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ikadub [295]
2 years ago
13

It takes a hose 4 minutes to fill a rectangular aquarium 8 inches long, 11 inches wide, and 12 inches tall. How long will it tak

e the same hose to fill an aquarium measuring 22 inches by 27 inches by 35 inches? minutes Round your answer to the nearest minute
Mathematics
1 answer:
hjlf2 years ago
5 0

Answer:

9 minutes

Step-by-step explanation:

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Find r(t) if r'(t) = 5t4i + 6t5j + t k and r(1) = i + j.
Vladimir [108]
\mathbf r(t)=\displaystyle\int(5t^4\,\mathbf i+6t^5\,\mathbf j+t\,\mathbf k)\,\mathrm dt
\mathbf r(t)=(t^5+C_1)\,\mathbf i+(t^6+C_2)\,\mathbf j+\left(\dfrac12t^2+C_3\right)\,\mathbf k

Given \mathbf r(1)=\mathbf i+\mathbf j, we have

\begin{cases}1^5+C_1=1\\\\1^6+C_2=1\\\\\dfrac121^2+C_3=0\end{cases}\implies C_1=0,C_2=0,C_3=-\dfrac12

so that the particular solution is

\mathbf r(t)=t^5\,\mathbf i+t^6\,\mathbf j+\dfrac12(t^2-1)\,\mathbf k
8 0
3 years ago
Simplify the expression -3(10x + 4y) + 6(6x − 2y)
IgorC [24]
-30x-12y+36x-12y

Combine the x' s first

6x-12y-12y

Combine the y's

6x-24y is your answer
4 0
3 years ago
Read 2 more answers
Help me please ASAP
brilliants [131]

ans is c it is simple c only meet the need of questions

4 0
2 years ago
The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y
Ivahew [28]

The area of an equilateral triangle of side "s" is s^2*sqrt(3)/4. So the volume of the slices in your problem is 

(x - x^2)^2 * sqrt(3)/4. 

Integrating from x = 0 to x = 1, we have 

[(1/3)x^3 - (1/2)x^4 + (1/5)x^5]*sqrt(3)/4 

= (1/30)*sqrt(3)/4 = sqrt(3)/120 = about 0.0144. 

Since this seems quite small, it makes sense to ask what the base area might be...integral from 0 to 1 of (x - x^2) dx = (1/2) - (1/3) = 1/6. Yes, OK, the max height of the triangles occurs where x - x^2 = 1/4, and most of the triangles are quite a bit shorter...

8 0
3 years ago
What is the simplified expression for the expression below?
kotykmax [81]

Answer:

A

Step-by-step explanation:

- 1/5 of 5x is  -1 or just -x and -1/5 of 20 is -4. Then the other one is-1/4 of 4 is -x and -1/4 of -28 is 7. Now combine like terms so -x + -x is -2x and 7+ -4 or 7-4 is 3

8 0
2 years ago
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