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3 years ago

9

Bailey likes the shape of her friend's pool, but she wants one that is half the volume. According to Cavalieri’s Principle, what

dimension could she change to accomplish that?

2 answers:

Cerrena [4.2K]3 years ago

8 0

Answer: I need a picture off the pool and measurements.

Step-by-step explanation: I need this in order to figure out the problem and give you a helpful answer.

Olin [163]3 years ago

4 0

Answer:

Width or length

Step-by-step explanation:

Cavalieri's Principle states that in two solids with equal altitude, if the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal.

So, if Bailey's pool section is half her friend's pool, then the new volume would be half of the original. To do that, she can half width or length

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Which of the following is the solution to the equation - y = 24?

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Answer:

The Answer to this equation Y = 32

Step-by-step explanation:

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3 years ago

In ΔBCD, the measure of ∠D=90°, the measure of ∠B=31°, and CD = 1.6 feet. Find the length of BC to the nearest tenth of a foot.

son4ous [18]

Answer:

3.1066≈3.1 feet

Step-by-step explanation:

3.1066≈3.1 feet

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2 years ago

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if x-1 is a factor of P(x)=x^3- 5x^2 + 7x-3 which of the following represents the complete factorization for P(x)?

kozerog [31]

Answer:

P(x) = (x-1)² (x-3)

Step-by-step explanation:

P(x)=x³- 5x² + 7x-3 = x² (x-1) - 4x(x-1) + 3(x-1) = (x²-4x+3)(x-1)

P(x) = (x-1)(x-3)(x-1) = (x-1)² (x-3)

3 0

3 years ago

What are the endpoint coordinates for the midsegment of △BCD that is parallel to BC?

natulia [17]

Answer:

<em>The endpoint coordinates for the mid-segment are: $(-2,-1)$ and $(1,0)$ </em>

Step-by-step explanation:

According to the given diagram, the coordinates of the vertices of $\triangle BCD$ are: $B(-3,1), C(3,3)$ and $D(-1,-3)$

Now, the endpoints of the mid-segment of $\triangle BCD$ which is parallel to $BC$ will be the mid-points of sides $BD$ and $CD$ .

<u>Formula for the coordinate of mid-point</u> : $(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})$ , where $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are two endpoints.

So, the mid-point of $BD$ will be: $(\frac{-3-1}{2},\frac{1-3}{2})=(\frac{-4}{2},\frac{-2}{2})=(-2,-1)$

and the mid-point of $CD$ will be: $(\frac{3-1}{2},\frac{3-3}{2})=(\frac{2}{2},\frac{0}{2})=(1,0)$

Thus, the endpoint coordinates for the mid-segment of $\triangle BCD$ that is parallel to $BC$ are $(-2,-1)$ and $(1,0)$

4 0

2 years ago

Read 2 more answers

A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 1584 cubic feet

liq [111]

Answer:

The room dimensions that will minimize the cost of the paint are 12 ft x 12 ft x 11 ft.

Step-by-step explanation:

We can find first the volume equation using the formula of the volume of a box.

$V= xyz$

Thus we get the constraint function

$1584 = xyz$

Then since we are asked to minimize the cost, we can write the cost function which is the area of each one of the walls and ceiling multiplied by the painting cost.

$C=0.11 xy+ 2(0.06)xz+2(0.06yz \\ C =0.11 xy+0.12xz+0.12yz$

Lagrange Multipliers to find minimum cost.

We can continue finding the partial derivatives to build the system of equations required for Lagrange Multipliers method.

$C_x=\lambda V_x \\ C_y = \lambda V_y \\ C_z = \lambda V_z$

And the constraint function

$xyz=1584$

So we get

$0.11y+0.12z=\lambda yz \\ 0.11x+0.12z=\lambda xz \\ 0.12x+0.12y=\lambda xy\\ xyz=1584$

We can multiply each side of each equation by the dimension which is missing to get the full volume on the right side.

$0.11xy+0.12xz=\lambda xyz \\ 0.11xy+0.12yz=\lambda xyz \\ 0.12xz+0.12yz=\lambda xyz$

Then we can set each the equations equal to each other, so from the first one and the second equation we get

$0.11xy+0.12xz= 0.11xy+0.12yz$

We can subtract 0.11xy from both sides.

$0.12xz=0.12yz$

And we can divide both sides by 0.12z to get

$x=y$

We can repeat the process by setting the first and third equation equal to each other.

$0.11xy+0.12xz= 0.12xz+0.12yz$

We can subtract 0.12 xz from both sides

$0.11xy=0.12yz$

And we can solve by z

$z= \cfrac{0.11x}{0.12}\\ z = \cfrac{11x}{12}$

So if we replace that as well y = x on the constraint for the volume euqation we get

$1584=x(x)\left(\cfrac{11}{12}x\right) \\ 1584=\cfrac{11}{12}x^3$

We can then solve for x

$x^3 = \cfrac{1584(12)}{11}$

And taking the cube root

$x = \sqrt[3]{\cfrac{1584(12)}{11}}$

$x = \sqrt[3]{1728}$

$x=12 ft$

So then we can use the equations we have found for y and z in terms of x

$y = x \\ y = 12 ft$

And

$z= \cfrac{11x}{12}\\z= \cfrac{11(12)}{12} \\ z=11ft$

Then the dimensions of the room that will minimize the cost are 12ft x 12 ft x 11 ft. Since you have to enter using commas you can write 12, 12, 11, please check as well if you have to insert the units that are feet for each.

5 0

3 years ago