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4 years ago

8

Dana is attaching a shelf to a wall and needs the shelf to be perpendicular to the wall. How many degrees should the shelf be re

lative to the wall?

2 answers:

KiRa [710]4 years ago

8 0

90° because perpendicular lines are never ending.

wolverine [178]4 years ago

4 0

Answer:

90°

Step-by-step explanation:

The shelf will be perpendicular to the wall if it intersects the wall at a right angle which is equal to 90°

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Use the Distributive Property and use 45+60=15×45+15×60 to write 45+60 as a product of the GF and a sum of two numbers.

salantis [7]

Multiple: 15 * 3 = 45
Multiple: 15 * 12 = 180
Add: 45 + 180 = 225
Unary plus: +15 = 15
Multiple: 225 * 15 = 3375
= (3375)
Multiple: 5 * 7 = 35
Add: +(35) = 35
= (35)

5 0

3 years ago

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify y

Drupady [299]

Answer:

$V = \frac{\pi^2}{8}$

$V = 1.23245$

Step-by-step explanation:

Given

$y = \cos 2x$

$y = 0; x = 0; x = \frac{\pi}{4}$

Required

Determine the volume of the solid generated

Using the disk method approach, we have:

$V = \pi \int\limits^a_b {R(x)^2} \, dx$

Where

$y = R(x) = \cos 2x$

$a = \frac{\pi}{4}; b =0$

So:

$V = \pi \int\limits^a_b {R(x)^2} \, dx$

Where

$y = R(x) = \cos 2x$

$a = \frac{\pi}{4}; b =0$

So:

$V = \pi \int\limits^a_b {R(x)^2} \, dx$

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {(\cos 2x)^2} \, dx$

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {\cos^2 (2x)} \, dx$

Apply the following half angle trigonometry identity;

$\cos^2(x) = \frac{1}{2}[1 + \cos(2x)]$

So, we have:

$\cos^2(2x) = \frac{1}{2}[1 + \cos(2*2x)]$

$\cos^2(2x) = \frac{1}{2}[1 + \cos(4x)]$

Open bracket

$\cos^2(2x) = \frac{1}{2} + \frac{1}{2}\cos(4x)$

So, we have:

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {\cos^2 (2x)} \, dx$

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {[\frac{1}{2} + \frac{1}{2}\cos(4x)]} \, dx$

Integrate

$V = \pi [\frac{x}{2} + \frac{1}{8}\sin(4x)]\limits^{\frac{\pi}{4}}_0$

Expand

$V = \pi ([\frac{\frac{\pi}{4}}{2} + \frac{1}{8}\sin(4*\frac{\pi}{4})] - [\frac{0}{2} + \frac{1}{8}\sin(4*0)])$

$V = \pi ([\frac{\frac{\pi}{4}}{2} + \frac{1}{8}\sin(4*\frac{\pi}{4})] - [0 + 0])$

$V = \pi ([\frac{\frac{\pi}{4}}{2} + \frac{1}{8}\sin(4*\frac{\pi}{4})])$

$V = \pi ([{\frac{\pi}{8} + \frac{1}{8}\sin(\pi)])$

$\sin \pi = 0$

So:

$V = \pi ([{\frac{\pi}{8} + \frac{1}{8}*0])$

$V = \pi *[{\frac{\pi}{8}]$

$V = \frac{\pi^2}{8}$

or

$V = \frac{3.14^2}{8}$

$V = 1.23245$

4 0

3 years ago

Dev gets 10% of the votes joe gets twice as many votes as Holly what percentage of the votes does the winner get?

il63 [147K]

90 between two people and one having double than holly would give Joe (the winner) 60%

4 0

3 years ago

Help me for a cookie

nekit [7.7K]

Answer:

145 degrees

Step-by-step explanation:

1. A straight line is 180 degrees

2. 180-35=145

3 0

3 years ago

What’s 27337 + 3939393

Lynna [10]

Answer:

3966730

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers