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2 years ago

What are the values of sin α and tan α, if α is an acute angle in a right triangle: cosα= 5/13

Mathematics

1 answer:

alisha [4.7K]2 years ago

8 0

Answer:

sin = 12/13 and tan = 12/5

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If f(x) = (1/8)(8^x), what is f(3)?

faust18 [17]

Answer:

f(3)=64

Step-by-step explanation:

f(3)=(1/8)(8 cubed)

f(3)= 8 to the negative one times 8 cubed

f(3)= 8 squared

f(3)=64

5 0

2 years ago

Read 2 more answers

Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

$a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3$

$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

$a(a'(d)) = d + 3 - 3$

$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

7 0

2 years ago

dude, I just got almost all of my points taken away from somebody that has 0 answers, 0 questions, and almost 2 million points..

Finger [1]

Answer:

Step-by-step explanation:

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2 years ago

Find how many ways can we find three students out of ten students

Marysya12 [62]

Answer:

Step-by-step explanation:

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3 years ago

There are 30 computers in the media lab there are 4 activity booklets for every 2 computers in the media lab.

AURORKA [14]

Answer:

There are 60 activity booklets in the media lab.

Step-by-step explanation:

- 30/2 = 15

Why divide those numbers?

For every 2 computers in a lab with 30 computers means you have to divide

- 15x4 = 60

Why multiply those numbers?

4 activity booklets for every 2 computers in a lab of 30 computers, so multiply

I hope this helps.

7 0

3 years ago