What is the unit rate if the candy is $7.80 for 2 pounds?

Answer:

x=3.536, y=7.356

Step-by-step explanation:

The point of intersection can be found out be equating the equations x^2+(y-4)^2=25 and y=x+4. Solving it we will get x=3.536, y=7.356

Answer: 1223 and the remainder is 9

Step-by-step explanation:

Answer:

[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]

Step-by-step explanation:

From the information given:

Lets first change the given relations into polar coordinates

So, the region of the inner circle into polar coordinates is as follows:

(x - 4)² + y² = 16

x² + y² - 8x = 0

r² - 8r cos θ = 0

r = 8 cos θ

For the outside circle:

x² + y² = 16

r² = 16

Thus, the intersection point are:

64cos²θ = 16

cos²θ = 1/4

θ = -(π/3) , (π/3)

Now: if we are to represent the sketch on a graph, the region of the integration D will be:

[tex]D = \bigg \{ (r,\theta )\bigg |-\dfrac{\pi}{3}\leq \theta \leq \dfrac{\pi}{3}, 4 \leq r \leq 8 cos \theta \bigg \}[/tex]

Therefore, the are of the required region can now be computed as follows:

[tex]A = \int \int _D \ dA[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \int ^{8 \ cos \theta}_{4} \ r dr d \theta[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \bigg (\dfrac{r^2}{2} \bigg ) ^{8 \ cos \theta}_{4} \ d \theta[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{1}{2} \bigg (64 \ cos ^2 \theta - 16 \bigg ) \ d \theta[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{16}{2} \bigg (4 \ cos ^2 \theta - 1 \bigg ) \ d \theta[/tex]

[tex]A = \dfrac{16}{2} * 2 \int ^{\pi/3}_{0} \bigg (4 \bigg ( \dfrac{ 1+ cos 2 \theta}{2} \bigg) - 1 \bigg ) \ d \theta[/tex]

[tex]A = 16 \int^{\pi/3}_{0} (1 + 2 cos 2 \theta ) d \theta[/tex]

[tex]A =16 ( \theta + sin2 \theta )^{\pi/3}_{0}[/tex]

[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) - (0-0) \end {bmatrix}[/tex]

[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) \end {bmatrix}[/tex]

[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]

The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.

The double integral formula for the area of a given curve is described below:

[tex]A = \iint\,r(\theta) \,dr\,d\theta[/tex] (1)

Where:

We notice that [tex]r \in [4, 8\cdot \cos \theta][/tex] and [tex]\theta \in \left[-\frac{\pi}{3}, \frac{\pi}{3} \right][/tex], then we have the following integral:

[tex]A = \int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \int \limits_{r= 4}^{r = 8\cdot \cos \theta}\,r\,dr\,d\theta[/tex]

Now we proceed to integrate the expression:

[tex]A = \frac{1}{2}\int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \,(64\cdot \cos^{2}\theta -16)\,d\theta = 32 \int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \,\cos^{2}\theta \, d\theta - 8\,\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]

[tex]A = 16\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } {\cos 2\theta} \, d\theta + 8\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]

[tex]A = 8\sqrt{3}+\frac{16\pi}{3}[/tex]

The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.

We kindly invite to check this question on double integrals: https://brainly.com/question/2289273

Answer:

(-1,3)

Step-by-step explanation:

for the x coordinate all you do is -5 + 4 because you are moving right, and moving right is positive, so if you are moving to the positive direction you add

for the y coordinate you have to do 5 - 2 because you are going left, and left is negitave, so you subtract

Answer:

12

Step-by-step explanation:

a=3b

b=2c

c=4d

a*c/b*d = (3(2(4d)))*(4d)/(2(4d))*d

            = 96d^2/8d^2

            = 12

Answer:

Isjsjsjjekeekkddkdkdkdjdjdjdjdjdj

Step-by-step explanation:

Susjjssjjswiwiwiwi2

Answer:

-682

Step-by-step explanation:

I worked it out and got -682

Answer:

Step-by-step explanation:

Step 1             f(x) = [tex]\frac{3x+4}{8}[/tex]                 Given

Step 2            y = [tex]\frac{3x+4}{8}[/tex]                    Change f(x) to y

Step 3            x = [tex]\frac{3y+4}{8}[/tex]                    Switch x and y

Step 4            8x = 3y + 4              multiply each side by 8

Step 5            8x - 4 = 3y               Subtract 4 from each side

Step 6            [tex]\frac{8x-4}{3}=y[/tex]                   Divide by 3 on each side

Step 7            [tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]           Replace y by [tex]f^{-1}(x)[/tex]

Therefore, inverse of the function will be,

[tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]

Sofia made a mistake in step 6. She should have divided both the sides by 3 instead of multiplying each side by 3.

Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.

The given function is [tex]f(x)=\dfrac{3x+4}{8}[/tex].

It is required to calculate the inverse of the function.

