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2 years ago

Find the value of x.

Mathematics

1 answer:

Westkost [7]2 years ago

8 0

Answer:

The answer is x= 8

Step-by-step explanation:

Since the side is tangent to the circle then the triangle is right-angled and applying the Pythagorean law, we get the value of x

${17}^{2} = {15}^{2} + {x}^{2} \\ {x }^{2} = 289 - 225 = 64 \\ x = 6$

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Futhe Mathematics <img src="https://tex.z-dn.net/?f=%28Cos%20%7B%7D%5E%7B4%7Dt%20-Sin%20%7B%7D%5E%7B4%7Dt%20%29%20%20%5Cdiv%2

Nastasia [14]

Answer:

cos2t/cos²t

Step-by-step explanation:

Here the given trigonometric expression to us is ,

$\longrightarrow \dfrac{cos^4t - sin^4t }{cos^2t }$

We can write the numerator as ,

$\longrightarrow \dfrac{ (cos^2t)^2-(sin^2t)^2}{cos^2t }$

Recall the identity ,

$\longrightarrow (a-b)(a+b)=a^2-b^2$

Using this we have ,

$\longrightarrow \dfrac{(cos^2t + sin^2t)(cos^2t-sin^2t)}{cos^2t}$

Again , as we know that ,

$\longrightarrow sin^2\phi + cos^2\phi = 1$

Therefore we can rewrite it as ,

$\longrightarrow \dfrac{1(cos^2t - sin^2t)}{cos^2t}$

Again using the first identity mentioned above ,

$\longrightarrow \underline{\underline{\dfrac{(cost + sint )(cost - sint)}{cos^2t}}}$

Or else we can also write it using ,

$\longrightarrow cos2\phi = cos^2\phi - sin^2\phi$

Therefore ,

$\longrightarrow \underline{\underline{\dfrac{cos2t}{cos^2t}}}$

And we are done !

$\rule{200}{4}$

Additional info :-

Derivation of cos²x - sin²x = cos2x :-

We can rewrite cos 2x as ,

$\longrightarrow cos(x + x )$

As we know that ,

$\longrightarrow cos(y + z )= cosy.cosz - siny.sinz$

So that ,

$\longrightarrow cos(x+x) = cos(x).cos(x) - sin(x)sin(x)$

On simplifying,

$\longrightarrow cos(x+x) = cos^2x - sin^2x$

Hence,

$\longrightarrow\underline{\underline{cos (2x) = cos^2x - sin^2x }}$

$\rule{200}{4}$

7 0

1 year ago

81 is 37.5% of what number?

laila [671]

Hi,

81 is 37.5% of 216.

"1. We assume, that the number 37.5 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 37.5, so we can write it down as 100%=37.5.

4. We know, that x% equals 81 of the output value, so we can write it down as x%=81.

5. Now we have two simple equations:

1) 100%=37.5

2) x%=81

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=37.5/81

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 81 is what percent of 37.5

100%/x%=37.5/81

(100/x)*x=(37.5/81)*x - we multiply both sides of the equation by x

100=0.46296296296296*x - we divide both sides of the equation by (0.46296296296296) to get x

100/0.46296296296296=x

216=x

x=216 "

Have a great day!

3 0

2 years ago

If a = -2, b = -6, c = -4, and d = -3, evaluate the following expressions.

abruzzese [7]

It’s Has to be B because if you had the negative numbers you get -12

6 0

2 years ago

There are between 90 and 115 cars in a parking lot. Exactly one-fourth of them are green. Exactly one-eighth of them have a stic

Schach [20]

There are 104 cars in the parking lot.

According to statement there are between 90 and 115 cars on the lot.

So, {X| 90 < x < 115} (This renders an infinite solution set finite)

AND exactly one eight of them have a sticker on the back, so the total number of cars must be evenly divisible by eight.

X ∈ {96, 104, 112,}

AND exactly one fourth of the cars are green, so the number of cars must be evenly divisible by 4. Here all above written numbers are divisible by 4. So, find the mean to calculate the number of cars in the parking lot.

x = (96+104+112)/3

x = 104

There are 104 cars in the parking lot.

Learn more about ELIMINATION METHOD here brainly.com/question/13729904

#SPJ4

5 0

1 year ago

Solve 3.4 [ 6 ( 4) +6^2] Please show your work! <3

VARVARA [1.3K]

Answer:

204

Step-by-step explanation:

3.4[6(4)+6^2]=

3.4[24+36]=

3.4[60]=

204

Hope this helps!

7 0

2 years ago