Answer:
To satisfy the hypotheses of the Mean Value Theorem a function must be continuous in the closed interval and differentiable in the open interval.
Step-by-step explanation:
As f(x)=2x3−3x+1 is a polynomial, it is continuous and has continuous derivatives of all orders for all real x, so it certainly satisfies the hypotheses of the theorem.
To find the value of c, calculate the derivative of f(x) and state the equality of the Mean Value Theorem:
dfdx=4x−3
f(b)−f(a)b−a=f'(c)
f(x)x=0=1
f(x)x=2=3
Hence:
3−12=4c−3
and c=1.
Answer:
6.9%
Step-by-step explanation:
Interest rate is the one variable in an amortization formula that cannot be determined explicitly. An iterative solution is required, which means the computation must be done by a calculator, spreadsheet, or web site.
My TI-84 TVM Solver tells me that for the given loan amount and payment schedule, the APR is about 6.9%.
First, lets determine the regular price of his purchase :
16.99 (3) + 34.99 (3) + 52.99 (2) + 5.99 (5) = 50.97 + 104.97 + 105.98 + 29.95 = 291.87
Therefore, the regular price of his purchase is $291.87 before sales tax.
If he receives 25% off of his total purchase, then the price is now :
291.87 * .75 = $218.90
We multiply by 75% because we are only paying 75% of the total purchase price since we received a 25% discount.
The total savings is
291.87 - 218.90 = $72.97
If sales tax is 10%, the total purchase price after sales tax is :
218.90 * 1.10 = $240.79
The sales tax is $21.89 since
240.79 -218.90 = 21.89
If he pays with 3 $100 bills, we should receive :
300 - 240.79 = $59.21
in change.
Overestimate because then the gardener could possibly save the left overs in case they get a chance to use it or they could give it to someone who may need it.
X intercept is when y = 0
3x -15(0) = 60
3x = 60
x = 20
y intercept is when x=0
3(0) -15y = 60
-15y = 60
y = -4
Answer is C
