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Norma-Jean [14]
3 years ago
15

Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (13, 84) lies

on its terminal side.
Mathematics
1 answer:
erma4kov [3.2K]3 years ago
3 0

Answer:

If P = (x,y) then formulas for each trigonometric functions are:

sin x = y/r

cos x = x/r

tan x = y/x

cot x = x/y

sec x = r/x

cosec x = r/y

where r = √(x²+y²).

First find r:

r = √(13²+84²)=√(169+7056)=√7225=85.

Then just substitute:

sin x = 84/85

cos x = 13/85

tan x = 84/13

cot x = 13/84

sec x = 85/13

cosec x = 85/84

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After triangle ACE is dilated by a factor of 6, it has an area of 180 square inches. What was its area before dilation?
Agata [3.3K]

Answer:

The area of triangle ACE before dilation is:  30 square inches

Step-by-step explanation:

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

  • If the scale factor > 1, the image is enlarged
  • If the scale factor is between 0 and 1, it gets shrunk
  • If the scale factor = 1, the object and the image are congruent

The length of the image can be determined by multiplying the length of the original point by a certain scale factor.

Given that after triangle ACE is dilated by a factor of 6, it has an area of 180 square inches.

Thus, it means the dilated area is 6 times the area before dilation.

Let x be the pre-dilation area

As the dilated area is 6 times the area before dilation, so

6x = 180

divide both sides by 6

6x/6 = 180/6

x = 30 square inches.

Therefore, the area of triangle ACE before dilation is:  30 square inches

4 0
3 years ago
A company hauls its 1 cubic foot boxes in the truck as shown.
Alenkinab [10]

Answer:

96

Step-by-step explanation:

3*4*8=96

4 0
3 years ago
Read 2 more answers
Find the values of k so that each remainder is three. <br> 10. (x^2+ 5x + 7) = (x + k)
Goryan [66]

Answer:

k=1\text{ or } k=4

Step-by-step explanation:

We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).

We are dividing:

(x^2+5x+7)\div(x+k)

So, a polynomial by a binomial factor.

Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.

We want our remainder to be 3. So, P(a)=P(-k)=3.

Therefore:

(-k)^2+5(-k)+7=3

Simplify:

k^2-5k+7=3

Solve for <em>k</em>. Subtract 3 from both sides:

k^2-5k+4=0

Factor:

(k-1)(k-4)=0

Zero Product Property:

k-1=0\text{ or } k-4=0

Solve:

k=1\text{ or } k=4

So, either of the two expressions:

(x^2+5x+7)\div(x+1)\text{ or } (x^2+5x+7)\div(x+4)

Will yield 3 as the remainder.

5 0
3 years ago
If Erica has 7$ And her sister holly has some money too how much do they have in total
Dmitry [639]

Answer:

you cant figure that out.

Step-by-step explanation:

6 0
3 years ago
Show all the steps!<br><br>3+2x=13-3x
Goshia [24]

Answer:

x=2

Step-by-step explanation:

3+2x=13-3x

 +3x      +3x

3+5x=13

-3      -3

5x=10

/5    /5

x=2

Hope this helps! :D

7 0
3 years ago
Read 2 more answers
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