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3 years ago

Verify the pythagorean identity 1 + c o t ^2 θ = c s c ^2 θ

Mathematics

1 answer:

Grace [21]3 years ago

6 0

Answer: The identity is verified. See the explanation.

Step-by-step explanation:

You must keep on mind the following identities:

$csc\theta=\frac{cos\theta}{sin\theta}\\\\csc\theta=\frac{1}{sin\theta}\\\\sin^2\theta+cos^2\theta=1$

Therefore, by substitution, you can rewrite the identity as shown below:

$1+cot^2\theta=csc^2\theta\\\\1+\frac{cos^2\theta}{sin^2\theta}=csc^2\theta$

Simpliying, you obtain:

$\frac{sin^2\theta+cos^2\theta}{sin^2\theta}=csc^2\theta\\\\\frac{1}{sin^2\theta}=csc^2\theta\\\\csc^2\theta=csc^2\theta$

The identity is verified.

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What is the next number in the sequence? 3, 6, 12, , ... place an x by the pattern of the sequence. add 2 subtract 2 times 2?

ch4aika [34]

3,6,12...

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3 years ago

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IrinaVladis [17]

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Step-by-step explanation:

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3 years ago

2. The following formula relates three quantities: Force (F), mass (m), and acceleration (a).

castortr0y [4]

Let

F--------> represent the force

m--------> represent the mass

a-------> represent the acceleration

we know that

The formula that relates three quantities: Force (F), mass (m), and acceleration (a) is equal to

$F=ma$

Part a) Solve this equation for a

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Divide both sides by the mass

$a=\frac{F}{m}$

therefore

the answer part a) is equal to

$a=\frac{F}{m}$

Part b) Let the force be 25 units and the mass be m = 10 units. What is the acceleration, a?

we know that

the formula of acceleration is equal to

$a=\frac{F}{m}$

in this problem

we have

$F=25\\m=10$

Substitute the values n the formula

$a=\frac{25}{10}$

$a=2.5$

therefore

the answer part b( is equal to

$a=2.5$

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we know that

$F=ma$

Solve for m

Divide both sides by the acceleration

$m=\frac{F}{a}$

in this problem

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$F=25\\a=5$

Substitute the values n the formula

$m=\frac{25}{5}$

$m=5$

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3 years ago

Read 2 more answers

The price of one share of a stock fell 4 dollars each day for 8 days. How much value did one share of the stock lose after 8 day

ivolga24 [154]

Answer:

After 8 days, the stock lost 32 dollars.

Step-by-step explanation:

If 4 dollars fell every day for 8 days, it would be 32 dollars because 4*8 is 32.

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2 years ago

The equation $y=-4.9t^2+3.5t+5$ describes the height (in meters) of a ball thrown upward at $3.5$ meters per second from $5$ met

Georgia [21]

Answer:

Step-by-step explanation:

The position function is

$s(t)=-4.9t^2+3.5t+5$ and if we are looking for the time t it takes for the ball to hit the ground, we are looking for the height of the ball when it is on the ground. Of course the height of anything on the ground is 0, so if we set s(t) = 0 and solve for t, we will find our answer.

$0=-4.9t^2+3.5t+5$ and factor that however you are currently factoring in class to get that

t = -.71428 seconds or

t = 1.42857 seconds (neither one of those is rational so they can't be expressed as fractions).

We all know that time will never be a negative value, so the time it takes this ball to hit the ground is

1.42857 seconds (round how you need to).

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3 years ago