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3 years ago

Answer p l e a s e ! !

Mathematics

1 answer:

sergiy2304 [10]3 years ago

8 0

Answer:

$3 = y$

Step-by-step explanation:

24 + 4y = 12y

- 4y - 4y

__________

$\frac{24}{8} = \frac{8y}{8} \\ \\ 3 = y$

I am joyous to assist you anytime.

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Find the volume of the solid whose base is the region Ix I Iy I < 1 and whose vertical cross sections perpendicular to the y-

gavmur [86]

Answer:

volume of the solid = $\frac{\pi }{3}$

Step-by-step explanation:

As given , the region : |x| + |y| $\leq$ 1

when y $\geq$ 0 ,

|x| + y = 1

⇒|x| = 1 - y

when y ≤ 0 ,

|x| - y = 1

⇒|x| = 1 + y

The given region is the rectangle with sides (0, 5) , (0, -5), (5, 0), (-5, 0)

As given , the vertical cross section are semicircle

As we know that the area of semi circle = $\frac{1}{2}$ $\pi x^{2}$

Now,

Volume = $\int\limits^0_-1 {\frac{\pi }{2} (1+y)^{2} } \, dy$ + $\int\limits^1_0 {\frac{\pi }{2} (1-y)^{2} } \, dy$

= $\frac{\pi }{2} (\frac{(1+y)^{3} }{3} )$ - $\frac{\pi }{2} (\frac{(1-y)^{3} }{3} )$

= $\frac{\pi }{6}$ [1-0] - $\frac{\pi }{6}$ [0-1]

= $\frac{\pi }{6} + \frac{\pi }{6} = 2\frac{\pi }{6} = \frac{\pi }{3}$

⇒volume of the solid = $\frac{\pi }{3}$

4 0

3 years ago

2/5of a number is 80. What is 34of the same number?

Masja [62]

Answer:

150

Step-by-step explanation:

First you have to find what number 80 is 2/5 of, to do this do the reciprocal of 2/5 which would be 5/2. Multiply 80 by 5/2 and you'll get 200, then find what 3/4 of 200. Multiply 200 by 3, then divide by 4 to get the answer of 150.

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3 years ago

which expression represents the distance between the two points x and y on the number line -4 and 3

Alika [10]

It would have to be 3 because distance can't be a negative number.

4 0

3 years ago

Read 2 more answers

Two workers finished a job in 12 days. How long would it take each worker to do the job by himself if one of the workers needs 1

Lorico [155]

Two workers finished a job in 7.5 days.

How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

let t = time required by one worker to complete the job alone

then

(t+8) = time required by the other worker (shirker)

let the completed job = 1

A typical shared work equation

7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1

multiply by t(t+8), cancel the denominators, and you have

7.5(t+8) + 7.5t = t(t+8)

7.5t + 60 + 7.5t = t^2 + 8t

15t + 60 = t^2 + 8t

form a quadratic equation on the right

0 = t^2 + 8t - 15t - 60

t^2 - 7t - 60 = 0

Factor easily to

(t-12) (t+5) = 0

the positive solution is all we want here

t = 12 days, the first guy working alone

then

the shirker would struggle thru the job in 20 days.

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2 years ago

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Consider the following problem: a box with an open top is to be constructed from a square piece of cardboard, 3 feet wide, by cu

Alecsey [184]

Answer:

) See annex

b) See annex

x = 0,5 ft

y = 2 ft and

V = 2 ft³

Step-by-step explanation: See annex

c) V = y*y*x

d-1) y = 3 - 2x

d-2) V = (3-2x)* ( 3-2x)* x ⇒ V = (3-2x)²*x

V(x) =( 9 + 4x² - 12x )*x ⇒ V(x) = 9x + 4x³ - 12x²

Taking derivatives

V¨(x) = 9 + 12x² - 24x

V¨(x) = 0 ⇒ 12x² -24x +9 = 0 ⇒ 4x² - 8x + 3 = 0

Solving for x (second degree equation)

x =[ -b ± √b²- 4ac ] / 2a

we get x₁ = 1,5 and x₂ = 0,5

We look at y = 3 - 2x and see that the value x₂ is the only valid root

then

x = 0,5 ft

y = 2 ft and

V = 0,5*2*2

V = 2 ft³

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2 years ago