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Supposing y = arcsin(x), find dy/dx

Suppose:
y = arcsin(x)
Then, x = sin(y)
And, dx/dy = cos(y) ----- (1)
Using: dy/dx = 1/(dx/dy);
Thus 1 becomes: dy/dx = 1/cos(y) ------ (2)
Using: sin^2(y) + cos^2(y) = 1;

Answered by James N. Maths tutor
5878 Views

There are 420 balls in a ball pool. There is a combination of violet, blue, yellow and green balls. 2/7 are violet, 35% are blue and the ratio of yellow to green is 4:5. How many of each colour ball is there in the ball pool?

Together, the total number of balls is 420. 2/7 of the total 420 balls are violet. Therefore the number of violet balls can be calculated by the equation 2/7 x 420/1 = 840/7=120. There are 120 vio...

Answered by Lauren W. Maths tutor
3108 Views

Find the coordinates of the turning points of the curve y = 4/3 x^3 + 3x^2-4x+1

First differentiating by the rule that xn differentiates to nxn-1 we have that dy/dx = 4x2+6x-4.
At the turning points of a curve the differential is equal to 0 so w...

Answered by Theo E. Maths tutor
8307 Views

Solve the linear simultaneous equations: 3x + 5y = 45, 2x - 9y = -7

x = 10, y = 3. From the second equation, we have x = (9y - 7)/2. Substituting this expression for x into the first equation gives 3(9y - 7)/2 + 5y = 45. 3(9y - 7) + 10y = 90. 27y - 21 + 10y = 90. 37y = 11...

Answered by Cameron W. Maths tutor
3246 Views

integrate xcosx

use integration by parts

Answered by Sebastian B. Maths tutor
3158 Views

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