If a circle has a circumference of C, what is the area of the circle in terms of C?

Answers

Answer 1

Answer: First you have to write down the formula on how to get the circumference of the circle (C = 2pi * Radius) and the Area of the circle which is (A=Pi*Radius^2). In getting the radius you need to transform the formula of the circumference by making the radius to be the unknown variable so it would become(R=C/2pi), after that you need to replace the radius in the formula of the area by the transformed formula of the circumference and you will come up of the formula of (A=Pi(C/2pi)^2).

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I am confused on this , I’ve tried twice and got it wrong.

Answers

Answer:

$f^-^1(x)=-x^2+6x-5 \ \text{for the domain}\ [3, \infty)$

Step-by-step explanation:

Consider the function $f(x)=√(4-x)+3$ for the domain $(- \infty, 4]$ .

Find $f^-^1(x)$ , where f^(-1) is the inverse of f.

Also state the domain of f^(-1) in interval notation.

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We can start solving this problem by finding the inverse of f(x). This is done by switching the x- and y- variables, and solving for y.

$y=√(4-x)+3 \rightarrow x=√(4-y)+3$
$x=√(4-y)+3$

We can start solving for y by subtracting 3 from both sides of the equation.

$x-3=√(4-y)$

Get rid of the radical by squaring both sides of the equation.

$(x-3)^2=(√(4-y))^2$
$(x-3)(x-3)=4-y$

Use FOIL to multiply the binomial (x-3) together.

$x^2-3x-3x+9=4-y$

Combine like terms.

$x^2-6x+9=4-y$

Subtract 4 from both sides of the equation.

$x^2-6x+5=-y$

Divide both sides of the equation by -1.

$-x^2+6x-5=y$
$f^-^1(x)=-x^2+6x-5$

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The domain and range of a function are flipped for its inverse, meaning that to find the domain of the inverse function, you can find the range of the original function f(x), and that will be your inverse function's domain.

The range of $f(x)=√(4-x) +3$ is $y \geq 3$ , since the vertical shift of the graph is at k = 3. You can also graph this function on a calculator to see that the graph does indeed start at y = 3.

Now that we know the domain and range of the original function, we know that these are flipped for the inverse function.

Original function:

Domain: $x\leq 4$
Range: $y\geq 3$

Inverse function:

Domain: $x\geq 3$
Range: $y\leq 4$

The final answer is:

The inverse $f^-^1(x)=-x^2+6x-5 \ \text{for the domain}\ [3, \infty)$ .

You can also write the domain as: $x\geq 3$ .

If the volume of a cylinder is 75pi cubic inches and the height is 3 inches then what is the radius of the base of the cylinder?

Answers

The formula for the volume of a cylinder is:

V=π*r²*h

We already know that...

V=75π
&
h=3in
so we can solve for the radius

V=π*r²*h
75π=π*r²*3
Divide both sides by pi
75=r²*3
Divide both sides by 3
25=r²
find the square root of both sides
5in=r

The radius of the base of the cylinder is 5in

Answer= 5in.

Find the percent of the area under the normal curve between the mean and 0.83 divisions of the mean.

Answers

0.296730608171932
= 29.6731%

Can someone please help me with these two questions

Answers

the # 1 the answer is A
# 2 C

The answer is X=6,-6 u just have to foil it out (X-6)(x+6)=0 X-6=0 X+6=0 X=6,-6

The ratio of chaperones to students on a field trip is 2:7. There are 14 chaperones on the field trip. In all, how many chaperones and students are on the field trip

Answers

To find the total number of chaperones and students on the field trip, you can use the given ratio and the fact that there are 14 chaperones. The ratio of chaperones to students is 2:7.

Let C represent the number of chaperones and S represent the number of students. According to the ratio:

2:7 = 14:C

To solve for C, you can set up a proportion:

2/7 = 14/C

Now, cross-multiply:

2C = 7 * 14

2C = 98

Now, divide both sides by 2 to find the number of chaperones (C):

C = 98 / 2

C = 49

So, there are 49 chaperones and 7 times as many students:

Students (S) = 7 * Chaperones (C) = 7 * 49 = 343

In total, there are 49 chaperones and 343 students on the field trip.

There are chickens and pigs in a farm yard? There are 68 feet and 23 tails in the farm yard. How many chickens and how many pigs does grandma have?

Answers

You have animals with 4 legs, and animals with 2 legs. Both animals only have one tail. So, given that they only have one tail, there are only 23 animals in the farmyard.
Now, the equation would be,
$(68)/(x) =23$
$68=23x$
$(68)/(23) =x$

Answer:

12 chickens and 11 pigs

Step-by-step explanation:

We know that...

Chickens have 2 feet and 1 tail.

Pigs have 4 feet and 1 tail.

Let c represent chickens.

Let p represent pigs.

We need to create two equations. One for feet, and one for tails.

Tails:

Because each animal has 1 tail, we can say that the number of pigs, (p) plus the number of chickens, (c) must equal 23. So...

c + p = 23

Feet:

Because each chicken has two feet, and each pig has 4 feet, we can say that 2 times the number of chickens, (c) plus 4 times the number of pigs, (p) needs to equal 68. So...

2c + 4p = 68

Now we have two equations.

2c + 4p = 68

and

c + p = 23

We can use the substitution method to find c and p. The substitution method involves solving for one of the variables with one of the equations, then placing it into the other equation, so that you only have one variable to solve for, which you can do with simple algebra.

Solve for c

c + p = 23

c = 23 - p

Add that to the other equation.

2c + 4p = 68

2(23 - p) + 4p = 68

Solve for p

46 - 2p + 4p = 68

46 + 2p = 68

2p = 22

p = 11

Now that we know p, we can plug that into one of the equations to find c.