30*(100%+40%)
30*140%
140% as a decimal is (140/100) which is 1.4
30*1.4=42
42/120=0.32.
Ali should sell each can for $0.32
Hope this helps :)
Answer:
<u><em>Similarity:</em></u>
In Both cosine and sine graphs, a positive and negative number vertically flips the graph and tells whether the graph starts at maximum (positive) or minimum (negative).
<u><em>Difference:</em></u>
The difference between the sine and the cosine graph is the point where they start.
The graph of positive cosine starts at the maximum while that of the negative cosine starts at the minimum.
The graph of a positive sine starts at the middle, goes up and then down while that of the negative sine starts at the middle goes down and then up.
Note that x² + 2x + 3 = x² + x + 3 + x. So your integrand can be written as
<span>(x² + x + 3 + x)/(x² + x + 3) = 1 + x/(x² + x + 3). </span>
<span>Next, complete the square. </span>
<span>x² + x + 3 = x² + x + 1/4 + 11/4 = (x + 1/2)² + (√(11)/2)² </span>
<span>Also, for the x in the numerator </span>
<span>x = x + 1/2 - 1/2. </span>
<span>So </span>
<span>(x² + 2x + 3)/(x² + x + 3) = 1 + (x + 1/2)/[(x + 1/2)² + (√(11)/2)²] - 1/2/[(x + 1/2)² + (√(11)/2)²]. </span>
<span>Integrate term by term to get </span>
<span>∫ (x² + 2x + 3)/(x² + x + 3) dx = x + (1/2) ln(x² + x + 3) - (1/√(11)) arctan(2(x + 1/2)/√(11)) + C </span>
<span>b) Use the fact that ln(x) = 2 ln√(x). Then put u = √(x), du = 1/[2√(x)] dx. </span>
<span>∫ ln(x)/√(x) dx = 4 ∫ ln u du = 4 u ln(u) - u + C = 4√(x) ln√(x) - √(x) + C </span>
<span>= 2 √(x) ln(x) - √(x) + C. </span>
<span>c) There are different approaches to this. One is to multiply and divide by e^x, then use u = e^x. </span>
<span>∫ 1/(e^(-x) + e^x) dx = ∫ e^x/(1 + e^(2x)) dx = ∫ du/(1 + u²) = arctan(u) + C </span>
<span>= arctan(e^x) + C.</span>
1st angle = 2 * 2nd angle
3rd angle = 2nd angle + 80
1st angle = 2x
2nd angle = x
3rd angle = 80 + x
2x + x + 80 + x = 180
4x = 100
x = 25
1st angle = 50
2nd angle = 25
3rd angle = 105
If you are asking 7/8 - 1/x= 3/4,
first put 3/4 to 6/8 to make it easier.
Move the 7/8 over to the right. You will get 1/x=-1/8.
Simplify, it is x=-8.
Check=7/8 - 1/8=6/8
It checks out.
