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3 years ago

What is the area of the triangle in the coordinate plane?

Mathematics

1 answer:

Sophie [7]3 years ago

8 0

<span>49.0 units2

1/2 x 7 x 14</span>

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Find the volume of the prism.

Salsk061 [2.6K]

The volume of the prism is (B) 864 mm3

7 0

3 years ago

Find the volume of the solid formed by revolving the region bounded by LaTeX: y = \sqrt{x} y = x and the lines LaTeX: y = 1 y =

Strike441 [17]

Answer:

The volume is:

$\displaystyle\frac{37\pi}{10}$

Step-by-step explanation:

See the sketch of the region in the attached graph.

We set the integral using washer method:

$\displaystyle\int_a^b\pi r^2dx$

Notice here the radius of the washer is the difference of the given curves:

$x-\sqrt{x}$

So the integral becomes:

$\displaystyle\int_1^4\pi(x-\sqrt{x})^2dx$

We solve it:

Factor $\pi$ out and distribute the exponent (you can use FOIL):

$\displaystyle\pi\int_1^4x^2-2x\sqrt{x}+x\,dx$

Notice: $x\sqrt{x}=x\cdot x^{1/2}=x^{3/2}$

So the integral becomes:

$\displaystyle\pi\int_1^4x^2-2x^{3/2}+x\,dx$

Then using the basic rule to evaluate the integral:

$\displaystyle\pi\left[\frac{x^3}{3}-\frac{2x^{5/2}}{5/2}+\frac{x^2}{2}\right|_1^4$

Simplifying a bit:

$\displaystyle\pi\left[\frac{x^3}{3}-\frac{4x^{5/2}}{5}+\frac{x^2}{2}\right|_1^4$

Then plugging the limits of the integral:

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(4)^{5/2}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Taking the root (rational exponents):

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(2)^{5}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Then doing those arithmetic computations we get:

$\displaystyle\frac{37\pi}{10}$

6 0

3 years ago

Y=7x-14 x intercept

Zanzabum

Answer:

y equal -7

Step-by-step explanation:

i think so but it will help you

5 0

3 years ago

5/15 = n/9 someone help me (proportions)

goblinko [34]

Answer:

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

If Miguel types 40 words per minute and he types for 30 minutes how many words will he have typed total? *

krok68 [10]

Answer:

1200 words

Step-by-step explanation:

If he types 40 words a minute, you have to multiply that by thirty because he typed 40 words 30 timers. 40 x 30=1200

8 0

3 years ago

Read 2 more answers