The number of years it would take sales to reach $1,750,000 is 14.65 years.
<h3>What is the number of years?</h3>
The formula that can be used to determine the number of years it would take for the sales to reach $1,750,000 is:
Number of years : In (FV / PV) / r
Where:
- FV = future level of sales - $1,750,000
- PV = present level of sales = 850,000
- r = rate of growth - 4.931998%
Number of years : In ($1,750,000 / 850,000) / 0.04931998
Number of years : In (2.06) / 0.04931998
Number of years : 14.65 years
To learn more about how to determine the number of years, please check: brainly.com/question/21841217
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Answer:
x= 7
Step-by-step explanation:
1st step: Multiply the factor (outside number) with the numbers and variable(s) in the box. This results in 2(x-3) = 2x-6
2nd Step: continue the rest of the equation since there are no more brackets left so 2x-6-12=-4
3rd Step: send -12 to the other side of the equation (side changes sign changes) so it will become 2x-6=-4+12 (You are actually supposed to make the variable alone on one side of the equation so that you would be able to calculate its value)
4th step: 2x-6=8 ---> send -6 to the other side as well which will then result in 2x=14
5th step: since 2 is being multiplied by x, when you send it to the other side (to make x alone) you will divide 14 by 2 ( sign of 2 changes from multiplication to division)
Final Step: x=7
Part A
Everything looks good but line 4. You need to put all of the "2h" in parenthesis so the teacher will know you are squaring all of 2h. As you have it right now, you are saying "only square the h, not the 2". Be careful as silly mistakes like this will often cost you points.
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Part B
It looks like you have the right answer. Though you'll need to use parenthesis to ensure that all of "75t/(2pi)" is under the cube root. I'm assuming you made a typo or forgot to put the parenthesis.
dh/dt = (25)/(2pi*h^2)
2pi*h^2*dh = 25*dt
int[ 2pi*h^2*dh ] = int[ 25*dt ] ... applying integral to both sides
(2/3)pi*h^3 = 25t + C
2pi*h^3 = 3(25t + C)
h^3 = (3(25t + C))/(2pi)
h^3 = (75t + 3C)/(2pi)
h^3 = (75t + C)/(2pi)
h = [ (75t + C)/(2pi) ]^(1/3)
Plug in the initial conditions. If the volume is V = 0 then the height is h = 0 at time t = 0
0 = [ (75(0) + C)/(2pi) ]^(1/3)
0 = [ (0 + C)/(2pi) ]^(1/3)
0 = [ (C)/(2pi) ]^(1/3)
0^3 = (C)/(2pi)
0 = C/(2pi)
C/(2pi) = 0
C = 0*2pi
C = 0
Therefore the h(t) function is...
h(t) = [ (75t + C)/(2pi) ]^(1/3)
h(t) = [ (75t + 0)/(2pi) ]^(1/3)
h(t) = [ (75t)/(2pi) ]^(1/3)
Answer:
h(t) = [ (75t)/(2pi) ]^(1/3)
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Part C
Your answer is correct.
Below is an alternative way to find the same answer
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Plug in the given height; solve for t
h(t) = [ (75t)/(2pi) ]^(1/3)
8 = [ (75t)/(2pi) ]^(1/3)
8^3 = (75t)/(2pi)
512 = (75t)/(2pi)
(75t)/(2pi) = 512
75t = 512*2pi
75t = 1024pi
t = 1024pi/75
At this time value, the height of the water is 8 feet
Set up the radius r(t) function
r = 2*h
r = 2*h(t)
r = 2*[ (75t)/(2pi) ]^(1/3) .... using the answer from part B
Differentiate that r(t) function with respect to t
r = 2*[ (75t)/(2pi) ]^(1/3)
dr/dt = 2*(1/3)*[ (75t)/(2pi) ]^(1/3-1)*d/dt[(75t)/(2pi)]
dr/dt = (2/3)*[ (75t)/(2pi) ]^(-2/3)*(75/(2pi))
dr/dt = (2/3)*(75/(2pi))*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)
Plug in t = 1024pi/75 found earlier above
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75(1024pi/75))/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (1024pi)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*(1/64)
dr/dt = 25/(64pi)
getting the same answer as before
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Thinking back as I finish up, your method is definitely shorter and more efficient. So I prefer your method, which is effectively this:
r = 2h, dr/dh = 2
dh/dt = (25)/(2pi*h^2) ... from part A
dr/dt = dr/dh*dh/dt ... chain rule
dr/dt = 2*((25)/(2pi*h^2))
dr/dt = ((25)/(pi*h^2))
dr/dt = ((25)/(pi*8^2)) ... plugging in h = 8
dr/dt = (25)/(64pi)
which is what you stated in your screenshot (though I added on the line dr/dt = dr/dh*dh/dt to show the chain rule in action)
Answer:
D. making loans to businesses for capital investment.
Step-by-step explanation:
We can define the responsibilities of investment bans like- these banks specialize in complex financial transactions like underwriting.
These also play the role of broker or financial adviser for institutional clients. These banks helps organisations to raise capital.
These also help companies and governments issue new securities.
So, the answer is -
Investment banks generally provide all the following services except: making loans to businesses for capital investment.
Answer:
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Step-by-step explanation:
