Answer:
The diameter will increase at a rate of 1/30π cm/min
Step-by-step explanation:
Here we want to calculate the rate at which the diameter will increase
Mathematically, the area of a sphere is given as;
A = 4πr^2
But r = d/2
so A = 4 * π * d/2 * d/2 = πd^2
dA/d(d) = 2πd
Thus dd/dA = 1/2πd = 1/2 * π * 15 = 1/30π
Given dA/dt = 10
Mathematically;
d(d)/dt = d(d)/dA * dA/dt
dd/dt = 1/30π * 10 = 10/30π = 1/3π cm/min
Answer:the product of the length and the width of the rectangle could be expressed as
(x^2 - 3y)(x^2 + 3y)
Step-by-step explanation:
If the area of a rectangle is expressed as x^4 - 9y^2, we would determine the dimensions by simplifying the given expression. The simplified expression becomes
(x^2 - 3y)(x^2 + 3y)
Let us check by multiplying each term in one parenthesis by each term in the other parenthesis to get the given expression. It becomes
(x^2 - 3y)(x^2 + 3y) = x^4 + 3x^2y - 3x^2y - 9y^2 = x^4 - 9y^2
Implicit defferentation
remember that dy/dx y= dy/dx
so
take derivitive of both sides

solve for

minus 2x both sides

divide both sides by 2y


when is the slope equal to

solve for





find where the circle and this line intersects
substitute

for y




times both sides by


sqrt both sides, take positive and negative roots
x=+/-10
sub back




the points are (10,-24) and (-10,24)
Answer: m∠W = 56
because UVWX is a rhombus
=> UV // WX
=> 2y + 2y - 68 = 180
<=> 4y = 248
<=> y = 62
=> m∠W = 2.62 - 68 = 56
Step-by-step explanation: