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2 years ago

Two-Dimensional Nets and Surface Area - Quiz - Level F

Mathematics

2 answers:

stepan [7]2 years ago

7 0

Answer:

deez

Step-by-step explanation:

nutz

8_murik_8 [283]2 years ago

7 0

Answer:

84ft^2

Step-by-step explanation: I ready lol

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The triangle T has vertices at (-2, 1), (2, 1) and (0,-1). (It might be an idea to

Firdavs [7]

Rewrite the boundary lines y = -1 - x and y = x - 1 as functions of y :

y = -1 - x ==> x = -1 - y

y = x - 1 ==> x = 1 + y

So if we let x range between these two lines, we need to let y vary between the point where these lines intersect, and the line y = 1.

This means the area is given by the integral,

$\displaystyle\iint_T\mathrm dA=\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy$

The integral with respect to x is trivial:

$\displaystyle\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy=\int_{-1}^1x\bigg|_{-1-y}^{1+y}\,\mathrm dy=\int_{-1}^1(1+y)-(-1-y)\,\mathrm dy=2\int_{-1}^1(1+y)\,\mathrm dy$

For the remaining integral, integrate term-by-term to get

$\displaystyle2\int_{-1}^1(1+y)\,\mathrm dy=2\left(y+\frac{y^2}2\right)\bigg|_{-1}^1=2\left(1+\frac12\right)-2\left(-1+\frac12\right)=\boxed{4}$

Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line y = 1 and (0, -1)), so its area is 1/2*4*2 = 4.

6 0

3 years ago

A rectangular retaining wall has an area of

Veronika [31]

Answer:

The height of wall is 3 feet and length of wall is 5 feet

Step-by-step explanation:

Given as :

The Area of retaining wall = 15 square feet

Let The width of wall = W feet

The Height of wall = ( W - 2 ) feet

Now, Area of Rectangle = Height width

Or , 15 ft² = ( W - 2 ) ft × W ft

Or, 15 = W² - 2 W

Or, W² - 2 W - 15 = 0

Or, W² - 5 W + 3 W - 15 = 0

Or, W ( W - 5 ) + 3 ( W - 5 ) = 0

So , ( W - 5 ) ( W + 3 ) = 0

So, W = 5 , - 3

∴ The width of wall = W = 5 feet

And The Height of wall = ( W - 2 ) = 5 - 2 = 3 feet

Hence The height of wall is 3 feet and length of wall is 5 feet. Answer

8 0

2 years ago

F(x)=x^+4x+2 what is the average rate of change from x=3 to x=5

mars1129 [50]

Answer:

Step-by-step explanation:

f(x)=x^+4x+2 First, let's evaluate when x=3, x=4 and x=5.

f(3) = 3²+4(3)+2 = 9 + 12 + 2 = 23

f(4) = 4²+4(4)+2 = 16 + 16 + 2 = 34

f(5) = 5²+4(5)+2 = 25 + 20 + 2 = 47

Now, let's find the rate of change.

34 - 23 = 11

47 - 34 = 13

Finally, the average rate of change.

(11 + 13) / 2 = 12

8 0

3 years ago

Solving inequalities by multiplication and division 1. -8 < 8w

Alex73 [517]

Answer:

w > -1

Step-by-step explanation:

Hello There!

We want to simplify this expression to be more specific we want to isolate the variable (w) using inverse operations

So we want to get rid of the 8 in 8w

8w is the same as 8 times w (multiplication)

The inverse of multiplication is division so to get rid of the 8 we want to divide by 8 but remember whatever we do to one side we want to do to the other side. So we divide each side by 8

-8/8 = - 1

8w/8=w

we're left with w > -1

6 0

2 years ago

Read 2 more answers

What’s 6(x – 1) = 9(x + 2) ?

strojnjashka [21]

Answer:

-8=x

Step-by-step explanation:

6x-6=9x+18

-6-18=9x-6x

-24=3x

x=-8

hope i helped

brainliest pls

im trying to level up

5 0

2 years ago

Read 2 more answers