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3 years ago

The area of a circle is 100pi m2. What is the circumference, in meters? Express your

Mathematics

1 answer:

lukranit [14]3 years ago

3 0

Answer: 20pi

Step-by-step explanation:

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3 years ago

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3 years ago

Read 2 more answers

Suppose that, for a particular social networking company, the annual revenue from rich media advertisements, in millions of doll

Juli2301 [7.4K]

Answer:

a. Revenue of the company at the beginning of 2010 is 75 million dollar (loss)

b. Rate at which the revenue changing in the year 2010 is 76 million dollar per year ( decreasing)

Step-by-step explanation:

For part a,

Given that x is the number of years at the beginning of 2007.

Therefore, $x=0$ for year 2007.

Hence at the year 2010 value of x will be $x=3$ .

Substitute the value of x=3 in R(x),

$R\left(x\right)=-x^{4}+8x^{3}-38x^{2}+44x$

$R\left(x\right)=-\left(81\right)+8\left(27\right)-38\left(9\right)+132$

$R\left(x\right)=-81+216-342+132$

$R\left(x\right)=-75$

Negative sign indicates that there is loss of revenue at the start of the year 2010

Therefore, there is loss of revenue at the beginning of 2010 which is 75 million dollar.

For part b,

To calculate rate, differentiate the given function with respect to x.

$\dfrac{d}{dx}R\left(x\right)=\dfrac{d}{dx}\left (-\left(x\right)^{4}+8\left(x\right)^{3}-38\left(x\right)^{2}+44\left(x\right)\right)$

Applying sum and difference rule of derivative,

$\dfrac{d}{dx}R\left(x\right)=-\dfrac{d}{dx}\left(x^4\right)+\dfrac{d}{dx}\left(8x^3\right)-\dfrac{d}{dx}\left(38x^2\right)+\dfrac{d}{dx}\left(44x\right)$

Applying constant multiple rule of derivative,

$\dfrac{d}{dx}R\left(x\right)=-\dfrac{d}{dx}\left(x^4\right)+8\dfrac{d}{dx}\left(x^3\right)-38\dfrac{d}{dx}\left(x^2\right)+44\dfrac{d}{dx}\left(x\right)$

Applying power rule of derivative,

$\dfrac{d}{dx}R\left(x\right)=-\left(4x^{4-1}\right)+8\left(3x^{3-1}\right)-38\left(2x^{2-1}\right)+44\left(1x^{1-1}\right)$

$\dfrac{d}{dx}R\left(x\right)=-4\left(x^{3}\right)+8\left(3x^{2}\right)-38\left(2x^{1}\right)+44$

$\dfrac{d}{dx}R\left(x\right)=-4x^3+24x^2-76x+44$

Substituting the value x=3,

$\dfrac{d}{dx}R\left(x\right)=-4\left(3\right)^3+24\left(3\right)^2-76\left(3\right)+44$

$\dfrac{d}{dx}R\left(x\right)=-4\left(27\right)+24\left(9\right)-76\left(3\right)+44$

$\dfrac{d}{dx}R\left(x\right)=-108+216-228+44$

$\dfrac{d}{dx}R\left(x\right)=-76$

Negative sign indicates that rate is decreasing.

Rate at which the revenue is changing in the year 2010 is 76 million dollar per year.

8 0

3 years ago

If the area of Bianca’s rectangular backyard patio is represented by the expression x2 – 18x + 81, and the length of the patio i

Verizon [17]

1) $width=x-9$

2) Rectangular shape is square shape patio !

Step-by-step explanation:

Here we have , the area of Bianca’s rectangular backyard patio is represented by the expression x2 – 18x + 81, and the length of the patio is represented by the expression x − 9: We need to find

1. what is the expression for the width of the patio? Explain and show all work.

We know that area of rectangle = $Length(width)$

⇒ $x^2-18x+81=(x-9)(width)$

Factorizing RHS:

⇒ $x^2-9x-9x+81=(x-9)(width)$

⇒ $x(x-9)-9(x-9)=(x-9)(width)$

⇒ $(x-9)(x-9)=(x-9)(width)$

⇒ $width=x-9$

2. what special rectangular shape is the patio?

Now , we see that

$Length = x-9\\Width=x-9$

A rectangle whose length & width are equal is known as a square ! Hence , Rectangular shape is square shape patio !

8 0

3 years ago

Two sides of a triangle have the measures 7 and 10. Is it true or false that the range of possible measures for the third side i

adelina 88 [10]

Answer:

True

Step-by-step explanation:

We know that The triangle inequality states that the sum of the two sides of the triangle is always greater than the third side.

Here given that two sides of the triangle are 7 and 10

Let the third side be x

Here a = 7 , b = 10 , c = x

According to the triangle inequality

a + b > c

7 + 10 > x

x < 17

Also c + b > a

x + 10 > 7

x > -3

Also a + c > b

7 + x > 10

x > 3

Combining all the above results we get

3 < x < 17

All the values of x in the above region forms a triangle

Given x values lies in the region so they form a triangle

4 0

3 years ago