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LuckyWell [14K]
3 years ago
14

Suppose that water is being pumped into a trough. the trough is $$15 feet long, and every cross section of the trough is an equi

lateral triangle, with a vertex of the triangle pointing toward the ground. find the rate of change of the height of the water when the height is $$4 feet, if the volume of water is increasing at a rate of $$8 cubic feet per second.
Mathematics
1 answer:
Dovator [93]3 years ago
4 0
I think it is the answer so that might be
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The area is 44.18 , hope this helps
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Heba ate 1/12 of a box of cereal. Now the box is 3/4 full
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5/6

Step-by-step explanation:

1/12 + 3/4 = 9/12

9/12 + 1/12 = 10/12

simplify 10/12

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If x = -6, which inequality is true?
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Solve 2cos ²y -siny -1=0 for 0° ≤y≤360°
natima [27]

 

\displaystyle\bf\\2cos^2y -sin\,y -1=0~~~for~~0^o\leq y \leq360^o\\\\cos^2y=1-sin^2y\\\\2(1-sin^2y) -sin\,y -1=0\\\\2-2sin^2y-sin\,y-1=0\\\\-2sin^2y-sin\,y+2-1=0\\\\-2sin^2y-sin\,y+1=0~~~\Big|\times(-1)\\\\2sin^2y+sin\,y-1=0

.

\displaystyle\bf\\\boxed{\bf sin\,y=x}\\\\2x^2+x-1=0\\\\x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-1\pm\sqrt{1-4\cdot2\cdot(-1)}}{2\cdot2}=\\\\=\frac{-1\pm\sqrt{1+8}}{4}=\frac{-1\pm\sqrt{9}}{4}=\frac{-1\pm3}{4}\\\\x_1=\frac{-1+3}{4}=\frac{2}{4}=\boxed{\bf\frac{1}{2}}\\\\x_2=\frac{-1-3}{4}=\frac{-4}{4}=\boxed{\bf-1}\\\\sin\,y=\frac{1}{2}\\\\\boxed{\bf y_1=\frac{\pi}{6}~~or~~(30^o)}\\\\\boxed{\bf y_2=\frac{5\pi}{6}~~or~~(150^o)}\\\\sin\,y=-1\\\\\boxed{\bf y_3=\frac{3\pi}{2}~~or~~(270^o)}

 

 

5 0
3 years ago
****WILL GIVE BRAINLIEST TO FIRST ANSWERER****
xz_007 [3.2K]
Let's plug in each coordinate and see what we get:

(2, 0, 0)
-> 2A + 0 + 0 = D
-> 2A = D
-> A = D/2

(0, 6, 0)
-> 0 + 6B + 0 = D
-> 6B = D
-> B = D/6

(0, 0, 5)
-> 0 + 0 + 5C = D
-> 5C = D
-> C = D/5

plugging this back into the equation:
(D/2)x + (D/6)y + (D/5)z = D    [then divide through by D]
(1/2)x + (1/6)y + (1/5)z = 1
and since we have to have integer coefficients, 
multiply through by 30

so we get
15x + 5y + 6z = 30



Second question

<span>Take a look at the bottom-left point in the picture.
If you move three points in the y-direction, you'll reach to the  point A.
 If you instead move up 4 points (or in the z-direction), you reach D.
And finally, if you walk back to point F from point E, you'll have moved back 4 points in the x direction. </span>

<span>This gives us our measurements, or dimensions: 3 x 4 x 4.
If this were a rectangular prism, the dimensions would just be each of them multiplied.
 But since it's triangular, you need to divide it by two. That gives you a total volume of
(3x4x4)/2 = 24.</span>

5 0
3 years ago
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