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lukranit [14]
2 years ago
7

X

Mathematics
1 answer:
Alex777 [14]2 years ago
8 0
I think the answer is X
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Find the scale factor of a cube with volume 216 ft^3 to a cube with volume 1000 ft^3.
Bad White [126]

Answer:

Scale factor of  cube to the smaller cube is 5 : 3.

Step-by-step explanation:

Ratio of the volumes of two cubes = \frac{\text{volume of large prism}}{\text{Volume of small prism}}

                                                          = \frac{1000}{216}

                                                          = \frac{125}{27}

Scale factor of these cubes = \sqrt[3]{\text{ratio of the volumes of the cubes}}

                                              = \sqrt[3]{\frac{\text{volume of large prism}}{\text{Volume of small prism}}}

                                              = \sqrt[3]{\frac{125}{27} }

                                              = \frac{5}{3}

                                              = 5 : 3

Therefore, scale factor of  cube to the smaller cube is 5 : 3.

6 0
3 years ago
Help! William earns $13,644.80 per hear, and has his federal taxes withheld from each weekly check. In addition, a total of $53.
leva [86]
So 52 weeks in a year so

13,644.8/52=262.4 per week

53.8 is deducted from 262.4

so the deduction is 53.8 then the answer is
262.4-53.8=208.6

the 10% and 15% part is of the yearly income and 53.8 is 15% of 262.4 so that part doesn't matter

the answer of net pay is 208.6 dollars
8 0
3 years ago
Population Growth A lake is stocked with 500 fish, and their population increases according to the logistic curve where t is mea
Alexus [3.1K]

Answer:

a) Figure attached

b) For this case we just need to see what is the value of the function when x tnd to infinity. As we can see in our original function if x goes to infinity out function tend to 1000 and thats our limiting size.

c) p'(t) =\frac{19000 e^{-\frac{t}{5}}}{5 (1+19e^{-\frac{t}{5}})^2}

And if we find the derivate when t=1 we got this:

p'(t=1) =\frac{38000 e^{-\frac{1}{5}}}{(1+19e^{-\frac{1}{5}})^2}=113.506 \approx 114

And if we replace t=10 we got:

p'(t=10) =\frac{38000 e^{-\frac{10}{5}}}{(1+19e^{-\frac{10}{5}})^2}=403.204 \approx 404

d) 0 = \frac{7600 e^{-\frac{t}{5}} (19e^{-\frac{t}{5}} -1)}{(1+19e^{-\frac{t}{5}})^3}

And then:

0 = 7600 e^{-\frac{t}{5}} (19e^{-\frac{t}{5}} -1)

0 =19e^{-\frac{t}{5}} -1

ln(\frac{1}{19}) = -\frac{t}{5}

t = -5 ln (\frac{1}{19}) =14.722

Step-by-step explanation:

Assuming this complete problem: "A lake is stocked with 500 fish, and the population increases according to the logistic curve p(t) = 10000 / 1 + 19e^-t/5 where t is measured in months. (a) Use a graphing utility to graph the function. (b) What is the limiting size of the fish population? (c) At what rates is the fish population changing at the end of 1 month and at the end of 10 months? (d) After how many months is the population increasing most rapidly?"

Solution to the problem

We have the following function

P(t)=\frac{10000}{1 +19e^{-\frac{t}{5}}}

(a) Use a graphing utility to graph the function.

If we use desmos we got the figure attached.

(b) What is the limiting size of the fish population?

For this case we just need to see what is the value of the function when x tnd to infinity. As we can see in our original function if x goes to infinity out function tend to 1000 and thats our limiting size.

(c) At what rates is the fish population changing at the end of 1 month and at the end of 10 months?

For this case we need to calculate the derivate of the function. And we need to use the derivate of a quotient and we got this:

p'(t) = \frac{0 - 10000 *(-\frac{19}{5}) e^{-\frac{t}{5}}}{(1+e^{-\frac{t}{5}})^2}

And if we simplify we got this:

p'(t) =\frac{19000 e^{-\frac{t}{5}}}{5 (1+19e^{-\frac{t}{5}})^2}

And if we simplify we got:

p'(t) =\frac{38000 e^{-\frac{t}{5}}}{(1+19e^{-\frac{t}{5}})^2}

And if we find the derivate when t=1 we got this:

p'(t=1) =\frac{38000 e^{-\frac{1}{5}}}{(1+19e^{-\frac{1}{5}})^2}=113.506 \approx 114

And if we replace t=10 we got:

p'(t=10) =\frac{38000 e^{-\frac{10}{5}}}{(1+19e^{-\frac{10}{5}})^2}=403.204 \approx 404

(d) After how many months is the population increasing most rapidly?

For this case we need to find the second derivate, set equal to 0 and then solve for t. The second derivate is given by:

p''(t) = \frac{7600 e^{-\frac{t}{5}} (19e^{-\frac{t}{5}} -1)}{(1+19e^{-\frac{t}{5}})^3}

And if we set equal to 0 we got:

0 = \frac{7600 e^{-\frac{t}{5}} (19e^{-\frac{t}{5}} -1)}{(1+19e^{-\frac{t}{5}})^3}

And then:

0 = 7600 e^{-\frac{t}{5}} (19e^{-\frac{t}{5}} -1)

0 =19e^{-\frac{t}{5}} -1

ln(\frac{1}{19}) = -\frac{t}{5}

t = -5 ln (\frac{1}{19}) =14.722

7 0
3 years ago
Over a four-week period, Gail earned the following commissions:
stellarik [79]

Answer:$257.5

Step-by-step explanation: add all the amounts then divide by 4

5 0
3 years ago
Read 2 more answers
Last year, Lein earned $1,600 more than her husband. Together they earned $48,100. How much did each of them earn?
Illusion [34]
Lein earned $25,650
Her husband earned $22,450
5 0
3 years ago
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