Given:
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Substitute values and simplify to solve:
[tex]\displaystyle \frac{6--6}{2--4}=\frac{6+6}{2+4}=\frac{12}{6} =2[/tex]
Answer:
The slope is 2
Step-by-step explanation:
The formula for slope is y2-y1/x2-x1
So just fill out the points and do the calculations.
It’s sales season, and there are 15 bags of potato chips in Cecilia shop.Alfred told me that there are 5 times fewer bags of potato chips in Cecilia shop than there are in his. Work out how many bags of potato chips there are in Alfred shop
Using multiplication, In Alfred's store, there are 75 bags of potato chips.
The fundamental concept of repeatedly adding the same number is represented by the process of multiplication.
The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
When we need to merge groups of similar sizes, we employ it. For instance, if there are 5 baskets, each containing 4 apples, we can use multiplication to get the total number of apples, which is 5 x 4 = 20 apples.
In Cecilia's store, there are five times fewer bags of potato chips than there are in Alfred's. This indicates that Alfred's has five times as many bags as Cecilia's does. We must multiply to determine how many bags there are in Alfred's store:
15 x 5 = 75
In Alfred's store, there are 75 bags of potato chips.
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PLEASE HELP, i have done the work 3 times and i keep on getting the same answer
Bath towels sell for $13.25 each, while hand towels sell for $4.50 each. Theresa buys some of each type of towel for a total of $62.25. If she spends $17.25 more on bath towels than she spends on hand towels, how many of each type does she buy?
Theresa bought 5 bath towels and 2 hand towels for a total amount of $62.25.
Theresa buys 5 bath towels and 2 hand towels.
Bath towels: $13.25 x 5 = $66.25
Hand towels: $4.50 x 2 = $9.00
Total: $66.25 + $9.00 = $75.25
Since Theresa spent a total of $62.25, she saved $13.25. The difference between the amount she spent on bath towels and the amount she spent on hand towels should be equal to the amount she saved.
Bath towels: $66.25 - $17.25 = $49.00
Hand towels: $9.00 + $17.25 = $26.25
Total: $49.00 + $26.25 = $75.25
Therefore, Theresa bought 5 bath towels ($66.25) and 2 hand towels ($9.00).
Theresa bought 5 bath towels and 2 hand towels for a total of $62.25.
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Suppose we want to choose 6 colors, without replacement , from 8 distinct colors. If the order of the choices is relevant, how many ways can this be done?
If the order of the choices is relevant ,72 times can this be done.
What is nPr in permutation formula?Suppose we want to choose 6 colors, without replacement , from 8 distinct colors. If the order of the choices is relevant
The permutation of arranging 'r' things from a collection of 'n' objects into an order or sequence is known as nPr in mathematics. Permutation is calculated using the formula nPr = (n!) / (n-r)! N permutations = nPr = n!/ (n-r)! Combination, nCr, is the selection of r items from a collection of n objects such that the order of the objects does not matter.
N permutations are as follows: 9P6 = 8!/(8-6)! = 8*7*6*5*4 = 6,720.
N combinations = nCr = n!/((n-r)!r!) is the response to b.
N combinations = = 8C6 = = 8!/((8-6)!6!) = (8*7*6)/(2*1) = 72
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the tripple point is the set temperature and pressure where a substance occurs as a solid, liquid, and gas simultaneously at equilibrium.
The triple point of a substance, Tₜ, is the temperature and pressure at which the three phases of the substance, solid, liquid, and gas, can coexist in thermodynamic equilibrium.
The triple point can be calculated using the Clausius-Clapeyron equation, which states that the pressure and temperature of the triple point are related by the equation:
ln(Pₜ/P₀) = (ΔHₜ / R) (1/Tₜ - 1/T₀)
where Pₜ and Tₜ are the pressure and temperature of the triple point, P₀ and T₀ are the pressure and temperature of an arbitrary reference point, ΔHₜ is the enthalpy of vaporization, and R is the universal gas constant.
To calculate the triple point, values for P₀ and T₀ are selected and the enthalpy of vaporization is determined from tabulated data. Then, the equation is rearranged to solve for Tₜ, and the pressure and temperature of the triple point can be found.
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A water tank already contains 55 gallons of water in Baxter begins to fill it. water flows into the tank at a rate of 8 gallons per minute. write a linear equation to model this situation. Find the volume of the water in the sink 25 minutes after Baxter begins filling the tank.how many minutes will Baxter fill the tank if the maximum volume of water is 395 gallons?
Answer:42.5
Step-by-step explanation:
A linear equation can be used to model this situation, where the volume of water in the tank (V) is equal to the initial volume plus the rate of flow multiplied by the number of minutes (t).
V = 55 + 8t
This equation can be used to find the volume of the water in the tank at a specific time. To find the volume of the water in the tank 25 minutes after Baxter begins filling it, we can substitute 25 for t in the equation:
V = 55 + 8(25) = 55 + 200 = 255 gallons
To find how many minutes it will take for Baxter to fill the tank if the maximum volume of water is 395 gallons, we can use the equation to solve for t.
395 = 55 + 8t
Subtract 55 from both sides:
340 = 8t
Divide both sides by 8:
t = 42.5
So, it will take 42.5 minutes for Baxter to fill the tank with a maximum volume of 395 gallons.
A linear equation can be used to model a situation where a quantity is changing at a constant rate.
Let V be the volume of water in the tank at time t in minutes.
The rate of change of the volume of water is 8 gallons per minute, so we can write the equation as:
V = 55 + 8t
This equation tells us that the volume of water in the tank is 55 gallons when t = 0 (at the start of filling the tank) and it increases by 8 gallons for every minute after that.
To find the volume of water in the tank 25 minutes after Baxter starts filling it, we can plug in t = 25 into the equation:
V = 55 + 8(25)
V = 55 + 200
V = 255 gallons
To find how many minutes it will take to fill the tank to the maximum volume of 395 gallons, we can use the equation and solve for t:
V = 55 + 8t
395 = 55 + 8t
340 = 8t
t = 340/8
t = 42.5 minutes
So it will take 42.5 minutes to fill the tank to the maximum volume of 395 gallons.
How many groups of 1/3 in 9? Evaluate. 9÷ 3 7
The number of groups of one third in 9 is 27
How to evaluate the expressionThe problem requires the use of division
To determine the number of groups of 1/3 in 9, we can divide 9 by 1/3:
= 9 / (1/3)
= 9 * 3
= 27
Therefore, there are 27 groups of 1/3 in 9.
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A machinist must cut 12 strips of metal that are each 2 ft 6 7/8 in. long. What is the total length needed in inches?
The total length needed in inches for the 12 strips of metal is 370¹/₂ inches.
How is the total length determined?The total length for the 12 strips of metal is determined using a combination of the mathematical operation of multiplication and unit conversion.
The 2 feet are converted to 24 inches (2 x 12) using unit conversion and multiplication.
The total length is determined by multiplication, involving the multiplicand and the multiplier, which results in a product called the result.
The number of strips of metal = 12
The length of each strip = 2 ft and 6⁷/₈ inches = 30⁷/₈ inches
1 foot = 12 inches
The total length = 370¹/₂ inches (30⁷/₈ inches x 12)
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the length of a rectangle is 4 in longer than its width. if the perimeter of the rectangle is 56 in , find its length and width.
Let w be the width of the rectangle. Then, the length is w + 4. The perimeter is 2(w + 4) + 2w = 56, so 2w + 8 = 56, and w = 24. The length is 28.
The given information is that the length of the rectangle is 4 inches longer than its width, and the perimeter of the rectangle is 56 inches. To find the length and width of the rectangle, we need to solve a system of equations. First, let w be the width of the rectangle, so that the length of the rectangle is w + 4. To find the perimeter of the rectangle, we can use the formula 2(w + 4) + 2w = 56. Substituting in w for the width, we get 2w + 8 = 56. Solving this equation for w, we get w = 24. The length of the rectangle is w + 4, so the length is 28. Therefore, the width of the rectangle is 24 inches and the length is 28 inches.
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The sum of 11 and three-fourths of a number is less than 112
Answer:
81
Step-by-step explanation:
Label the triangle using the information given, then find the cos(l)-
The following is true about AGHI:
mZH = 90°
GH = 4
HI=7
GI = 8.1
Find the expression for cos(1).
The triangle AGHI can be labeled by using the given information.
Find the expression for cos(1)?The triangle is labeled AGHI.cos(l) = (GH^2 + HI^2 - GI^2) / (2 * GH * HI) = (4^2 + 7^2 - 8.1^2) / (2 * 4 * 7) = 0.848048096156426.The triangle AGHI is an isosceles triangle, with two sides of equal length (GH and HI). The angle formed between GH and HI is mZH, which is a right angle. The length of the side GI is 8.1.To find the cos(l) of the triangle, we use the law of cosines, which states that c2 = a2 + b2 - 2abcos(l). In this case, c is 8.1, a is 4, and b is 7. Substituting these values into the equation yields cos(l) = (42 + 72 - 81.2) / (2(4)(7)) = -0.67.Therefore, the cos(l) of the triangle AGHI is -0.67.Label the triangle AGHI:The right-angle of the triangle is at the vertex of Z, so angle ZHG is 90°. The side opposite to angle ZHG is GH, which is equal to 4. The side adjacent to angle ZHG is HI, which is equal to 7. The side opposite to angle HGI is GI, which is equal to 8.1.To find the expression for cos(l), we can use the Cosine Law. Cos(l) = (GH^2 + HI^2 - GI^2)/2(GH)(HI). Substituting the given values, we get Cos(l) = (4^2 + 7^2 - 8.1^2)/2(4)(7). Hence, the expression for cos(l) is equal to -0.10205.To learn more about The triangle is labeled AGHI refer to:
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21/24=7/8=49/x find x
Answer:
x is approximately 3.449.
