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2 years ago

Find the exact value of cos(arcsin(1/4)). For full credit, explain your reasoning.

1 answer:

5 0

First way
arcsin(1/4) means that 1/4 sin of the angle.

sin(α)=1/4
sin²α+cos²α=1
(1/4)²+cos²α=1
cos²α=1-1/16 =15/16
cosα=+/-(√15)/4

<span>Second way
</span>
sin(α)=1/4 =opposite leg/hipotenuse
cos(α)=adjacent leg/hypothenuse
adjacent leg =√(hypotenuse²- Opposite²)=√(16-1)=√15
cosα=+/-√15/4

For one value of sinα, possible 2 values of cosα.

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I don’t know this and need help with the answer

ki77a [65]

9+10=21 that is the answer

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3 years ago

Which equation is the inverse of y = 9x2 – 4? mc008-1.jpg mc008-2.jpg mc008-3.jpg mc008-4.jpg

murzikaleks [220]

Answer: y = +/- [√x+4) ] / 3

Explanation:

1) To find the inverse of the function y = 9x^2 - 4, exhange the variables x and y, and then solve for the new y.

2) Exchange of the variables: y = 9x^2 - 4 → x = 9y^2 - 4

3) Solve for y:

9y^2 = x + 4

y^2 = [x + 4] / 9

y = +/- [ √ (x + 4) ] / 3

8 0

3 years ago

Read 2 more answers

I need help with questions 1,2, and 3. Would gratefully appreciate it (:

motikmotik

Answer:

Step-by-step explanation:

(2):

First let's organise the data:

33 miles ... x mph ... 4h - downstream

33 miles ... y mph ... 7h - up the stream

x = 33/4 = 8.25 mph

y = 33/7 = 4.71 mph

(3)

P(x) = $x^2 - 2x - 3$

To find the amount of key rings sold when the profit is 5000$ we have to equate P(x) with 5, because in the problem the profit of the key rings is displayed in terms of thousands.

$x^2 - 2x - 3 = 5\\x^2 - 2x - 8 = 0\\x_1 = 4, x_2 = -2$

Since the number of keyrings sold has to be positive the only answer is 4 thousand key rings.

3 0

3 years ago

Could someone please help me asap!! Pleasseeeee and thanks.

kherson [118]

Answer:

Step-by-step explanation:

a² - b² = (a + b) (a - b)

1)x² - 36 = x² - 6² = (x + 6)(x-6)

2) 4x² - 16 = 4x² - 4*4 = 4(x² - 4)

= 4(x² -2²)

= 4(x + 4)(x-4)

3) 9x² -1 = 3²x² - 1² = (3x)² - 1²

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8 0

3 years ago

A chocolate factory produces mints that weigh 10 grams apiece. The standard deviation of the weight of a box of 10 mints is 3 gr

frozen [14]

The confidence that the box you bought did not come from the factory is 90 %.

<u>Step-by-step explanation:</u>

Since we have given that

Population Mean weight (\mu)= 10 grams a piece

Standard deviation of the weight of a box = 3 grams

Number of mints = 10

We need to buy a box of mints that weighs 95 grams.

Sample mean is given by

x = $\frac{95}{10}=9.5$ grams .

First we find out the standard error which is given by

$s=\frac{\sigma}{\sqrt{n}}\\\\=\frac{3}{\sqrt{10}}\\\\$ = 0.94868

Since it is normal distribution, so, we will find z-score.

$z=\frac{x-\mu}{s}\\\\z=\frac{9.5-10}{0.94868}\\\\z=-0.527\\\\$

z = - 0.53

The area to the left of a z-score of -0.53 = 0.29805.

So, it may be 90% or 95 % confidence.

For 95% confidence level,

$\alpha=\frac{1-0.95}{2}=0.025$

Similarly,

For 90% confidence level,

$\alpha=\frac{1-0.90}{2}=0.05$

The value is much smaller than 0.05.

So, we will get 90% confidence and the critical value = 1.645

Margin of error is given by

(Standard deviation) $\times$ (critical\ value) = 0.94868 $\times$ 1.645

=1.56

So, confidence interval will be

(10-1.56,10+1.56)

=(8.44,11.56)

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3 years ago