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3 years ago

Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

Mathematics

1 answer:

Elan Coil [88]3 years ago

4 0

Answer:

(40/3)*pi

Step-by-step explanation:

lets first find the area of the little circle

A=pi*r^2

A=pi*3^2

A=9pi

Now, lets find the area of the big circle

A=pi*r^2

A=pi*(3+4)^2

A=pi*7^2

A=49pi

now lets subtract the area of the little circle from the area of the big circle

49pi-9pi=40pi, now we found the area of the "bagel)

lets find what portion of the bagel is the shaded region

120/360=1/3

now lets multiply the bagel area by the fraction

40pi*(1/3)=

(40/3)*pi or (40*pi)/3

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Which statement is always false?

FinnZ [79.3K]

Answer:

All parallelograms are squares

Step-by-step explanation:

Reasoning:

You can have a parallelogram with side lengths, i dont know, 5 and 3, right? That isn't a square :)

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3 years ago

Can you help me find the slope for #2

Flauer [41]

-3
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3 years ago

Read 2 more answers

At what point does the curve have maximum curvature? Y = 4ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as

MAXImum [283]

<u>Answer-</u>

At $x= \frac{1}{2304e^4-16e^2}$ the curve has maximum curvature.

<u>Solution-</u>

The formula for curvature =

$K(x)=\frac{{y}''}{(1+({y}')^2)^{\frac{3}{2}}}$

Here,

$y=4e^{x}$

Then,

${y}' = 4e^{x} \ and \ {y}''=4e^{x}$

Putting the values,

$K(x)=\frac{{4e^{x}}}{(1+(4e^{x})^2)^{\frac{3}{2}}} = \frac{{4e^{x}}}{(1+16e^{2x})^{\frac{3}{2}}}$

Now, in order to get the max curvature value, we have to calculate the first derivative of this function and then to get where its value is max, we have to equate it to 0.

${k}'(x) = \frac{(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})}{(1+16e^{2x} )^{2}}$

Now, equating this to 0

$(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x}) =0$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}-(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}=(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{1}{2}}=48e^{2x}$

$\Rightarrow (1+16e^{2x})}=48^2e^{2x}=2304e^{2x}$

$\Rightarrow 2304e^{2x}-16e^{2x}-1=0$

Solving this eq,

we get $x= \frac{1}{2304e^4-16e^2}$

∴ At $x= \frac{1}{2304e^4-16e^2}$ the curvature is maximum.

6 0

3 years ago

What is the name of the expression under the radical symbol in a radical function?

vfiekz [6]

An expression is defined as a set of numbers, variables, and mathematical operations. The name of the expression under the radical symbol in a radical function is called a radicand.

<h3>What is an Expression?</h3>

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The radical is the symbol that is used to represent the root in the expression n√x. The name of the expression under the radical symbol in a radical function is called a radicand.

Learn more about Expression:

brainly.com/question/13947055

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5 0

2 years ago

Iq scores are normally distributed with a mean of 100 and a standard deviation of 15 what is the probability that a randomly sel

a_sh-v [17]

So we are given the mean and the s.d.. The mean is 100 and the sd is 15 and we are trying the select a random person who has an I.Q. of over 126. So our first step is to use our z-score equation:

z = x - mean/s.d.

where x is our I.Q. we are looking for

So we plug in our numbers and we get:

126-100/15 = 1.73333

Next we look at our z-score table for our P-value and I got 0.9582

Since we are looking for a person who has an I.Q. higher than 126, we do 1 - P. So we get

1 - 0.9582 = 0.0418

Since they are asking for the probability, we multiply our P-value by 100, and we get

0.0418 * 100 = 4.18%

And our answer is

4.18% that a randomly selected person has an I.Q. above 126
Hopes this helps!

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3 years ago