Step-by-step explanation:
We are given the following proportion: 21/24 = 7/8 = 49/x
To find x, we can cross-multiply and simplify:
21/24 = 7/8 = 49/x
247= 218 = 49*x
168 = 168 = 49x
x = 168/49 = 3.44948979591836734693877551020408
x = 3.449489795918367
So, x is approximately 3.449.
11
What is the value of this expression?
3 1/6 + 8 2/9 - 1 1/2
Answer:[tex]\frac{89}{9}[/tex] or [tex]9 \frac{8}{9}[/tex] or 9.8
Put a line above the 8 after the decimal point signaling that it will always be 8 after the decimal point.
Step-by-step explanation:
6*3+1=19
9*8+2=74
1*2+1=3
[tex]\frac{19}{6} + \frac{74}{9} - \frac{3}{2} = \frac{89}{9}[/tex]
Surveying A triangular parcel of ground has sides of lengths 725 feet, 650 feet, and 575 feet. Find the measure of the largest angle.
cos⁻¹ ( 7/23) is the measure of the largest angle.
What is known as a triangle?
The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.
The triangle's three angles add up to a total of 180 degrees.
The lengths are given as a = 725 feet, b = 650 feet, and c = 575 feet.
Since, we know the fact that angle opposite to largest side is greatest. Hence, the largest angle would be opposite to side a.
Now, use the law of cosine
cosA = b² + c² - a²/2bc
On substituting the values, we get
cosA = (650)² + ( 575 )² - ( 725)²/2*650*575
= 422500 + 330625 - 525625/747500
= 227500/747500
= 7/23
A = cos⁻¹ ( 7/23)
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which of the following statements could be used to generate a random number between 1 and 9, inclusive, and assign it to the variable dice?
The result is between 1 and 9, which is assigned to the variable dice.
To generate a random number between 1 and 9, inclusive, we can use the formula: (Math.random() * (9 - 1 + 1)) + 1. This formula randomly generates a number between 0 and 1, and then multiplies it by the range (9 - 1 + 1) to give us a result between 0 and 8. We then add 1 to this result to ensure that the final number is between 1 and 9.
To assign this number to the variable dice, we can use the following statement:
var dice = Math.floor((Math.random() * (9 - 1 + 1)) + 1);
Math.random() generates a random number between 0 and 1, which is then multiplied by the range (9 - 1 + 1) to give us a result between 0 and 8. Math.floor rounds this number down to the nearest whole number. We then add 1 to ensure that the result is between 1 and 9, which is assigned to the variable dice.
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The largest angle of a triangle is four times the middle angle. The smallest angle measures 24° less than the middle angle. Find the measure of each angle.
Answer:
Largest angle=136
middle angle=34
smallest angle=10
Step-by-step explanation:
largest angle= A, 4B
middle angle= B
smallest angle= C, B-24
A+B+C=180
4B+B+B-24=180
5B+B=204
6B=204
B=34
A=4(34), 136
B=34
C=34-24, 10
A car dealership wants to conduct a survey of
100
100 people who bought a new or used car at the dealership in the last three months. Of the people who bought a car at the dealership in the last three months,
2
,
000
2,000 bought a new car
1
,
600
1,600 of the new car buyers received a loan
500
500 bought a used car
300
300 of the used car buyers received a loan
Complete the table below to show the number of people the dealership should survey in each group so that the sample is representative of whether the buyers bought a new car or a used car and whether the buyers received a loan
According to the report, 80% of those who purchased new cars received loans, compared to 60% of those who purchased older cars.
How do you determine the population size for a survey?The population size estimate is calculated by dividing the total number of people getting a service or the total number of unique items delivered (M) by the percentage of people reporting receiving the service or item in a representative survey (P).
Given a car dealership wants to conduct a survey of 100 people who bought a new or used car at the dealership in the last three months.
number of people new car old car received Loan No loan
2,000 yes No 1600 400
500 No Yes 300 200
Percentages of people who received Loans bought new cars:
Percentage = 2000-400 / 2000
Percentage = 1600/2000
Percentage = 80%
Percentages of people who received Loans bought used cars:
Percentage = 300 * 100 / 500
Percentage = 3/5 * 100
Percentage = 60%
Therefore, According to the survey, 60% of the people Who bought used cars got loans while 80% of people who bought new cars gets loan.
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What is 9 out of 20?
PLEASE HELP ME ASAP!!
Therefore, as a result, the answer to the given triangle issue is
ΔA"B"C "≅ ΔABC is congruent.
