What is the name of this circle?

17. A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find

Pavlova-9 [17]

Answer:

$r = 3.74cm$

Step-by-step explanation:

Given

Hemisphere

$Radius = 7cm$

Cone

$Height = 49m$

Required

Determine the radius of the cone

First, we calculate the volume (V1) of the hemisphere.

$V_1 = \frac{2}{3}\pi r^3$

Substitute 7 for r

$V_1 = \frac{2}{3}\pi * 7^3$

$V_1 = \frac{2}{3}\pi * 343$

$V_1 = \frac{686}{3}\pi$

Volume (V2) of a cone is:

$V_2 = \frac{1}{3}\pi r^2h$

Because the lead is cast into a cone, then they have the same volume.

So, we have:

$\frac{686}{3}\pi = \frac{1}{3}\pi r^2h$

$686 = r^2h$

Substitute 49 for h

$686 = r^2 * 49$

Divide both sides by 49

$r^2 = \frac{686}{49}$

$r^2 = 14$

$r = \sqrt{14$

$r = 3.74cm$

Hence, the radius of the cone is 3.74cm

5 0

3 years ago

The coordinate plane below represents a city.

alex41 [277]

Answer:

Part A) The system of inequalities is

$x\geq2$ and $y\geq2$

Part B) In the procedure

Part C) The schools that Natalie is allowed to attend are A,B and D

Step-by-step explanation:

Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions

we have

Points C(2,2), F(3,4)

The system of inequalities could be

$x\geq2$ -----> inequality A

The solution of the inequality A is the shaded area at the right of the solid line x=2

$y\geq2$ -----> inequality B

The solution of the inequality B is the shaded area above of the solid line y=2

see the attached figure N 1

Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

Verify point C

C(2,2)

Inequality A

$x\geq2$ -----> $2\geq2$ ----> is true

Inequality B

$y\geq2$ ------> $2\geq2$ ----> is true

therefore

Point C is a solution of the system of inequalities

Verify point D

F(3,4)

Inequality A

$x\geq2$ -----> $3\geq2$ ----> is true

Inequality B

$y\geq2$ ------> $4\geq2$ ----> is true

therefore

Point D is a solution of the system of inequalities

Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.

we have

$y < -2x+2$

The solution of the inequality is the shaded area below the dotted line $y=-2x+2$

The y-intercept of the dotted line is the point (0,2)

The x-intercept of the dotted line is the point (1,0)

To graph the inequality, plot the intercepts and shade the area below the dotted line

see the attached figure N 2

therefore

The schools that Natalie is allowed to attend are A,B and D

6 0

4 years ago

This is a timed quiz. Pls, help. 50 points. 6th-grade math.

bonufazy [111]

Answer:

They did not survey customers at restaurants across Monster World.

plz mark me as brainliest.

6 0

4 years ago

Read 2 more answers

Describe fully the single transformation that takes shape p to shape q

sergiy2304 [10]

Answer:

it flip it to the left side and it becomes a p

it flip it to the right side and it becomes a q

Step-by-step explanation:

3 0

3 years ago

Please do elimination method 2x-9y=-36 -14x+18y=-18

Varvara68 [4.7K]

Answer:

The solution to the system of equations will be:

$x=9,\:y=6$

Step-by-step explanation:

Given the system of equations

$\begin{bmatrix}2x-9y=-36\\ -14x+18y=-18\end{bmatrix}$

Multiply 2x-9y=-36 by 7

$14x-63y=-252$

so the system of equations becomes

$\begin{bmatrix}14x-63y=-252\\ -14x+18y=-18\end{bmatrix}$

Adding both equations

$-14x+18y=-18$

$+$

$\underline{14x-63y=-252}$

$-45y=-270$

solve -45y = -270 for y

$-45y=-270$

divide both sides by -45

$\frac{-45y}{-45}=\frac{-270}{-45}$

Simplify

$y=6$

For 14x-63y = -270 plug in y = 6

$14x-63\cdot \:6=-252$

$14x-378=-252$

Add 378 to both sides

$14x-378+378=-252+378$

Simplify

$14x=126$

Divide both sides by 14

$\frac{14x}{14}=\frac{126}{14}$

Simplify

$x=9$

Therefore, the solution to the system of equations will be:

$x=9,\:y=6$

7 0

3 years ago