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Law Incorporation [45]
3 years ago
14

Line goes through (8,-1) and has a slope of -3/4.

Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
3 0

Answer:

y= -3/4 x+5

Step-by-step explanation:

Set up y= -3/4 x+b. Plug in the coordinate and you get b=5. So, you get your answer. Hope it helps :)

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8400/2 then simplify

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3 years ago
Integrate cosx/sqrt(1+cosx)dx
Step2247 [10]
<span>Take the integral: integral (cos(x))/sqrt(cos(x)+1) dx
For the integrand (cos(x))/sqrt(1+cos(x)), substitute u = 1+cos(x) and du = -sin(x) dx: = integral (u-1)/(sqrt(2-u) u) du
For the integrand (-1+u)/(sqrt(2-u) u), substitute s = sqrt(2-u) and ds = -1/(2 sqrt(2-u)) du: = integral -(2 (1-s^2))/(2-s^2) ds
Factor out constants: = -2 integral (1-s^2)/(2-s^2) ds
For the integrand (1-s^2)/(2-s^2), cancel common terms in the numerator and denominator: = -2 integral (s^2-1)/(s^2-2) ds
For the integrand (-1+s^2)/(-2+s^2), do long division: = -2 integral (1/(s^2-2)+1) ds
Integrate the sum term by term: = -2 integral 1/(s^2-2) ds-2 integral 1 ds
Factor -2 from the denominator: = -2 integral -1/(2 (1-s^2/2)) ds-2 integral 1 ds
Factor out constants: = integral 1/(1-s^2/2) ds-2 integral 1 ds
For the integrand 1/(1-s^2/2), substitute p = s/sqrt(2) and dp = 1/sqrt(2) ds: = sqrt(2) integral 1/(1-p^2) dp-2 integral 1 ds
The integral of 1/(1-p^2) is tanh^(-1)(p): = sqrt(2) tanh^(-1)(p)-2 integral 1 ds
The integral of 1 is s: = sqrt(2) tanh^(-1)(p)-2 s+constant
Substitute back for p = s/sqrt(2): = sqrt(2) tanh^(-1)(s/sqrt(2))-2 s+constant
Substitute back for s = sqrt(2-u): = sqrt(2) tanh^(-1)(sqrt(1-u/2))-2 sqrt(2-u)+constant
Substitute back for u = 1+cos(x): = sqrt(2) tanh^(-1)(sqrt(sin^2(x/2)))-2 sqrt(1-cos(x))+constant
Factor the answer a different way: = sqrt(1-cos(x)) (csc(x/2) tanh^(-1)(sin(x/2))-2)+constant
Which is equivalent for restricted x values to:
Answer: | | = (2 cos(x/2) (2 sin(x/2)+log(cos(x/4)-sin(x/4))-log(sin(x/4)+cos(x/4))))/sqrt(cos(x)+1)+constant</span>
3 0
3 years ago
Help me with question 1 please
GrogVix [38]

Answer:

DB = 6

Step-by-step explanation:

See the attached figure to the question.

Since O is the center of the given circle, so AB and CD are diameters of the circle.

Hence, AO = CO = OD = OB = radius of the circle = 6

In Δ OAC, we have AO = OC. Hence, ∠ A = ∠C = 60° {Given that ∠OAC = 60°}

So, ∠ AOC will automatically become 60°. {As the sum of all the angles of a triangle is 180°}

So, Δ AOC is equilateral triangle.

Now, ∠ AOC = ∠ BOD = 60°  {Since, they are vertically opposite angles}

Now, in Δ BOD, we have DO = OB. Hence, ∠ D = ∠ B = 60° {As the sum of all the angles of a triangle is 180°}

So, Δ BOD is also an equilateral triangle.

So, DB = BO = DO = 6. (Answer)

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What is the measure of the angle shown with the question mark?
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