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Verdich [7]
4 years ago
10

Find the area in the first quadrant under the curve y = 1 / (x^2+6x+10)

Mathematics
1 answer:
Nata [24]4 years ago
5 0
The area is given by

\displaystyle\int_0^\infty\frac{\mathrm dx}{x^2+6x+10}

Complete the square in the denominator:

x^2+6x+10=x^2+6x+9+1=(x+3)^2+1

then substitute x+3=\tan y, so that \mathrm dx=\sec^2y\,\mathrm dy. Then as x\to0^+, we have y\to\arctan3; as x\to\infty, we have y\to\dfrac\pi2. So the integral becomes

\displaystyle\int_{\arctan3}^{\pi/2}\frac{\sec^2y}{\tan^2y+1}\,\mathrm dy=\int_{\arctan3}^{\pi/2}\mathrm dy=\dfrac\pi2-\arctan3
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If f(x) = 3x -2 and g(x).= 4x + 1.<br> what is the sum of f(2) and g(-3)
ira [324]

Answer:

The sum of f(2) and g(-3) is -7.

Step-by-step explanation:

f(x) = 3x - 2

f(2) = 3(2)-2

f(2) = 6 -2 = 4

g(x) = 4x + 1

g(-3) = 4(-3) +1

g(-3) = -12 + 1 = -11

f(2) + g(-3) = 4 + (-11)

f(2) + g(-3) = -7

5 0
3 years ago
Which is the simplest radical form of √52?
Zielflug [23.3K]
Short answer: 2 * sqrt(13)
Remark
There are a number of ways to look at this. I'll pick the easiest.

Step one
Factor 52 until there are no more prime factors to be used.

52 = 2 * 26
52 = 2 * 2 * 13. That's as far as you can go.

Rule
For every 2 equal prime factors, 1 of them can be taken out side of the root sign. The other one disappears.

sqrt(52) = sqrt(2*2* 13) = 2*sqrt(13)

Answer 2sqrt(13) <<<< answer
4 0
3 years ago
A circular mirror has a diameter of 12 inches. And a circular frame that is 3 inches wide surrounds the mirror. What is the comb
Lapatulllka [165]

Answer:

254.5 in.^2

Step-by-step explanation:

diameter of mirror = 12 in.

radius of mirror = diameter/2 = 13 in. / 2 = 6 in.

frame width = 3 in.

radius if combined mirror and frame = 6 in. + 3 in. = 9 in.

A = (pi)(r^2)

A = 3.14159 * (9 in.)^2

A = 3.14159 * 81 in.^2

A = 254.5 in.^2

8 0
3 years ago
A standard brick is 3.625 inches wide, 2.25 inches high, and 7.625 inches long. How many bricks could be in a pallet of bricks t
Snezhnost [94]

Answer: Option D. 1,778

Solution:

Standard brick:

Width: w=3.625 in

Height: h=2.25 in

Length: l=7.625 in

Volumen of one standard brick: v

v=w*h*l

v=(3.625 in)*(2.25 in)*(7.625 in)

v=62.19140625 in^3

Pallet of bricks:

Side: s=4 feet

s=(4 feet)*(12 in / 1 feet)→s=48 in

Volume of a pallet of bricks: V=s^3

V=(48 in)^3

V=110,592 in^3

Number of bricks could be in  a pallet: n

n=V/v

n=(110,592 in^3) / (62.19140625 in^3)

n=1,778.252119

n=1,778

6 0
3 years ago
Read 2 more answers
What is the equation of the axis of symmetry for the parabola y= 1/4(x+2)^2-7
Nezavi [6.7K]
Your answer is -2 as the axis of symmetry is at -b/2a. So if you were to expand the equation, you would get y= x^2/4 +x -6 where b is 1 and 2a is ½ . Therefore -1 / ½ gives you -2
7 0
4 years ago
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