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abruzzese [7]
3 years ago
6

A wall of a building is made from blocks that are each 1 cubic foot. The wall is 6 feet high and 6 feet wide. A window is made b

y removing some blocks as shown below. The window is 2 feet high by 2 feet wide. Suppose the wall is expanded to be 12 feet high by 12 feet wide, and the window is expanded to be 4 feet high by 4 feet wide. How will this change the volume of the wall?
Mathematics
2 answers:
Soloha48 [4]3 years ago
5 0

Answer:

This will increase the volume of the wall by 104 cubic feet

mixas84 [53]3 years ago
3 0

This will increase the volume of the wall by 104 cubic feet

i copied that dude above me so i dont expect any stars or thanks i mainly did this so he can get brainlyest

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Renaming improper fractions as whole or mixed numbers 17-4
murzikaleks [220]
17/4 as a mixed fraction would be 4 1/4
4 0
3 years ago
Write a two-column proof. Given: line BD bisects angle CBE. Prove: angle ABD approximately equal to angle FBD.
ale4655 [162]

Answer:

The proof is derived from the summarily following equations;

∠FBE + ∠EBD = ∠CBA + ∠CBD

∠FBE + ∠EBD = ∠FBD

∠CBA + ∠CBD = ∠ABD

Therefore;

∠ABD ≅ ∠FBD

Step-by-step explanation:

The two column proof is given as follows;

Statement {}                                       Reason          

\underset{BD}{\rightarrow} bisects ∠CBE {}                            Given

Therefore;

∠EBD ≅ ∠CBD  {}                              Definition of angle bisector

∠FBE ≅ ∠CBA {}                                Vertically opposite angles are congruent

Therefore, we have;

∠FBE + ∠EBD = ∠CBA + ∠CBD {}     Transitive property

∠FBE + ∠EBD = ∠FBD {}                    Angle addition postulate

∠CBA + ∠CBD = ∠ABD {}                   Angle addition postulate

Therefore;

∠ABD ≅ ∠FBD        {}                          Transitive property.

3 0
2 years ago
4x^2 -18x^2=0<br><br> HELP PLEASE My teacher doesn’t explain it well
tigry1 [53]

Answer:

x=0

Step-by-step explanation:

4x²-18x²=0 (combine like terms)

-14x²=0

x²/-14=0/-14

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8 0
2 years ago
A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (&gt; r) from th
jeyben [28]

Consider a circle with radius r centered at some point (R+r,0) on the x-axis. This circle has equation

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\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx

where 2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}.

So the volume is

\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx

Substitute

x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt

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\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt

Notice that \sin t\cos^2t is an odd function, so the integral over \left[-\frac\pi2,\frac\pi2\right] is 0. This leaves us with

\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt

Write

\cos^2t=\dfrac{1+\cos(2t)}2

so the volume is

\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}

6 0
2 years ago
How do I turn this into a radical?
dimaraw [331]
6sqrt(2) i’m pretty sure
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2 years ago
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