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matrenka [14]
3 years ago
11

What is the inverse of-65​

Mathematics
1 answer:
user100 [1]3 years ago
4 0

Answer:

- 1/65

Step-by-step explanation:

the multiplicative inverse of - 65 is - 1/65

(- 1/65) x (- 65) = 1

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Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 9t + 9 cot(t/2), [π/4, 7π/4]
agasfer [191]

Answer:

the absolute maximum value is 89.96 and

the absolute minimum value is 23.173

Step-by-step explanation:

Here we have cotangent given by the following relation;

cot \theta =\frac{1 }{tan \theta} so that the expression becomes

f(t) = 9t +9/tan(t/2)

Therefore, to look for the point of local extremum, we differentiate, the expression as follows;

f'(t) = \frac{\mathrm{d} \left (9t +9/tan(t/2)  \right )}{\mathrm{d} t} = \frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9  \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2}

Equating to 0 and solving gives

\frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9  \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2} = 0

t=\frac{4\pi n_1 +\pi }{2} ; t = \frac{4\pi n_2 -\pi }{2}

Where n_i is an integer hence when n₁ = 0 and n₂ = 1 we have t = π/4 and t = 3π/2 respectively

Or we have by chain rule

f'(t) = 9 -(9/2)csc²(t/2)

Equating to zero gives

9 -(9/2)csc²(t/2) = 0

csc²(t/2)  = 2

csc(t/2) = ±√2

The solutions are, in quadrant 1, t/2 = π/4 such that t = π/2 or

in quadrant 2 we have t/2 = π - π/4 so that t = 3π/2

We then evaluate between the given closed interval to find the absolute maximum and absolute minimum as follows;

f(x) for x = π/4, π/2, 3π/2, 7π/2

f(π/4) = 9·π/4 +9/tan(π/8) = 28.7965

f(π/2) = 9·π/2 +9/tan(π/4) = 23.137

f(3π/2) = 9·3π/2 +9/tan(3·π/4) = 33.412

f(7π/2) = 9·7π/2 +9/tan(7π/4) = 89.96

Therefore the absolute maximum value = 89.96 and

the absolute minimum value = 23.173.

7 0
3 years ago
A restaurant sells a coffee refill mug for $6.75. Each refill costs $1.25. Last month Keith spent $31.75 on a mug and refills. W
Ronch [10]
The answer is 3975 that the aswer
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3 years ago
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PLEASE HELP!! Serious answers only please!!
klemol [59]

Answer:

Step-by-step explanation:

Use the distributive property to get rid of the brackets.

9i + 2*7 + 2*3i        Use the multiplication property to simplify the imaginary terms

9i + 2*3i + 2*7        Do the same to the real term

9i + 6i + 14              Use the addition of like terms property

15i + 14                    And that's your answer.

You may not like my terminology, but you have to remember that every text teaches this differently.

7 0
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Round 7,883 to nearest thousand
Stels [109]

Answer:

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Step-by-step explanation:

the nearest thousand is 8,000 as it is past 7,500.

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3 years ago
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Please help me I don’t understand
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Answer:

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Step-by-step explanation:

8 0
2 years ago
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