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3 years ago

Don’t answer this please only for my friends.l

Mathematics

1 answer:

valentinak56 [21]3 years ago

5 0

Answer:

Step-by-step explanation:

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Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^3, x = 2, and y = 1 about the y-axis.

andrezito [222]

Since the rotation is about the y-axis, I'll integrate by dy.

$\displaystyle y=x^3\\x=\sqrt[3]y\\\\V=\pi \int \limits_1^8(2^2-(\sqrt[3]y)^2)\, dy\\V=\pi \Big[4x-\dfrac{3}{5}x^{\tfrac{5}{3}}\Big]_1^8\\V=\pi \left(4\cdot8-\dfrac{3}{5}\cdot8^{\tfrac{5}{3}\right-\left(4\cdot1-\dfrac{3}{5}\cdot1^{\tfrac{5}{3}\right)\right)\\V=\pi \left(32-\dfrac{96}{5}-\left(4-\dfrac{3}{5}\right)\right)\\V=\pi \left(\dfrac{64}{5}-\dfrac{17}{5}\right)\\V=\dfrac{47\pi}{5}$

3 0

3 years ago

A scientist has 100 milligrams of a radioactive element. The amount of radioactive element remaining after t days can be determi

grandymaker [24]

The mass of the first shipment at time t is
$m_{1}=100( \frac{1}{2} )^{ \frac{t}{10}}$

The mass of the second shipment at time t is
$m_{2}=100( \frac{1}{2} )^{ \frac{t-3}{10} }$

At time t, the ratio of m₁ to m₂ is
$\frac{m_{1}}{m_{2}} = \frac{100}{100}. \frac{(1/2)^{t/10}}{(1/2)^{(t-3)/10}} \\ = \frac{(1/2)^{t/10}}{(1/2)^{t/10}}. \frac{1}{(1/2)^{-3/10}} \\ = (1/2)^{3/10} \\ = 0.8123$

Therefore as a percentage,
$\frac{m_{1}}{m_{2}} =100*0.8123 = 81.23 \%$

Answer: B. 81.2%

4 0

4 years ago

Plsssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss help

Lunna [17]

Answer:

37.68cm

Step-by-step explanation:

C = 2 $\pi$ r

C = circumference

$\pi$ = the constant pi (3.14)

r = radius of the circle (6cm)

d = diameter of the circle (12cm)

d = 2r

C = 2 · 3.14 · 6

C = 37.68cm

8 0

4 years ago

write a ratio for the following description: for every 6 cups of flour in a bread recipe there are two cups of milk

8090 [49]

6:2 because there are 6 cups of flour and 2 cups of milk if u put the 2 first it means 2 cups to 6 cups and you need to answer it the exact way the it is asked I am in elementary school and I know this

8 0

3 years ago

Read 2 more answers

A triangular plaque has side lengths of 8 inches, 13 inches, and 15 inches.

lianna [129]

<h3>Answer: A) 52 square inches</h3>

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Explanation:

a = 8, b = 13, and c = 15 are the sides of the triangle

s = (a+b+c)/2 = (8+13+15)/2 = 18 is the semi-perimeter, aka half the perimeter.

Those values are then plugged into Heron's Formula below

$A = \sqrt{s*(s-a)*(s-b)*(s-c)}\\\\A = \sqrt{18*(18-8)*(18-13)*(18-15)}\\\\A = \sqrt{18*(10)*(5)*(3)}\\\\A = \sqrt{2700}\\\\A = \sqrt{900*3}\\\\A = \sqrt{900}*\sqrt{3}\\\\A = 30\sqrt{3}\\\\A \approx 51.9615\\\\A \approx 52\\\\$

The triangular plaque has an area of approximately 52 square inches.

6 0

3 years ago