Answer:
Future value of annuity (FV) = $13,782.12 (Approx)
Step-by-step explanation:
Given:
Periodic payment p = $500
Interest rate r = 13% = 13%/4 = 0.0325 (Quarterly)
Number of period n = 5 x 4 = 20 quarter
Find:
Future value of annuity (FV)
Computation:
![Future\ value\ of\ annuity\ (FV)=p[\frac{(1+r)^n-1}{r} ] \\\\Future\ value\ of\ annuity\ (FV)=500[\frac{(1+0.0325)^{20}-1}{0.0325} ] \\\\Future\ value\ of\ annuity\ (FV)=13,782.1219 \\\\](https://tex.z-dn.net/?f=Future%5C%20value%5C%20of%5C%20annuity%5C%20%28FV%29%3Dp%5B%5Cfrac%7B%281%2Br%29%5En-1%7D%7Br%7D%20%5D%20%5C%5C%5C%5CFuture%5C%20value%5C%20of%5C%20annuity%5C%20%28FV%29%3D500%5B%5Cfrac%7B%281%2B0.0325%29%5E%7B20%7D-1%7D%7B0.0325%7D%20%5D%20%5C%5C%5C%5CFuture%5C%20value%5C%20of%5C%20annuity%5C%20%28FV%29%3D13%2C782.1219%20%5C%5C%5C%5C)
Future value of annuity (FV) = $13,782.12 (Approx)
Part A. You have the correct first and second derivative.
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Part B. You'll need to be more specific. What I would do is show how the quantity (-2x+1)^4 is always nonnegative. This is because x^4 = (x^2)^2 is always nonnegative. So (-2x+1)^4 >= 0. The coefficient -10a is either positive or negative depending on the value of 'a'. If a > 0, then -10a is negative. Making h ' (x) negative. So in this case, h(x) is monotonically decreasing always. On the flip side, if a < 0, then h ' (x) is monotonically increasing as h ' (x) is positive.
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Part C. What this is saying is basically "if we change 'a' and/or 'b', then the extrema will NOT change". So is that the case? Let's find out
To find the relative extrema, aka local extrema, we plug in h ' (x) = 0
h ' (x) = -10a(-2x+1)^4
0 = -10a(-2x+1)^4
so either
-10a = 0 or (-2x+1)^4 = 0
The first part is all we care about. Solving for 'a' gets us a = 0.
But there's a problem. It's clearly stated that 'a' is nonzero. So in any other case, the value of 'a' doesn't lead to altering the path in terms of finding the extrema. We'll focus on solving (-2x+1)^4 = 0 for x. Also, the parameter b is nowhere to be found in h ' (x) so that's out as well.
Answer:
7.6 ≤w
Step-by-step explanation:
Hey there!
In order to solve this inequality, you need to simplify the inequality like the following:
Subtract 3.4 from both sides
7.6 ≤w
This means that w is greater than or equal to 7.6
Answer:
segment EG over segment LN equals segment FG over segment MN
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
The corresponding sides are
EF and LM
EG and LN
FG and MN
The corresponding angles are
∠E≅∠L
∠F≅∠M
∠G≅∠N
therefore
EF/LM=EG/LN=FG/MN=3/1
