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vredina [299]
2 years ago
10

What is the surface area of a sphere with a radius of 15 cm?

Mathematics
1 answer:
malfutka [58]2 years ago
5 0

Answer:

2827.43 cm^2

Step-by-step explanation:

Hope this helped! <3 Have a great day :) Brainliest please?

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This is finding exact values of sin theta/2 and tan theta/2. I’m really confused and now don’t have a clue on how to do this, pl
Lostsunrise [7]

First,

tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)

and given that 90° < <em>θ </em>< 180°, meaning <em>θ</em> lies in the second quadrant, we know that cos(<em>θ</em>) < 0. (We also then know the sign of sin(<em>θ</em>), but that won't be important.)

Dividing each part of the inequality by 2 tells us that 45° < <em>θ</em>/2 < 90°, so the half-angle falls in the first quadrant, which means both cos(<em>θ</em>/2) > 0 and sin(<em>θ</em>/2) > 0.

Now recall the half-angle identities,

cos²(<em>θ</em>/2) = (1 + cos(<em>θ</em>)) / 2

sin²(<em>θ</em>/2) = (1 - cos(<em>θ</em>)) / 2

and taking the positive square roots, we have

cos(<em>θ</em>/2) = √[(1 + cos(<em>θ</em>)) / 2]

sin(<em>θ</em>/2) = √[(1 - cos(<em>θ</em>)) / 2]

Then

tan(<em>θ</em>/2) = sin(<em>θ</em>/2) / cos(<em>θ</em>/2) = √[(1 - cos(<em>θ</em>)) / (1 + cos(<em>θ</em>))]

Notice how we don't need sin(<em>θ</em>) ?

Now, recall the Pythagorean identity:

cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1

Dividing both sides by cos²(<em>θ</em>) gives

1 + tan²(<em>θ</em>) = 1/cos²(<em>θ</em>)

We know cos(<em>θ</em>) is negative, so solve for cos²(<em>θ</em>) and take the negative square root.

cos²(<em>θ</em>) = 1/(1 + tan²(<em>θ</em>))

cos(<em>θ</em>) = - 1/√[1 + tan²(<em>θ</em>)]

Plug in tan(<em>θ</em>) = - 12/5 and solve for cos(<em>θ</em>) :

cos(<em>θ</em>) = - 1/√[1 + (-12/5)²] = - 5/13

Finally, solve for sin(<em>θ</em>/2) and tan(<em>θ</em>/2) :

sin(<em>θ</em>/2) = √[(1 - (- 5/13)) / 2] = 3/√(13)

tan(<em>θ</em>/2) = √[(1 - (- 5/13)) / (1 + (- 5/13))] = 3/2

3 0
3 years ago
Given: x+2y=-6. Solve for y. y=x-6/2
Snowcat [4.5K]
x+2y=-6\\\\2y=-6-x\quad|:2\\\\y=\dfrac{-6-x}{2}\\\\\\\boxed{y=-3-\frac{x}{2}}
5 0
3 years ago
Match each set of points with the slope of the line formed by the ordered pairs.
Maksim231197 [3]

Answer:

(0,7) and (2,4) go to slope =-3/2

(1,-3) and (-1,-3) go to zero slope

(0,0) and (2,1) go to slope =1/2

(0,-1) and (2,-5) go to slope =-2

and (-1,3) and (-1,-3) go to no slope

Step-by-step explanation:

i did the edge 2020 thing

3 0
3 years ago
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Find f-1(x) if f(x)=2x+1
Mila [183]

Answer:

{f}^{ - 1} (x) = (2x + 1) ^{ - 1}  \\  \\ {f}^{ - 1} (x) =  \frac{1}{2x + 1}

I hope I helped you^_^

3 0
3 years ago
I need correct answer for this ​
dybincka [34]

Answer:

should be 82%

Step-by-step explanation:

Hope this helps!

6 0
2 years ago
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