What is the surface area of this prism?

Mathematics

1 answer:

Zigmanuir [339]3 years ago

7 0

Let's find the area of each shape that makes up the prism. Let's first start with the triangles.

There are two identical triangles on both ends of the prisms. They have a height of 12 and a base 18. Let's find the area of both of the triangles.
12×18=216
216 is the area of both triangles. Each triangle has an area of 108 though.
Let's find the area of the two rectangles.

There are two identical rectangles that are 30 m by 15 m. Let's find the area of both.
30×15=450×2=900
So, the area of both rectangles together is 900.
Let's find the area of the rectangle that acts as the base in the picture.

There's only one and it's 30 m by 18 m.
30×18=540
Let's add everything together.

540+900+216
1440+216
1656

So, the surface area is 1656 m².

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Evaluate the definite integral. 1/4 csc(2πt) cot(2πt) dt 1/12

Afina-wow [57]

Hey there, hope I can help!

$\frac{1}{4}\csc \left(2\pi t\right)\cot \left(2\pi t\right)dt\frac{1}{12}$

$\mathrm{Multiply\:fractions}: \:a\cdot \frac{b}{c}\cdot \frac{d}{e}=\frac{a\:\cdot \:b\:\cdot \:d}{c\:\cdot \:e} \ \textgreater \ \frac{1\cdot \:1\cdot \:dt}{4\cdot \:12}\csc \left(2\pi t\right)\cot \left(2\pi t\right)$

$\mathrm{Apply\:rule}\:1\cdot \:a=a \ \textgreater \ \frac{dt}{4\cdot \:12}\csc \left(2\pi t\right)\cot \left(2\pi t\right)$

$\mathrm{Multiply\:the\:numbers:}\:4\cdot \:12=48 \ \textgreater \ \frac{dt}{48}\csc \left(2\pi t\right)\cot \left(2\pi t\right)$

$\mathrm{Multiply\:fractions}: \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} \ \textgreater \ \frac{dt\csc \left(2\pi t\right)\cot \left(2\pi t\right)}{48}$

Hope this helps!

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3 years ago

5.<br> 12.8 ft<br> 9 ft<br> 9 ft

kykrilka [37]

Answer:

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3 years ago

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Jackson bought snacks for his team's practice. He bought a bag of apples for $2.74

garik1379 [7]

Answer:

each bottle of juice costs $2.34

Step-by-step explanation:

2.74+10x=26.14

10x=26.14-2.74

10x=23.40

x=23.40/10

x=2.34

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2 years ago

Aisha ate 1/4 of the carrots in the bag. Enrique ate 3/12 of the carrots in the bag. Compare the amounts of carrots they each at

Neko [114]

The amount of carrots they each ate are the same because 12 is a multiple of 4. There are 3 4’s in one 12. If you multiply 1/4 times 3 you will get 3/12 because 1 x 3 = 3. And 4 x 3 = 12

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3 years ago

It’s late work and I’ve forgotten how to do it

Veseljchak [2.6K]

You want to eliminate one of the terms (x or y) in one of the equations so you can solve for the other variable. You have to multiply by the opposite number of the coefficient to be able to eliminate the term in the other equation. If the x coefficient is 2, then you have to multiply the entire other equation by -2. If the y coefficient is -5, then you have to multiply the entire other equation by 5.

10)
-4x + 9y= 9
x - 3y= -6

STEP 1:
multiply the bottom equation by 4
4(x- 3y)= 4(-6)
4x - 12y= -24

STEP 2:
add the top equation and the equation from step 2

-4x + 9y= 9
4x - 12y= -24
the x term cancels out

-3y= 15
divide both sides by -3

y= -5

STEP 2:
substitute the y value in either original equation to solve for x

x - 3y= -6
x - 3(-5)= -6

x + 15= -6
subtract 15 from both sides

x= -21

ANSWER: x= -21; y= -5
____________________

12)
-7x + y= -19
-2x + 3y= -19

STEP 1:
multiply the top equation by -3 to eliminate the y term and to solve for x

-3(-7x + y)= -3(-19)
21x - 3y= 57

STEP 2:
add the bottom equation and the equation from step 2 to solve for x

-2x + 3y= -19
21x - 3y= 57
the y term cancels out

19x= 38
divide both sides by 19

x= 2

STEP 3:
substitute the x value in step 2 to solve for y; you can use either original equation

-7x + y= -19
-7(2) + y= -19

-14 + y= -19
add 14 to both sides

y= -5

ANSWER: x= 2; y=-5

Hope this helps! :)

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3 years ago