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Andrew [12]
3 years ago
10

A vat of milk has spilled on a tile floor. The milk flow can be expressed with the function r(t) = 4t, where t represents time i

n minutes and r represents how far the milk is spreading.
The spilled milk is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = πr2.

Part A: Find the area of the circle of spilled milk as a function of time, or A[r(t)]. Show your work. (6 points)

Part B: How large is the area of spilled milk after 4 minutes? You may use 3.14 to approximate π in this problem. (4 points)
Mathematics
1 answer:
Ulleksa [173]3 years ago
3 0
Part A

Area = π[r(t)^]2 = π[(4t)^2] =16π(t)^2

Part B

t = 4 min

Area = 16(3.14)(4)^2= 803.84
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Simplify the expression 2(10)+2(x-2)
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Step-by-step explanation:

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Pyramid A is a square pyramid with a base side length of 12 inches and a height of 8 inches. Pyramid B is a square pyramid with
yan [13]

Answer:

<em>The volume of pyramid B is 64 times the volume of pyramid A.</em>

<em></em>

Step-by-step explanation:

Given:

Two square pyramids A and B.

Side Length of A, s_A = 12 inches

Height of A, h_A = 8 inches

Side Length of B, s_B = 48 inches

Height of B, h_B = 32 inches

To find:

How many times bigger is the volume of pyramid B than pyramid A?

OR

V_B is how many times bigger than V_A ?

Solution:

First of all, let us have a look at the formula for volume of a pyramid:

V=\dfrac{1}{3} \times \text{Area of Base} \times \text{Height}

Here, base is square, so:

V=\dfrac{1}{3} \times s^2 \times h

Volume of pyramid A:

V_A=\dfrac{1}{3} \times s_A^2 \times h_A

\Rightarrow V_A=\dfrac{1}{3} \times 12^2 \times 8 = 384\ inch^3

Volume of pyramid B:

V_B=\dfrac{1}{3} \times s_B^2 \times h_B

\Rightarrow V_B=\dfrac{1}{3} \times 48^2 \times 32 \\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 4^2 \times 4\\\Rightarrow V_B=\dfrac{1}{3} \times 12^2 \times 8 \times 64\\\Rightarrow V_B= 24576\ inch^3 = 384\times 64\ inch^3\\\Rightarrow V_B = V_A\times 64\ inch^3

<em>The volume of pyramid B is 64 times the volume of pyramid A.</em>

3 0
3 years ago
Write in standard form: <img src="https://tex.z-dn.net/?f=%28%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%2B%20%5Cfrac%7B%5Csqrt%7B2%7D
lutik1710 [3]

Answer:

-1

Step-by-step explanation:

=(\frac{1}{\sqrt{2}}(1+i))^4\\=\frac{1}{4}(1+i)^2(i+i)^2\\=\frac{1}{4}(2i)(2i)\\=i^2\\=-1

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3 years ago
What is the slope of a line that contains the two points (0, 3) and (4, 5)?
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The formula for slope is (y2 -- y1) / (x2 -- x1).

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5 - 4 = 1

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Hope this Helps!!


5 0
2 years ago
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