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Archy [21]
3 years ago
9

If sine of x equals square root of 2 over 2, what is cos(x) and tan(x)? Explain your steps in complete sentences.

Mathematics
1 answer:
kolbaska11 [484]3 years ago
7 0
Sin x =  square root (2) / 2

In order for us to get for cos x and tan x, first we need to know what 
Hypotenuse, Adjacent, and Opposite sides.

sin x = opposite / hypotenuse.

adjacent = square root (hypotenuse^2 - opposite^2)
adjacent = square root (2^2 - square root(2)^2)
adjacent = square root (4 - 2)
adjacent = square root (2)

cos x = adjacent / hypotenuse
tan x = opposite / adjacent..

cos x = square root (2) / 2
tan x = square root (2) / <span>square root (2)  = 1

So, </span>cos x = square root (2) / 2 and tan x<span> = 1</span>
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Thanks for the help!
NikAS [45]

Answer:

A

Step-by-step explanation:

So we have the piecewise function:

f(x)= \begin{cases}\sqrt{2x} & \text{if }x

And we want to find f(8).

Since our input value is 8, choose the equation that fits our input.

The first equation demand x to be less than 3. 8 is not less than 3, so we won't use that.

The second equation demand x to e greater than or equal to 3 and less than 8. 8 is <em>not</em> less than 8. So, we won't use that.

The third equation demands x to be greater than or equal to 8. 8 is greater than or equal to 8, so we'll use the third equation.

So:

f(x)=42\text{ if }x\geq 8

f(8)=42

There're nothing more to do, we're done :)

The answer is A.

Edit: Improved Format

3 0
3 years ago
The value of r? Do not round your answer.
bearhunter [10]

Answer:

r = 31.2

Step-by-step explanation:

Δ ACE and Δ BCD are similar, thus the ratios of corresponding sides are equal, that is

\frac{AE}{BD} = \frac{CE}{CD}, substitute values

\frac{r}{19.5} = \frac{64}{40} ( cross- multiply )

40r = 1248 ( divide both sides by 40 )

r = 31.2

8 0
3 years ago
Please help me with this problem<br><br>​
Maru [420]

Answer:

g(x) = -5x

Step-by-step explanation:

If the point from f(x) is plotted using the slope, the coordinate would be located at (1, 5) since the slope of 5x tells us we go up 5 units from the origin and over 1 unit to the right.  That point will be reflected through the x-axis to land at (1, -5).  That means that the equation of the new line would be

g(x) = -5x

7 0
3 years ago
Read 2 more answers
Graph the line with slope 1/2<br> that passes through the point (-1,2).
enyata [817]

9514 1404 393

Answer:

  see the attachment for a graph

Step-by-step explanation:

With the given point and slope, the equation of the line can be written in point-slope form:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x +1) . . . . line with slope 1/2 through point (-1, 2)

__

Slope is the ratio of rise to run, so a slope of 1/2 means the line will rise 1 unit for each 2 units of run (to the right). If you're plotting this by hand, you can identify a second point that is 2 right and 1 up from the given point:

  (-1 +2, 2 +1) = (1, 3).

You can draw your line through those two points.

8 0
3 years ago
The proportion of American births that result in a birth defect is approximately 1/33 according to the Centers for Disease Contr
faltersainse [42]

Answer:

c. binomial distribution with n = 5 and p = 1/33.

Step-by-step explanation:

For each birth, there are only two possible outcomes. Either it results in a defect, or it does not. The probability of a birth resulting in a defect is independent of other births. So we use the binomial probability distrbution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

The proportion of American births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC).

This means that the probability of a birth resulting in a defect is p = \frac{1}{33}

A local hospital randomly selects five births.

This means that n = 5

So the correct answer is:

c. binomial distribution with n = 5 and p = 1/33.

8 0
3 years ago
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