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3 years ago

Find the volume of this composite figure. Show all work. Please!!!!!

Mathematics

1 answer:

Cloud [144]3 years ago

7 0

Answer:

718.75ft³

Step-by-step explanation:

Rectangular Prism=5x5x17.5=437.5

Cube=5x5x5=125

Triangular Prism=5x5x12.5x.5=156.25

437.5+125+156.25=718.75ft³

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Dy/dx = 2xy^2 and y(-1) = 2 find y(2)

Anarel [89]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2887301

—————

Solve the initial value problem:

dy
——— = 2xy², y = 2, when x = – 1.
dx

Separate the variables in the equation above:

$\mathsf{\dfrac{dy}{y^2}=2x\,dx}\\\\
\mathsf{y^{-2}\,dy=2x\,dx}$

Integrate both sides:

$\mathsf{\displaystyle\int\!y^{-2}\,dy=\int\!2x\,dx}\\\\\\
\mathsf{\dfrac{y^{-2+1}}{-2+1}=2\cdot \dfrac{x^{1+1}}{1+1}+C_1}\\\\\\
\mathsf{\dfrac{y^{-1}}{-1}=\diagup\hspace{-7}2\cdot \dfrac{x^2}{\diagup\hspace{-7}2}+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{y}=x^2+C_1}$

$\mathsf{\dfrac{1}{y}=-(x^2+C_1)}$

Take the reciprocal of both sides, and then you have

$\mathsf{y=-\,\dfrac{1}{x^2+C_1}\qquad\qquad where~C_1~is~a~constant\qquad (i)}$

In order to find the value of C₁ , just plug in the equation above those known values for x and y, then solve it for C₁:

y = 2, when x = – 1. So,

$\mathsf{2=-\,\dfrac{1}{1^2+C_1}}\\\\\\
\mathsf{2=-\,\dfrac{1}{1+C_1}}\\\\\\
\mathsf{-\,\dfrac{1}{2}=1+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-1=C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-\dfrac{2}{2}=C_1}$

$\mathsf{C_1=-\,\dfrac{3}{2}}$

Substitute that for C₁ into (i), and you have

$\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}}\\\\\\
\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}\cdot \dfrac{2}{2}}\\\\\\
\mathsf{y=-\,\dfrac{2}{2x^2-3}}$

So y(– 2) is

$\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot (-2)^2-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot 4-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{8-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{5}}\quad\longleftarrow\quad\textsf{this is the answer.}$

I hope this helps. =)

Tags: <em>ordinary differential equation ode integration separable variables initial value problem differential integral calculus</em>

7 0

3 years ago

A paper is 0.55 mm thick. How high pile of 274 sheets? The paper is 24.5 long and 18.5 cm wide. Calculate volume of the pile of

strojnjashka [21]

The height of the pile is 150.7 mm, and the volume is V = 6,830,477.5 mm³.

<h3>How high will be the pile of papers?</h3>

We know that each paper is 0.55mm thick, then if we pile 274 of these, the height of the pile will be:

H = 0.55mm*274 = 150.7mm

Now we want to get the volume of the pile of paper. Remember that for a rectangular prism of height H, width W, and length L, the volume is:

V = H*W*L

In this case, we have:

H = 150.7mm
W = 18.5 cm = 185 mm
L = 24.5 cm = 245 mm

Then the volume is:

V = (150.7mm)*(185 mm)*(245 mm) = 6,830,477.5 mm³

If you want to learn more about volumes:

brainly.com/question/1972490

#SPJ1

5 0

2 years ago

suppose you have a bag that hold 27 pieces of candy: 1 cream soda, 14 apple, and 12 root beer. you reach into the bag to pull ou

Alex787 [66]

I order to solve this you have to find out how how much root beer there is to the total amount of candy. 12/27. Then you find out what the percentage of root beer there is by dividing 12 by 27. It’ll give you a decimal point. Percentage has a maximum of 100%. And you’ll find out what percent based on this decimal. Factor it out of 1. The percentage you get is .44. By factoring out of 1 you can find out that the percentage is 44%. So the probability of finding a root beer out of all the candy is roughly 44%

7 0

3 years ago

Beach Cruises prints brochures and fliers to advertise their dolphin watching tours. To print, the brochure requires three pages

Nimfa-mama [501]

Answer:

500 divided by 80 equals 6.25. 6.25 divided by 100 equals 0.0625

Step-by-step explanation:

500 divided by 80 equals 6.25. 6.25 divided by 100 equals 0.0625

6 0

3 years ago

Can someone please help me with this algebra

kykrilka [37]

Answer:

Step-by-step explanation:

Because i did this problem

8 0

3 years ago