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nevsk [136]
3 years ago
14

Evaluate the integral: ∫dx/(sqrt((x^2)+16))

Mathematics
1 answer:
Lorico [155]3 years ago
7 0
Let x=4tanβ, then dx = 4sec²βdβ.  Now

    ∫(4sec²β)/(4secβ)dβ
=  ∫secβdβ
=  ln |tanβ - secβ| + c
=  ln |(x/4) - (√(x²+16)/4| + C
=  ln |x/√(x²+16)
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At CFIS Intermediate school, 40% of the 500 students ride their bikes or walk to school. How many students ride their bikes or w
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3 years ago
1. Solve the given equation on the domain [0,2pi]
Mekhanik [1.2K]

Answer:

1.x = pi/3 or 4pi/3

2. x = -pi/6 +2pi*n  or 5pi/6 + 2pi *n  where n is an integer

Step-by-step explanation:

1. sqrt(3) tan x = 3

Divide each side by sqrt(3)

sqrt(3)/sqrt(3) tan x = 3/sqrt(3)

tan x = sqrt(3) * sqrt(3)/sqrt(3)

tan x = sqrt(3)

Take the inverse of each side

arctan (tanx) = arctan (sqrt(3))

x = arctan (sqrt(3))

x =pi/3  or - 2pi/3

Since the domain is between 0 and 2pi, add 2pi to - 2pi/3  since the trig functions  are circular

x = pi/3  or -2pi/3 + 6pi/3

x = pi/3 or 4pi/3


2.  3 tan x = -sqrt(3)

Divide each side by 3

3/3 tan x = -sqrt(3)/3

tan x = -sqrt(3)/3

Take the arctan of each side

arctan (tan x) = arctan ( -sqrt(3)/3)

x = arctan ( -sqrt(3)/3)

x =-pi/6 or 5pi/6

We want all values for x so add 2pi*n to each value where n is an integer

x = -pi/6 +2pi*n  or 5pi/6 + 2pi *n  where n is an integer

6 0
3 years ago
Scratchpad
My name is Ann [436]
X squared + 8 squared = 10 squared

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3 years ago
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Evgesh-ka [11]
First of all,
The total weight of the six dogs are:
71+34+15+23+18+56=217 pounds
Then, we know that the average weight of the seven dogs are 40 pounds, so the total weights of the seven dogs are:
40×7=280 pounds.
Lastly, we know that the six dogs weights are 217 pounds and the total weight of the seven dogs are 280 dogs, so the seventh weight of the dog is:
280-217=63 pounds. As a result, the seventh weight of the dogs at the vet is 63 pounds. Hope it help!
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