Answer:
![Height = 8.660\ in](https://tex.z-dn.net/?f=Height%20%3D%208.660%5C%20in)
![Width = 17.321\ in](https://tex.z-dn.net/?f=Width%20%3D%2017.321%5C%20in)
Step-by-step explanation:
Given
![Area= 150in^2](https://tex.z-dn.net/?f=Area%3D%20150in%5E2)
![Side\ Margin = 1\ in](https://tex.z-dn.net/?f=Side%5C%20Margin%20%3D%201%5C%20in)
![Top\ \&\ Bottom\ Margins = 2\ in](https://tex.z-dn.net/?f=Top%5C%20%5C%26%5C%20Bottom%5C%20Margins%20%3D%202%5C%20in)
Required
Determine the smallest dimension to use
To answer this question, I'll make use of the attached figure as a point of reference.
The area of the printed matter is:
![Area = Length * Width](https://tex.z-dn.net/?f=Area%20%3D%20Length%20%2A%20Width)
![A_1 = H * W](https://tex.z-dn.net/?f=A_1%20%3D%20H%20%2A%20W)
Substitute 150 for A1
![150 = H * W](https://tex.z-dn.net/?f=150%20%3D%20H%20%2A%20W)
Make H the subject
![H = \frac{150}{W}](https://tex.z-dn.net/?f=H%20%3D%20%5Cfrac%7B150%7D%7BW%7D)
The area of the full paper is:
![Area = Length * Width](https://tex.z-dn.net/?f=Area%20%3D%20Length%20%2A%20Width)
![A_2 = (W + 2+2) * (H + 1 + 1)](https://tex.z-dn.net/?f=A_2%20%3D%20%28W%20%2B%202%2B2%29%20%2A%20%28H%20%2B%201%20%2B%201%29)
![A_2 = (W + 4) * (H + 2)](https://tex.z-dn.net/?f=A_2%20%3D%20%28W%20%2B%204%29%20%2A%20%28H%20%2B%202%29)
Substitute 150/W for H
![A_2 = (W + 4) * (\frac{150}{W} + 2)](https://tex.z-dn.net/?f=A_2%20%3D%20%28W%20%2B%204%29%20%2A%20%28%5Cfrac%7B150%7D%7BW%7D%20%2B%202%29)
Open brackets
![A_2 = W(\frac{150}{W} + 2) + 4(\frac{150}{W} + 2)](https://tex.z-dn.net/?f=A_2%20%3D%20W%28%5Cfrac%7B150%7D%7BW%7D%20%2B%202%29%20%2B%204%28%5Cfrac%7B150%7D%7BW%7D%20%2B%202%29)
![A_2 = 150 + 2W + \frac{600}{W} + 8](https://tex.z-dn.net/?f=A_2%20%3D%20150%20%2B%202W%20%2B%20%5Cfrac%7B600%7D%7BW%7D%20%2B%208)
Collect Like Terms
![A_2 =2W + \frac{600}{W} + 8+150](https://tex.z-dn.net/?f=A_2%20%3D2W%20%2B%20%5Cfrac%7B600%7D%7BW%7D%20%2B%208%2B150)
![A_2 =2W + \frac{600}{W} + 158](https://tex.z-dn.net/?f=A_2%20%3D2W%20%2B%20%5Cfrac%7B600%7D%7BW%7D%20%2B%20158)
Differentiate with respect to w and set the result to 0
![A_2' = 2 - \frac{600}{W^2} + 0](https://tex.z-dn.net/?f=A_2%27%20%3D%202%20-%20%5Cfrac%7B600%7D%7BW%5E2%7D%20%2B%200)
![A_2' = 2 - \frac{600}{W^2}](https://tex.z-dn.net/?f=A_2%27%20%3D%202%20-%20%5Cfrac%7B600%7D%7BW%5E2%7D)
Set to 0
![0 = 2 - \frac{600}{W^2}](https://tex.z-dn.net/?f=0%20%3D%202%20-%20%5Cfrac%7B600%7D%7BW%5E2%7D)
Collect Like Terms
![2 = \frac{600}{W^2}](https://tex.z-dn.net/?f=2%20%3D%20%5Cfrac%7B600%7D%7BW%5E2%7D)
Cross Multiply
![2 * W^2 = 600](https://tex.z-dn.net/?f=2%20%2A%20W%5E2%20%3D%20600)
Make
the subject
![W^2 = \frac{600}{2}](https://tex.z-dn.net/?f=W%5E2%20%3D%20%5Cfrac%7B600%7D%7B2%7D)
