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likoan [24]
3 years ago
15

2) Dividing polynomial by using long division, (x ^2+ 4x - 15) \(x-3)

Mathematics
1 answer:
AleksandrR [38]3 years ago
3 0
X+7+6/x-3 (sorry if it’s not correct but that’s what I got)
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Water is added to a cylindrical tank of radius 5 m and height of 10 m at a rate of 100 L/min. Find the rate of change of the wat
nirvana33 [79]

Answer:

V = \pi r^2 h

For this case we know that r=5m represent the radius, h = 10m the height and the rate given is:

\frac{dV}{dt}= \frac{100 L}{min}

Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}

And replacing we got:

\frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}

And that represent 0.127 \frac{cm}{min}

Step-by-step explanation:

For a tank similar to a cylinder the volume is given by:

V = \pi r^2 h

For this case we know that r=5m represent the radius, h = 10m the height and the rate given is:

\frac{dV}{dt}= \frac{100 L}{min}

For this case we want to find the rate of change of the water level when h =6m so then we can derivate the formula for the volume and we got:

\frac{dV}{dt}= \pi r^2 \frac{dh}{dt}

And solving for \frac{dh}{dt} we got:

\frac{dh}{dt}= \frac{\frac{dV}{dt}}{\pi r^2}

We need to convert the rate given into m^3/min and we got:

Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}

And replacing we got:

\frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}

And that represent 0.127 \frac{cm}{min}

5 0
3 years ago
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given
Fed [463]
See attachment for one such shell. The volume is given by the sum of infinitely many thin shells like this, each with radius x and height determined by the vertical distance between the upper blue curve and the lower orange curve for any given x, i.e. 8e^x-8e^{-x}.

The volume is then

2\pi\displaystyle\int_0^1x\left(8e^x-8e^{-x}\right)\,\mathrm dx=16\pi\int xe^x(e^{2x}-1)\,\mathrm dx=\dfrac{32\pi}9(e^3-4)\approx179.677
7 0
3 years ago
Please answer math question
slavikrds [6]

Answer:

y = -4x + 9

O.R. y = 9- 4x

(both answers are equivalent, the same)

Step-by-step explanation:

1. finding gradient of perpendicular line to the equation given.

2. use the point provided in the wuestion and substitute it into the linear form of your slope-intercept form, which in my country is called the linear form, meaning straight line graph.

3. get answers by finding the y-intercept of the equation wanted.

note:

y = mx + c is how and what i use in my school as the linear form, altho every school is different and I understand that, so do check again with your teacher if it is how you do such type of questions.

5 0
3 years ago
X2+Y2=25
Fofino [41]
x^{2} + y^{2} =25 is equation of circle which have radius equal 5 and center in (0,0) point

8 0
3 years ago
PLEASE ANSWER THIS QUICK, IF YOU CAN YOU GET BRAINLEST!!!!
lesya692 [45]

Answer:

6

Step-by-step explanation:

6 0
2 years ago
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