Someone please explain this

Mathematics

2 answers:

jeyben [28]3 years ago

7 0

Answer:

the first one is the second one

the second one is the third one

maks197457 [2]3 years ago

3 0

Question 1 is 5 and question 2 is -20

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I will give 5 points

ikadub [295]

Use the sum of cubes factoring rule

$a^3 + b^3 = (a+b)(a^2 - ab + b^2)$

to transform the left hand side into the right hand side.

$\frac { \sin^{3} \theta + \cos^{3} \theta } { \sin \theta + \cos \theta } = 1 - \sin \theta \cdot \cos \theta\\\\\frac { (\sin \theta + \cos \theta)(\sin^2 \theta - \sin \theta \cdot \cos\theta + \cos^2 \theta) } { \sin \theta + \cos \theta } = 1 - \sin \theta \cdot \cos \theta\\\\$

$\sin^2 \theta - \sin \theta \cdot \cos\theta + \cos^2 \theta = 1 - \sin \theta \cdot \cos \theta\\\\(\sin^2 \theta + \cos^2\theta)- \sin \theta \cdot \cos\theta = 1 - \sin \theta \cdot \cos \theta\\\\1- \sin \theta \cdot \cos\theta = 1 - \sin \theta \cdot \cos \theta \ \ \checkmark\\\\$

Throughout the entire process, the right hand side stayed the same.

On the last step, I used the pythagorean identity.

8 0

2 years ago

What is the length of the hypotenuse of a right triangle with sides that measure 7 cm and 24 cm?

Paul [167]

The length of the hypotenuse of a right triangle with sides that measure 7 cm and 24 cm is 25 cm

<u>Solution:</u>

Given a right angled triangle,

The sides measure 7 cm and 24 cm

We have to find the length of hypotenuse

For a right angled triangle, by Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

From above definition we get,

$c^2 = a^2 + b^2$