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Lyrx [107]
3 years ago
12

Let sin ? = 4/5, and cos ? = ?3/5, and find the indicated value

Mathematics
1 answer:
Charra [1.4K]3 years ago
4 0
Let the unknown angle be x.
That is
sin x = 4/5
cos x = 3/5

By drawing a right triangle in the first quadrant,
hypotenuse = 5
Adjacent side = 3
opposite side = 4

That is tan x  = 4/3
From the calculator,
x = arctan(4/3) = 53 deg (nearest integer)

Answer: 53 deg. (nearest integer)
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Thuy rolls a number cube 7 times. which expression represents the probability of rolling a 4 exactly 2 times?
Nady [450]
The result of rolling a number cube 7 times is a 7-digit number composed of digits 1,2,3,4,5 and 6 so that digits can repeat. The total number of possibilities is 6^7.

The number of possibilities where 4 appears exactly two times is 5^5*(7!-6!/2).
 5^5 is the number of 5-digits numbers composed of digits 1,2,3,5 and 6 so that digits can repeat.
7! is the number of permutations of digits 1,2,3,4,4,5 and 6.
6! is the number of permutations of digits 1,2,3,{4,4},5 and 6.
We don't want to subtract all numbers where digits 4 appear side by side. That's why we must divide 6! by 2.

Finally, the probability is P=5^5(7!-6!/2)/7^7
6 0
3 years ago
Read 2 more answers
Three forces of 300 N in the direction of N30E, 400N in the direction of N60E and
andreyandreev [35.5K]

Split up each force into horizontal and vertical components.

• 300 N at N30°E :

(300 N) (cos(30°) i + sin(30°) j)

• 400 N at N60°E :

(400 N) (cos(60°) i + sin(60°) j)

• 500 N at N80°E :

(500 N) (cos(80°) i + sin(80°) j)

The resultant force is the sum of these forces,

∑ F = (300 cos(30°) + 400 cos(60°) + 500 cos(80°)) i

… … …  + (300 sin(30°) + 400 sin(60°) + 500 sin(80°)) j N

∑ F ≈ (546.632 i + 988.814 j) N

so ∑ F has a magnitude of approximately 1129.85 N and points in the direction of approximately N61.0655°E.

4 0
2 years ago
Write a recursive rule for the sequence.<br><br> 3, 8, 13, 18, 23, ...
adoni [48]

Answer:

Step-by-step explanation:

c.d. d=8-3=5

a_{n}=a_{n-1}+5

3 0
3 years ago
When you subtract 76 by 8 and make it a pattern, then what rule can it be?
ludmilkaskok [199]

Answer:9.5

Step-by-step explanation:

5 0
2 years ago
A metal plate measuring 32cm by 12cm is cut into
Reil [10]

Answer:

24

Step-by-step explanation:

First find the area of the metal plate: 32*12=384

Find the are of each small square to see how much space it takes: 4*4=16

Divide the two to see how many can fit: 24

Tell me if you have any questions!

5 0
3 years ago
Read 2 more answers
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