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2 years ago

Given cosΘ=2/3 and sinΘ>0, find sinΘ

Mathematics

1 answer:

adelina 88 [10]2 years ago

3 0

Answer:

sinΘ = √5/3

Step-by-step explanation:

Mathematically, we know that the cos of an angle is the ratio of the adjacent to the hypotenuse

The sine of an angle is the ratio of the opposite to the hypotenuse

So in this case, from the cosine given; adjacent is 2 and hypotenuse is 3

From the Pythagoras’ theorem, we can get the opposite

Mathematically, the square of the hypotenuse equals the sum of the squares of the two other sides

Let us have the opposite as x

3^2 = 2^2 + x^2

9 = 4 + x^2

x^2 = 9-4

x^2 = 5

x = √5

This root can be positive or negative

But since the sine is positive, we shall be considering only the positive root

Thus;

sine theta = √5/3

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almond37 [142]

Answer:

the answer is a

Step-by-step explanation:

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2 years ago

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Step-by-step explanation:

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2 years ago

A home’s value increases at an average rate of 5.5% each year. The current value is $120,000. What function can be used to find

Wewaii [24]

Answer:

$y=120,000(1.055)^x$

Step-by-step explanation:

we know that

The equation of a exponential growth function is given by

$y=a(1+r)^x$

where

y is the value of the home

x is the number of years

a is the initial value

r is the rate of change

we have

$a=\$120,000\\r=5.5\%=5.5/100=0.055$

substitute

$y=120,000(1+0.055)^x$

$y=120,000(1.055)^x$

7 0

2 years ago

A movie theater is 10 blocks north and 5 blocks east of a post office. A mall is 7 blocks north and 9 blocks east of the post of

MAXImum [283]

The complete question required that we determine how far is the movie theater to the mall.

<h3>Distance between the movie theatre and the mall </h3>

According to the question;

Upon representation of the movie theatre and mall position on the coordinate plane relative to the post office; we have;

Movie theater, T = (5, 10)
Mall, M = (9, 7).

The distance between the two points can therefore be evaluated by Pythagoras theorem as follows;

Distance, D² = (9-5)² + (7-10)²

D² = 4² + (-3)²

D² = 16 + 9

D² = 25

D = √25 = 5 blocks.

Ultimately, the movie theater is 5 blocks away from the mall.

Read more on distance between two points;

brainly.com/question/23848540

5 0

1 year ago

In Image:

iris [78.8K]

Answer:

The answer to your question is x ≠ -10 x ≠ 2 x ≠ -2

Solution $\frac{(x- 8)(x + 2)}{(x + 8)(x - 2)}$

Step-by-step explanation:

Process

1.- Factor all the polynomials

$\frac{x^{2} -3x - 40}{x^{2} + 8x - 20} / \frac{x^{2}+ 13x + 40}{x^{2}+ 12x + 20}$ = $\frac{(x-8)(x + 5)}{(x + 10)(x- 2)} / \frac{(x+ 8)(x + 5)}{(x + 10)(x + 2)}$

2.- Invert the second term

= $\frac{(x- 8)(x + 5)}{(x +10)(x - 2)} \frac{(x+ 10)(x + 2)}{(x + 8)(x +5)}$

3.- Simplify

= $\frac{(x- 8)(x + 2)}{(x + 8)(x - 2)}$

4.- x must be different to

x ≠ -10 x ≠ 2 x ≠ -2

This values are from the factor expressions and then equal to zero.

8 0

2 years ago