Three hundred four million nine hundred sixty seven thousand
Start with #47. To find the critical values, you must differentiate this function. x times (4-x)^3 is a product, so use the product rule. The derivative comes out to f '(x) = x*3*(4-x)^2*(-1) + (4-x)^3*1 = (4-x)^2 [-3x + 4-x]
Factoring this, f '(x) = (4-x)^2 [-3x+4-x]
Set this derivative equal to zero (0) and solve for the "critical values," which are the roots of f '(x) = (4-x)^2 [-3x+4-x]. (4-x)^2=0 produces the "cv" x=4.
[-3x+ (4-x)] = 0 produces the "cv" x=1. Thus, the "cv" are {4,1}.
Evaluate the given function at x: {4,1}. For example, if x=1, f(1)=(1)(4-1)^3, or 2^3, or 8. Thus, one of the extreme values is (1,8).
Answer:
27
Step-by-step explanation:
The triangle shown is an isoceles triangle. This means that there are two congruent base angles and a vertex angle. In this case, angle X and angle Y are the base angles, so we can set up an equation to first find the value of t.
5t - 13 = 3t + 3
2t - 13 = 3 (Subtract 3t from both sides)
2t = 16 (Add 13 to both sides)
t = 8 (Divide both sides by 2)
Now that we have the value of t, we can plug it back in to the expression for angle X to find its measure.
5(8) - 13
40 - 13
27
So, the measure of angle X is 27
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