![W^2 = 300](https://tex.z-dn.net/?f=W%5E2%20%3D%20300)
Take positive square root of both sides
![W = 17.321](https://tex.z-dn.net/?f=W%20%3D%2017.321)
Recall that:
![H = \frac{150}{W}](https://tex.z-dn.net/?f=H%20%3D%20%5Cfrac%7B150%7D%7BW%7D)
![H = \frac{150}{17.321}](https://tex.z-dn.net/?f=H%20%3D%20%5Cfrac%7B150%7D%7B17.321%7D)
![H = 8.660](https://tex.z-dn.net/?f=H%20%3D%208.660)
Hence, the smallest dimension of the paper is:
![Height = 8.660\ in](https://tex.z-dn.net/?f=Height%20%3D%208.660%5C%20in)
![Width = 17.321\ in](https://tex.z-dn.net/?f=Width%20%3D%2017.321%5C%20in)
Answer:
H = 2 S = 50 A = 50.2
Step-by-step explanation:
A=2πrh+2πr2
S = 2tr2 + 2trh
S = 2 (t x r) + (h x 2t) x r Try out ^2 for Radius
S = 2t x r^2 + r x h x 2t Rearrange back and cross out for square^2
S = 6t x 4 + 6t x r x h Cross out for t
S = 6 x 4 + 6 x 2 x h Balance out...
S= 24 + 12 x 2 Find h = 2
S = 36 + 24
S= 50 sq2
A = 50. 2
R = 2
H = 2
Checker
Area = 6.28318530718 x 4 + 6.28318530718 x 2 x 2 = 50.27sq2
Answer:
60
Step-by-step explanation:
im so smart. its on khan academy.
Answer:
624
Step-by-step explanation:
The sequence is 49, 47, 45,...., 7, 5, 3. This is an arithmetic sequence, because the difference between terms is the same.
The sum of the first n terms of an arithmetic sequence is:
S = n/2 (a₁ + an)
where a₁ is the first term and an is the nth term.
Here, we know that a₁ = 49 and an = 3. But we need to find what n is. To do that, we use definition of an arithmetic sequence:
an = a₁ + (n-1) d
where d is the common difference (in this case, -2)
3 = 49 + (n-1) (-2)
2(n-1) = 46
n - 1 = 23
n = 24
So there are 24 terms in the sequence.
The sum is:
S = 24/2 (49 + 3)
S = 12 (52)
S = 624
There are 624 bricks in the wall.
Yes Suzanne made an error in solving the equation
<h3><u>Solution:</u></h3>
Given that Suzanne did this work to solve an equation did she make an error
Given equation: x - 5 = 3x - 2 - 7 - 5x
Equation by Suzanne: x - 5 = 2x - 9
Yes Suzanne has made error in solving the equation
As per original equation,
x - 5 = 3x - 2 - 7 - 5x
On the right hand side, when we combine like terms of "x" we get,
x - 5 = -2x -2 - 7
x - 5 = -2x - 9
But the Suzzane has got x - 5 = 2x - 9 which is wrong. Since she missed negative sign before 2
<em><u>Rules for adding positive and negative numbers:</u></em>
To add integers having the same sign, keep the same sign and add the absolute value of each number. To add integers with different signs, keep the sign of the number with the largest absolute value and subtract the smallest absolute value from the largest.
<em><u>Correct form of solving:</u></em>
x - 5 = -2x -2 - 7
x - 5 = -2x - 9