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frez [133]
2 years ago
9

Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 3 (*sqaure root sign*) t (20 − t), [0,

20]
Mathematics
1 answer:
mafiozo [28]2 years ago
5 0

9514 1404 393

Answer:

  • maximum: 15∛5 ≈ 25.6496392002
  • minimum: 0

Step-by-step explanation:

The minimum will be found at the ends of the interval, where f(t) = 0.

The maximum is found in the middle of the interval, where f'(t) = 0.

  f(t)=\sqrt[3]{t}(20-t)\\\\f'(t)=\dfrac{20-t}{3\sqrt[3]{t^2}}-\sqrt[3]{t}=\sqrt[3]{t}\left(\dfrac{4(5-t)}{3t}\right)

This derivative is zero when the numerator is zero, at t=5. The function is a maximum at that point. The value there is ...

  f(5) = (∛5)(20-5) = 15∛5

The absolute maximum on the interval is 15∛5 at t=5.

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The Pythagorean theorem is a² + b² = c². Solve for b. b=±c+a−−−−√ b=±c2−a2−−−−−−√ b=±c2+a2−−−−−−√ b=±c−a−−−−√
uysha [10]

a^{2} +b^{2} =c^{2}

As we have to solve for b, it means we have to isolate b

So first of all subtract a^{2} from both sides

So we get

b^{2} =c^{2} -a^{2}

Now we need b , but its b^2 , so we can take square root on both sides.


taking square roots on both sides

b= +- \sqrt{c^2 -a^2}


Hence option B is correct

4 0
3 years ago
Twice the difference of a number + -3 is 4 find the number
NNADVOKAT [17]

Answer:

The number is 5

Step-by-step explanation:

If we need to find the hidden number, Which for simplicity's sake we will denote as "n", lets first write out the equation.

"2 x [n + (-3)] = 4"

We can work through this problem backwards. if we need two times the sum of "n" and (-3) to get to 4, the only number that can be multiplied by 2 to get a product of 4 is 2, so "n" + (-3) must equal 2. so, From here, we can figure out that since 5 + (-3) equals 2, "n" Must equal 5. so, if we plug in 5 for "n" the equation looks like this:

"2 x [5 + (-3)] = 4"

So, since the equation makes sense, the answer is, "n = 5"

7 0
3 years ago
What is a basic ratio for 5:15
enot [183]
5:15
Divide both sides by 5 to get it down to the lowest bases.
1:3
3 0
3 years ago
Find the value of x.<br> 7<br> Х<br> 3<br> Z<br> x= [?]<br> V<br> Give your answer in simplest form.
mixas84 [53]

Answer:

21

Step-by-step explanation:

y^2=7*3\\y^2=21\\y^2=\sqrt{21}

4 0
2 years ago
Lowest common multiple of 8 and 56
Gnom [1K]
LCM would have to be 2 I think
6 0
3 years ago
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