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fredd [130]
3 years ago
12

Explain why domain restrictions for inverse trigonometric functions are necessary​

Mathematics
1 answer:
luda_lava [24]3 years ago
8 0

ANSWER

The domain of the trigonometric functions must be restricted in order to become invertible.

EXPLANATION

Trigonometric functions are periodic functions.

This functions are not invertible over the entire domain of the real numbers because they fail the horizontal line test.

However if we restrict the domain of trigonometric functions, they will now pass the horizontal line test and hence become invertible.

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1. Find the 90% Cl for the population mean if sample
Elden [556K]

Answer:

The answer is below

Step-by-step explanation:

1)

mean (μ) = 12, SD(σ) = 2.3, sample size (n) = 65

Given that the confidence level (c) = 90% = 0.9

α = 1 - c = 0.1

α/2 = 0.05

The z score of α/2 is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.65

The margin of error (E) is given as:

E=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} } =1.65*\frac{2.3}{\sqrt{65} } =0.47

The confidence interval = μ ± E = 12 ± 0.47 = (11.53, 12.47)

2)

mean (μ) = 23, SD(σ) = 12, sample size (n) = 45

Given that the confidence level (c) = 88% = 0.88

α = 1 - c = 0.12

α/2 = 0.06

The z score of α/2 is the same as the z score of 0.44 (0.5 - 0.06) which is equal to 1.56

The margin of error (E) is given as:

E=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} } =1.56*\frac{12}{\sqrt{45} } =2.8

The confidence interval = μ ± E = 23 ± 2.8 = (22.2, 25.8)

8 0
3 years ago
Round two decimal places<br><br>729015430.40641995​
erastovalidia [21]

Answer:

729015430.40641995​ = 729015430.41

Step-by-step explanation:

Since the 3 decimal place is 6, you round up. If you round up for 0 you get 1. Therefore your answer is 729015430.41.

5 0
3 years ago
Alex has two designs to build a chest. In each design, the chest is a rectangular prism.
ExtremeBDS [4]

We need volumes

#Chest A

V=LBH

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8 0
2 years ago
Read 2 more answers
Circumference and area of a circular piece of glass
Vadim26 [7]

Answer:

Area = πr²

Circumference = 2πr

You can use pie as both 22/7 Or 3.14

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

8 0
3 years ago
Find the sum. 1-2+3-4+5-6+7-8...99-100
zysi [14]

Answer:

-50

Step-by-step explanation:

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8...99 - 100

just means,

1 - 2 = -1

3 - 4 = -1

5 - 6 = - 1

7 - 8 = - 1

99 - 100 = -1

basically, -1 + -1 + -1 + -1 + ....+ -1 or -1 - 1 - 1 - 1 - ... - 1

(-1)^{n}

Treating Grandi's series as a divergent geometric series we may use the same algebraic methods that evaluate convergent geometric series to obtain a third value:

S = 1 − 1 − 1 + ..., so

1 − S = 1 − (1 − 1 − 1 ...) = 1 − 1 − 1 ... = S

1 - S = S

1 = 2*S

resulting in S = 1/2. The same conclusion results from calculating −S, subtracting the result from S, and solving 2S = 1

1/2 of the last term is 100 x 1/2 = 50

This because you are using 2 numbers per -1

example: 1 - 2 = -1 or 3 - 4 = -1 resulting in 50 of the -1 being subtracted

8 0
2 years ago
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