Answer:
ON = KJ
Step-by-step explanation:
JKL = NOP
We know the angles match
<J = <N
<K = <O
< L = <P
And we know
JK = NO
KL = OP
JL = NP
We are looking for ON = KJ
Answer:
33 1/3% of 360 is 120
Step-by-step explanation:
33 1/3 can be converted to 33.333% or simply just 1/3, divide 360 by 3 to get your answer which is 120.
Answer:
the Larger poster is 9ft long by 6ft wide
Step-by-step explanation:
In order to find the length and width values of the large poster we first need to find the width of the smaller poster since we are already given the length. Since we are also provided with the perimeter we can add the length twice and subtract it from the perimeter which would give us the value of both width sides of the rectangle, then we simply divide by 2 to get the value of the individual width.
10ft = 3ft + 3ft + w + w
10ft = 6ft + 2w
4ft = 2w
2ft = w
Since the larger poster is 3 times as big for the length and the width we simply multiply the smaller poster's length and width by 3...
L = 3 * 3 = 9ft
W = 2 * 3 = 6ft
Finally, we can see that the Larger poster is 9ft long by 6ft wide
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>
The answer to 2-(-8)+(-3)= 7
