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3 years ago

Can u show the step and thanks

Mathematics

1 answer:

Rudiy273 years ago

4 0

Answer:

B) 378 students could be expected to attend the game.

Step-by-step explanation:

Out of 40 students, 45% agreed,

45% of 40

= 45/100 * 40

= 18 students,

18 students out of 40 agreed.

So, Out of 840 students 18/40 * 840 students would be expected to agree. We get :- 378

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Solve cos x - square 1-3 cos^2 x = 0 given that 0° < x < 360°

Furkat [3]

Rearrange the equation as

cos(x) - √(1 - 3 cos²x) = 0

cos(x) = √(1 - 3 cos²x)

Note that both sides have to be positive, since the square root function is non-negative. If we end up with any solutions that make cos(x) < 0, we must throw them out.

Take the square of both sides.

(cos(x))² = (√(1 - 3 cos²(x))²

cos²(x) = 1 - 3 cos²(x)

4 cos²(x) = 1

cos²(x) = 1/4

cos(x) = ± √(1/4)

cos(x) = ± 1/2

We throw out the negative case and we're left with

cos(x) = 1/2

This has general solution

x = arccos(1/2) + 360° n or x = -arccos(1/2) + 360° n

(where n is any integer)

x = 60° + 360° n or x = -60° + 360° n

Now just pick out the solutions that fall in the interval 0° ≤ x < 360°.

• From the first solution set, we have x = 60° when n = 0.

• From the second set, we have x = 300° when n = 1.

So the answer is D.

4 0

3 years ago

Do you hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg the longer leg is 7 feet longer than the

Lera25 [3.4K]

Answer:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

Step-by-step explanation:

We are given $h=1+2s$ where $h$ is the hypotenuse and $s$ is the length of the shorter leg.

We got this equation from reading that the "hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg". I replaced the "hypotenuse of a triangle" with $h$ , "is" with $=$ , "1 foot more than" with $1+$ and finally "twice the length of the shorter leg" with $2s$ .

We also have "longer leg is 7 feet longer than the shorter leg".

I'm going to replace "longer leg" with $L$ .

I'm going to replace "is" with $=$ .

I'm going to replace "7 feet longer than the shorter leg" with $7+s$ .

So we have the equation $L=7+s$ .

So we have a right triangle since something there is a side being referred to as the hypotenuse. We can use Pythagorean Theorem to find a relation between all these sides.

So by Pythagorean Theorem, we have: $s^2+L^2=h^2$ .