Describe the triangle.A triangle qualifies as a polygon because it has sides or vertices. It is a basic geometric form. Triangle ABC refers to a triangle well with sides A, B, and C. Whenever the edges are not collinear, a single plane and triangle are produced in Euclidean geometry. Any triangle with three sides & three corners is referred to as a polygon.
Here,
Triangle ABC is reflected across the y-axis to form triangle A'B'C.
After that, triangle A was created by dilation by a factor of 3 "B"C".
Again for triangles ABC and A"B"C, determine the correct response."
So,
We are conscious that reflection goes through a thorough alteration,
thus the original object's size and shape remain unchanged.
After consideration, figures always correspond to their pictures.
A'B'C, ABC, etc (i)
Dilation is a flexible technique. The shape remains the same even though the size has changed.
As a result, figures after dilation invariably resemble their photos.
ΔA'B'C' ≅ ΔA "B"C" ... (ii)
I and (ii) together give us
ΔA"B"C "≅ ΔABC
ABC and ABC are triangles that are similar.
Therefore, option A is the best decision.
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Simplify the expression and combine like terms. -3(4k + 7)
Answer: -12k-21
Step-by-step explanation:
you must distribute the -3
Find the inverse function of function B, your answer should begin with y=...
Answer: To find the inverse of a function, we first need to make sure that the function is one-to-one, meaning that no two different input values map to the same output value.
If the function B is one-to-one, we can find the inverse by switching the x and y values, and then solving for y.
y = B^-1(x)
We can then use algebraic manipulation to solve for y.
For example, if B(x) = 2x + 1, we can find the inverse by switching x and y:
x = 2y + 1
Solving for y:
y = (x - 1)/2
So the inverse function of B(x) = 2x + 1 is B^-1(x) = (x - 1)/2
Please note that if the function B is not one-to-one, it will not have an inverse.
Step-by-step explanation:
Which graph represents the solution to the following inequality? | x | ≤ 7
Option D shows the correctly represents the solution to the given inequality: | x | ≤ 7
What is method to find the solution to inequality?A number is a solution to that of an inequality in x if it can be used to replace x with a statement that is true.
You may add the same amount to both sides of an inequality to make it equal.The same amount can be subtracted from each side.Each side may be multiplied or divided by a single positive number.You must flip the inequality sign if you multiply as well as divide every side by the a negative number.The inequality = x ≤ 7.
Due to the fact that this inequality shows that the x value is less than or equal to 7, This graph showsGiven that the graph indicates that x may be greater than 7 or equal to 7, Option D represents the inequality.Consequently, the fourth graph illustrates the inequality x ≤ 7.To know more about the inequality, here
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Applications of linear equations
One number is 7 more than another number. If the smaller number is doubled and added to 3 times the larger number, the sum is 86. Find the two numbers.
Smaller number=
Larger number=
(Type the integers or decimals.)
Answer:
Bigger number: 20
Smaller number: 13
Step-by-step explanation:
Let smaller number = x
Bigger number. = x + 7
From the question; 2x + 3(x + 7) = 86
2x + 3x + 21 = 86
5x + 21 = 86
5x = 86 - 21
5x = 65
x = 13
Therefore the smaller number is 13, and the bigger number is 13 + 7 = 20
easy please help!! Popcorn at a concession stand comes in two different-sized containers. The dimensions of the small container with a diameter of 4 in. are shown below.
A popcorn container shaped like a cylinder is shown. A dashed line across the top of the container is labeled four inches. The height of the container is labeled four and five tenths inches.
The large container of popcorn has the same height as the small container, but its diameter is 1.5 times greater. How do the volumes of the two containers of popcorn compare? Use 3.14 for π.
Select the answers from the drop-down lists to correctly complete each sentence.
The volume of the large container of popcorn is _______ in.^3
OPTIONS FOR BLANK :
A) 56.52
B) 84.78
C)127.17
D) 169.56
This is ______ times the volume of the small container.
OPTIONS FOR THIS BLANK :
A) 2.88
B) 2.25
C) 1.8
D) 1.5
Answer:
127.17 cubic inches2.25 timesStep-by-step explanation:
You want to know the volume of a cylindrical container 6 inches in diameter and 4.5 inches high, and you want to know how many times larger this volume is than if the diameter were 4 inches.
VolumeThe volume of a cylinder is given by the formula ...
V = πr²h
where r is half the diameter, and h is the height.
The volume of your large popcorn container is ...
V = 3.14·(3 in)²·(4.5 in) = 127.17 in³
The volume of the large container is 127.17 in³.
RatioFor a given height, the volume ratio is the square of the ratio of diameters. That ratio is given as 3/2, so the volume ratio is ...
(3/2)² = 9/4 = 2.25
The large container is 2.25 times the volume of the small container.
