PLEASE HELP ME JUST A LITTLE CONFUSED.

maksim [4K]

Y=1/3x + 2 as the y intercept is 2 and slope is 1/3

3 0

2 years ago

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

3 years ago

A group of preschoolers has 30 boys and 13 girls what is the ratio of boys to all children?

vekshin1

A group of preschoolers has 30 boys and 13 girls then the ratio of boys to all children would be 30:43.

What is a ratio?

A ratio in mathematics shows how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-total fruit ratio is 8:14.

A group of preschoolers has 30 boys and 13 girls.

Total children will be = 30 + 13 = 43

Ratio = number of boys/total children

= 30/43.

Hence, if A group of preschoolers has 30 boys and 13 girls then the ratio of boys to all children would be 30:43.

To learn more about the ratio, visit:

brainly.com/question/12024093

#SPJ1

7 0

1 year ago

Select the expression that makes the equation true (−3⋅10 3 )⋅(4⋅10 6 ) select 2 answers

scZoUnD [109]

The answer is letter c , because if you multiply the number 4 that is outside with the third power you will get 12 and with the second power you will get 8 and base number stays the same. As an answer you’ll get the same numbers as the expression

5 0

4 years ago

1) Find 5 points on the line y = 3/5 x - 4 by picking 5 x values, plugging in, and getting 5 y values. You must pick x

Taya2010 [7]

It’s 5 for sure it is

4 0

3 years ago