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3 years ago

Find the equation of the line tangent to the function at the given point f(x)=5x^2 at x=10

Mathematics

1 answer:

Svet_ta [14]3 years ago

8 0

f(x) = 5x²

f(10) = 5(10)² = 5(100) = 500

f'(x) = 10x

f'(10) = 10(10) = 100

Now, find the line that passes through (10, 500) and has a slope of 100

y - y₁ = m(x - x₁)

y - 500 = 100(x - 10)

y - 500 = 100x - 1000

y = 100x - 500

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the area of a circle is 28pi cm^2. find the area of a circle with a radius half the length of the original circle.

Verdich [7]

Answer:

The area of circle with radius half of original circle is 7 π cm² .

Step-by-step explanation:

Given as :

The Area of original circle = 28 π square centimeter

Let The radius of original circle = R

Let The area of circle with radius half of original circle = A square centimeters

Let The radius of circle with radius half of original circle = R'

Now, According to question

∵ Area of original circle = π × radius²

So, 28 π cm² = π × R²

Or, R² = $\frac{28\times \Pi }{\Pi }$

Or, R² = 28 cm²

∴ R = $\sqrt{28}$ cm

i.e R = 2 $\sqrt{7}$ cm

So, The radius of original circle = R = 2 $\sqrt{7}$ cm

<u>Again</u>

∵ The radius of circle with radius half of original circle = R'

So, R' = $\dfrac{R}{2}$

i.e R' = $\frac{2\sqrt{7}}{2}$

∴ R' = $\sqrt{7}$ cm

So, The area of circle with radius half of original circle = π × R'²

i.e A = π × R'²

Or, A = π ×( $\sqrt{7}$ ) ²

or, A = π × 7

So, The area of circle with radius half of original circle = 7 π cm²

Hence The area of circle with radius half of original circle is 7 π cm² . Answer

5 0

3 years ago

I need help .........

dezoksy [38]

What’s the question

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2 years ago

Read 2 more answers

Hi I need help with the question in the image. Step by step, thank you!

VashaNatasha [74]

The exponential function is $f(x) = 18(12)^{-x-4} + 2$

<h3>How to determine the equation?</h3>

An exponential function is represented as:

y = b^x

Where b represents the base.

The base is given as:

b = 12

So, we have:

y = (12)^x

It is vertically compressed by a factor of 1/8.

So, we have:

y = 18(12)^x

When reflected across the y-axis, we have:

$y = 18(12)^{-x}$

The horizontal asymptote is y = 2.

So, we have:

$y = 18(12)^{-x} + 2$

It passes through the point (-3, 4).

So, we shift the function to the right by 4 units

$y = 18(12)^{-x-4} + 2$

Express as a function

$f(x) = 18(12)^{-x-4} + 2$

Hence, the exponential function is $f(x) = 18(12)^{-x-4} + 2$

Read more about exponential functions at:

brainly.com/question/14355665

#SPJ1

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2 years ago

How do you find the area of a triangle ?

katovenus [111]

Answer:

to find the Area of a Triangle, you have to multiply the base times the height of the triangle to find the Area.

Step-by-step explanation:

For example..

If the Base ( bottom part of the triangle) was 10 and the height ( the vertical line of the triangle) was 5, you would multiply them together to get 50. So 5o would be the area of the Triangle.

<h2><em>Hope this helps and have a Great day!</em></h2>

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3 years ago

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(Will give Brainliest) These are composite figures. find the area of the figure and round your answer to one decimal place if ne

stiv31 [10]

Answer:

400

Step-by-step explanation:

this is most likely wrong cuz im dum

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3 years ago