Answer:
8 1/2 cups
Step-by-step explanation:
12 3/4 divided by 3= 4 1/4 times 2 = 8 2/4 = 8 1/2
Answer:
10) Correct
11) Each row is equal to 12 when you multiply them together.
12) 24
Step-by-step explanation:
12) You multiply 4*3*2 to get the volume of 24, which is also the number of cubes needed to make the shape.
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The measures of the angles ABCD are the same as the measures of the angles that is corresponding based on the reflected images.
<h3>How to show that the angles are equal</h3>
Based on the fact that this is a reflection, the angles would be equal measures.
What this means is that there is a preservation of the of the reflected image. This is the same logic for the length of the sides.
The reflection is known to be a rigid type of transformation that is known to have its angles and sides preserved.
Read more on reflection in mathematics here:
brainly.com/question/1908648
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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>
Answer:
0
Step-by-step explanation:
j(x) = -2 (3/2)^x
j(0) = -2(3/2)^0
-2(0)
=0
