Answer:
a. 20,579.52 cubic inches
b.10,289.76 cubic inches.
c. 13.49 inches
Step-by-step explanation:
Hi, to answer this question we have to calculate the volume of a sphere:
Volume of a sphere: 4/3 π r³
Since diameter (d) = 2 radius (r)
Replacing with the value given:
34 =2r
34/2=r
r= 17 in
Back with the volume formula:
V = 4/3 π r³
V =4/3 π (17)³
V = 20,579.52 cubic inches
The volume of the half-inflated balloon is equal to the volume of the sphere divided by 2.
20,579.52/2 = 10,289.76 cubic inches.
To find the radius of the half-inflated balloon we have to apply again the volume formula and substitute v=10,289.76
10,289.76= 4/3 π r³
Solving for r
10,289.76/ (4/3 π)= r³
2,456.5 = r³
∛2,456.5 = r
r = 13.49 inches
Answer:
The horizontal line is the x-axis and the vertical line is the y-axis.
Step-by-step explanation:
The horizontal line is the x-axis and the vertical line is the y-axis. It's a fact. You can graph the lines by inserting the equations using the graphing calculator, which is the tab next to the one you have right now ;)
The given line segment's midpoint is (3,-6)
Step-by-step explanation:
Step 1 :
Let A be the point (4,-2) and B be the point (2,-10)
We need to obtain the midpoint of AB
Let M (x,y) be the Midpoint.
Step 2 :
The x co-ordinate of a line segment's midpoint obtained by adding the x co-ordinate of its end point and dividing by 2.
The y co-ordinate of a line segment's midpoint obtained by adding the y co-ordinate of its end point and dividing by 2.
So we have x = (4 + 2) ÷ 2 = 3
y = (-2 - 10) ÷ 2 = -6
Hence M = (3,-6)
Step 3 :
Answer :
The given line segment's midpoint is (3,-6)
Answer:
The scale factor for the dilation of rectangle ABCD to rectangle MNOP is 
⇒ B
Step-by-step explanation:
In similar rectangles, their corresponding dimensions are proportional, which means 
= 
, where L is the length and W is the width
∵ Rectangle ABCD is similar to rectangle MNOP
∴ Their dimensions are proportional
∵ The dimensions of rectangle ABCD are 6 m, 14 m
∴ L
= 14 and W = 6
∵ The dimensions of rectangle MNOP are 4.5 m, 10.5 m
∴ L
= 10.5 and W = 4.5
∵ The rectangle MNOP is the image of rectangle ABCD after dilation
→ To find the scale factor of dilation find the ratio between the
corresponding dimensions in the two rectangles (image/pre-image)
∵ 
= 
=
∵ 
= 
=
∴ The scale factor for the dilation is
The scale factor for the dilation of rectangle ABCD to rectangle MNOP is
I could be wrong, but the second option looks correct.
