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3 years ago

Find the next number in the sequence 1, 1/4, 1/9 , 1/16, 1/25

Mathematics

1 answer:

Umnica [9.8K]3 years ago

3 0

(Add5) 1/9..(add 7) 1/16... (add9) 1/25... (add 11) and get -> 1/36

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Which portion of the unit circle satisfies the trigonometric inequality cos^2theta + sin^2theta is greater than or equal to 1. A

liberstina [14]

Answer:

Only points on the circle satisfy the given inequality.

Step-by-step explanation:

Given: Unit circle

To find: portion of the unit circle which satisfies the trigonometric inequality $\sin ^2\theta +\cos ^2\theta \geq 1$

Solution:

In the given figure, OA = 1 unit (as radius of the unit circle equal to 1)

$\sin \theta$ = side opposite to $\theta$ /hypotenuse

$\cos \theta$ = side adjacent to $\theta$ /hypotenuse

$\sin \theta =\frac{AB}{AO}\\\sin \theta =\frac{AB}{1}\\AB=\sin \theta$

$\cos \theta=\frac{OB}{AO}\\\cos \theta =\frac{OB}{1}\\OB=\cos \theta$

So, coordinates of A = $\left ( \cos \theta ,\sin \theta \right )$

For any point (x,y) on the unit circle with centre at origin, equation of circle is given by $x^2+y^2=1$

Put $(x,y)=\left ( \cos \theta ,\sin \theta \right )$

$\cos ^2\theta +\sin ^2\theta =1$

So, $(x,y)=\left ( \cos \theta ,\sin \theta \right )$ satisfies the equation $x^2+y^2=1$

For points $(x,y)=\left ( \cos \theta ,\sin \theta \right )$ inside the circle, $\cos ^2\theta +\sin ^2\theta$

For points $(x,y)=\left ( \cos \theta ,\sin \theta \right )$ outside the circle, $\cos ^2\theta +\sin ^2\theta >1$

So, only points on the circle satisfy the given inequality.

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2 years ago

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Can someone help me

Naddika [18.5K]

Answer:

Step-by-step explanation:

Hey, this question concerns the inscribed angle theorem.

The formula for this is:

∠ABC = 2*∠ADC

∴ ∠ABC = 40°

For proof, look up 'inscribed angle theorem (or central angle theorem)' on YT.

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Which rectangular prism has a surface area of 56 square units? [Note: Art is not drawn to scale.]

Volgvan

Answer:

Step-by-step explanation:

i took the quiz have a nice day :)

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