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Luba_88 [7]
3 years ago
9

A profit of a football club after a takeover is modeled by p(t) = t3 - 14t2 + 20t + 120, which t is the number of years after th

e takeover. In which years was the club making loss?
Mathematics
1 answer:
Bogdan [553]3 years ago
6 0
T = 5, so after 5 years
p(t) = t^3 - 14t^2 + 20t + 120

Take derivative to find minimum:
p’(t) = 3t^2 - 28t + 10

Factor to solve for t:
p’(t) = (3t - 2)(t - 5)
0 = (3t - 2)(t - 5)

0 = 3t - 2
2 = 3t
2/3 = t

Plug 2/3 into original equation, this is a maximum. We want the minimum:

0 = t - 5
5 = t

Plug back into original:
5^3 - 14(5)^2 + 20(5) + 120
125 - 14(25) + 100 + 120
125 - 350 + 220
- 225 + 220
p(5) = -5
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Work out the volume for this prism ​
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5 0
3 years ago
Is<br>Five times what number plus 10 equals 20<br>​
Natalka [10]

Answer:

2

Step-by-step explanation:

5*2=10

10+10=20

or

5*x+10=20

10-10=0

20-10=10

5*x=10

5/5=0

10/5=2

x=2

3 0
3 years ago
Read 2 more answers
Limit of x^2-81/x+9<br> As x goes toward -9
Semmy [17]
Hello,

Use the factoration

a^2 - b^2 = (a - b)(a + b)

Then,

x^2 - 81 = x^2 - 9^2

x^2 - 9^2 = ( x - 9).(x + 9)

Then,

Lim (x^2- 81) /(x+9)

= Lim (x -9)(x+9)/(x+9)

Simplity x + 9

Lim (x -9)

Now replace x = -9

Lim ( -9 -9)

Lim -18 = -18
_______________

The second method without using factorization would be to calculate the limit by the hospital rule.

Lim f(x)/g(x) = lim f(x)'/g(x)'

Where,

f(x)' and g(x)' are the derivates.

Let f(x) = x^2 -81

f(x)' = 2x + 0
f(x)' = 2x

Let g(x) = x +9

g(x)' = 1 + 0
g(x)' = 1

Then the Lim stay:

Lim (x^2 -81)/(x+9) = Lim 2x /1

Now replace x = -9

Lim 2×-9 = Lim -18

= -18




7 0
3 years ago
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