Answer:
125.8983
Step-by-step explanation:
Use the formula for volume of a cone: v= (1/3)(3.14)(radius squared)(height) so v = (1/3)(3.14)(20.25)(6) = 125.8983
Answer:
Step-by-step explanation:
Given that a small business assumes that the demand function for one of its new products can be modeled by
Substitute the given values for p and x to get two equations in c and k
Dividing on by other we get
Substitute value of k in any one equation
b) Revenue of the product is demand and price
i.e. R(x) = p*x =
Use Calculus derivative test to find max Revenue
R'(x) =
EquateI derivative to 0
1-0.000589x =0
x = 1698.037
When x = 1698 and p = 16.56469
Vertex aka max or min point is found by -b/2a in form
f(x)=ax^2+bx+c
f(x)=-1x^2+8x+20
vertex x value is -8/(2)(-1)=-8/-2=4
input back to find y value
f(4)=-(4^2)+8*4+20
f(4)=-16+32+20
f(4)=36
max (since the graph opens down) is (4,36)
axis of symmetry is the x coordinate
max is (4,36)
axis of symmetrry is x=4
Answer:
Step-by-step explanation:
1. Given the integral function , using trigonometric substitution, the substitution that will be most helpful in this case is substituting x as i.e .
All integrals in the form are always evaluated using the substitute given where 'a' is any constant.
From the given integral, where a = 7 in this case.
The substitute will therefore be
2.) Given
cross multiplying
3.) Rewriting the given integral using the substiution will result into;