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VikaD [51]
3 years ago
14

An engine cylinder 13.7 cm deep is being bored such that the radius increases by 0.13 mm divided by min. How fast is the volume

V of the cylinder changing when the diameter is 9.7 cm question mark Use 3.14 for pi. Round to the nearest hundredth.
Mathematics
1 answer:
zzz [600]3 years ago
6 0

Answer:

Step-by-step explanation:

Given that an engine cylinder 13.7 cm deep is being bored such that the radius increases by 0.13 mm divided by min.

We convert everything in mm for uniformity

We have formula for volume as

V=\pi r^2 h

Given that \frac{dr}{dt} =0.13

h is constant

V= 3.14 (r^2) (13.7)\\\frac{dV}{dt} =6.28 (137) r dr/dt\\= 6.28(137)\frac{ (97)}{2} 0.13

= 6954.67 mm/sec^3

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Graph the following piecewise function on a separate piece of graph paper and upload your graph below.
Alecsey [184]
ANSWER

To graph the function

f(x)=\left \{ {{x+4\:\:if\:\:-4\leq x

follow the steps below.

1. Find y- intercept by plugging in x=0.

x=0 is on the interval,  -4\leq x, so we substitute in to

f(x)=x+4

\Rightarrow f(0)=0+4

\Rightarrow f(0)=4

Hence the y-intercept is (0,4)

2. Find x-intercept by setting f(x)=0

This implies that

x+4=0, on -4\leq x

or

2x-1=0 on 3\leq x

We now solve for x on each interval,

x=-4, on -4\leq x

or

x=\frac{1}{2} on 3\leq x

But observe that

x=\frac{1}{2} does not belong to 3\leq x

This means it  can never be an intercept for this piece-wise function.

Hence our x-intercept is (-4,0)

3. Plotting the boundaries of the interval.

For f(x)=x+4 on  -4\leq x

f(-4)=-4+4

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This point (-4,0) coincides with the x-intercept.

f(3)=3+4

f(3)=7

So we have the point (3,7). But note that x=3 does not belong to this interval so we plot this point as a hole.

For f(x)=2x-1 on 3\leq x

f(3)=2(3)-1

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So we plot (3,5)

f(6)=2(6)-1

\Rightarrow f(6)=11

So we plot (6,11) also as a hole.

Plotting all these points we can now graph the function,

f(x)=\left \{ {{x+4\:\:if\:\:-4\leq x

See attachment for graph.

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The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number
andreyandreev [35.5K]

Answer:

39

Step-by-step explanation:

let the 2 digit number be ab = 10a + b ( considering place value )

The reversed  2 digit number is ba = 10b + a

The sum of the 2 digit number is

a + b = 12 ( subtract b from both sides )

a = 12 - b → (1)

Expressing as an equation

ba = ab + 54 , that is

10b + a = 10a + b + 54

Substitute a = 12 - b into the equation

10b + 12 - b = 10(12 - b) + b + 54 , simplify both sides

9b + 12 = 120 - 10b + b + 54

9b + 12 = - 9b + 174 ( add 9b to both sides )

18b + 12 = 174 ( subtract 12 from both sides )

18b = 162 ( divide both sides by 18 )

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Substitute b = 9 into (1)

a = 12 - 9 = 3

Thus

the original 2 digit number = ab = 39

The reversed 2 digit number = ba = 93

which is 54 more than the original number

7 0
3 years ago
Gary wanted to determine the average height of boys at the high school. His older brother is on the basketball team, so he asked
fomenos

Answer:

The answer would be "no because boys on the basketball team are likely to be taller than other boys at the school"

Step-by-step explanation:

Hope this helps:)...if not then sorry for wasting your time and may God bless you:)

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cricket20 [7]

Answer:

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Step-by-step explanation:

Divide 891 by 9, 9, and finally, 11. Or use a factorization calculator.

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