So, the steps involved in finding the inverse of the function will be,

Step 1:

Write the given function as,

[tex]f(x)=\dfrac{3x+4}{8}[/tex]

Step 2:

Change the function f(x) to y as,

[tex]y=\dfrac{3x+4}{8}[/tex]

Step 3:

Switch x and y as,

[tex]x=\dfrac{3y+4}{8}[/tex]

Step 4:

Multiply each side of the equation by 8 as,

[tex]8x=8\dfrac{3y+4}{8}\\8x=3y+4[/tex]

Step 5:

Now, subtract 4 from each side of the equation as,

[tex]8x-4=3y+4-4\\8x-4=3y[/tex]

Step 6:

Now, it is required to divide each side by 3.

[tex]\dfrac{8x-4}{3}=\dfrac{3y}{3}\\\dfrac{8x-4}{3}=y[/tex]

Step 7:

Now, replace y with [tex]f^{-1}(x)[/tex] as,

[tex]\dfrac{8x-4}{3}=f^{-1}(x)[/tex]

So, the required inverse function should be [tex]f^{-1}(x)=\dfrac{8x-4}{3}[/tex].

Therefore, Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.

For more details, refer to the link:

https://brainly.com/question/19606498

Answer:

solve for V= pier^/3

solve for R=Square root3Vpie over pie

Step-by-step explanation:

V=multiply 1/3(pier^2)

R= Take root of both sides and solve

Answer:

dividing by a fraction (1/3) is equivalent to multiplying by its inverse (3)

3+%2A+v+%2F+%28pi+%2A+r%5E2%29 = h

Step-by-step explanation:

Answer: the graph that passes through 0,1

Step-by-step explanation:

y=1/5x+1

You made a typo here. There are TWO equal signs. Post the correct question.

Answer:

{(-2, 5), (1, -1), (2, -2), (5, 2)}

Answer:

2/3

Step-by-step explanation:

360 - 240 = 120

120 x 3 = 360

if 120 is 1/3 of 360, then 240 is 2/3 of 360

(disregard the zeros you don't need them)

Answer:

The relationship between the base angles does not change. The measures of the base angles of the isosceles triangle remain equal even if the vertices of the isosceles triangle change.

Step-by-step explanation:

Here is the answer from Plato. Hope this helps :)

Answer:

The relationship between the base angles does not change. The measures of the base angles of the isosceles triangle remain equal even if the vertices of the isosceles triangle change.

Step-by-step explanation:

Exact Edmentum sample answer

Answer:

y = - x + 5

Step-by-step explanation:

A(1, 4)

B(4, 1)

[tex]m_{AB}[/tex] = [tex]\frac{1-4}{4-1}[/tex] = - 1

y - 1 = - 1 ( x - 4 )

y = - x + 5

I think its 2.5yrs

yeah thank you pls give me correct answer if I am wrong

Answer:

P = 25m - 15

Step-by-step explanation:

Kindly find attached the table of values for your reference.

Step one:

given data

let us set up the coordinate using the value of p and m

p=35

p1=10

m=2

m1=1Tthe cordinate is (p1,p),(m1,m)= (y1,y),(x1,x)

(1,10), (2, 35)

the slop is given as, slope m = (p- p1)/(m - m1)

m=(35-10)/(2-1)

m = 25

from the equation of line y=mx+c

y = 25x + c

10 = 25(1) + bc

c= -15

y = 25x - 15

in term of m and p we have  P = 25m - 15

Answer:

The bus traveled at 40 mph for 5 hours, and at 25 mph for the last hour.

Step-by-step explanation:

The time for the first part is t.  Therefore the time for the second part if (6-t).

40t + 25 (6-t) = 225

40t + 150- 25t = 225

15t = 75

t=5

Answer:

469 2/3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

From the table, we know at least 2 ordered pairs. We can use the slope formula on any 2 ordered pairs on the table to get 3.

Using number line, the difference in the amount of Pizza they ate is 0.75

To compare the amounts of pizza eaten by Sandy and James in 1 minute, we need to first calculate how many slices they eat in 1 minute.

Sandy can eat 6.5 slices in 2 minutes, which means she can eat 6.5/2 = 3.25 slices in 1 minute.

James can eat 3 slices in 1.5 minutes, which means he can eat 3/(1.5/2) = 4 slices in 1 minute.

Therefore, James can eat more pizza in 1 minute than Sandy.

To show the difference on a number line, we can mark 3.25 and 4 on the line, and subtract 3.25 from 4 to get the difference:

         0         1         2         3         4

         |---------|---------|---------|---------|

Sandy:                   3.25

James:                   4

Difference:             0.75

So the difference between the amounts of pizza eaten by James and Sandy in 1 minute is 0.75 slices.

Learn more on number line here;

https://brainly.com/question/12399107

#SPJ1

Answer:

I think it would be 22

Step-by-step explanation:

Answer: J = 33

Step-by-step explanation:

the corner of the triangle is 90 degrees so

90 + 57 = 147

Now the rest is 33 degrees.

Since it'll equal to 180 degrees.

Answer:

It's 33 degree

explanation:

Two triangles are similar so

angle K is equal angleQ=90DEGREE

ANGLE J=AngleP=33

Answer:

AB = 12

Step-by-step explanation: