Answer:
C - 1 / sin^2x
Step-by-step explanation:
as csc x = 1 / sin x
so, csc^2 x = 1 / sin^ 2x
The solution to the equation is x < 1.25
a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have
Evaluate the integral to solve for y :
Use the other known value, f(2) = 18, to solve for k :
Then the curve C has equation
b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:
The slope of the given tangent line 
is 1. Solve for a :
so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).
Decide which of these points is correct:
So, the point of contact between the tangent line and C is (-1, -3).
Answer: Jana and Tim will only spend the same amount on purchase orders to their manufacturers when they each order products with a total purchase value of $100.
Step-by-step explanation:
Jana and Tim would only be incurring same amount when both total purchase is to a value of $100. This is so because by purchasing a goods worth same amount, they both end up incurring $15 dollar additional cost. Jana would spend $15 on shipping her goods, while Tim would pay $4 Handling fees and $11 dollar shipping fee which would also amount to $15. What this means is total spent for both Jana and Tim would amount to $115 each.
Answer:
750 grams of 60% alloy
Step-by-step explanation:
Define x = amount of 60% alloy and y = amount of 20% alloy
Equating the amounts of gold:
0.6x+0.2y = 1000(0.5)
Since there must be 1000 grams total:
x+y = 1000
Writing the 2 resulting equations together:
0.6x + 0.2y = 500
x + y = 1000
Multiply the first equation by 5:
3x + y = 2500
x + y = 1000
Subtracting the 2nd equation from the 1st:
2x = 1500
x = 750
Answer: 750 grams of 60% alloy
