Answer:
X=17,384.37
Step-by-step explanation:
The present value of the perpetuity can be calculated by discounted for the different interest rates:
![PV_{perpetuity}=[\frac{1}{0.1}+\frac{(\frac{1}{0.08}-\frac{1}{0.1})}{1.1^{10}}]\times 15,000+15000\\\\\\=164,457.87+15,000=179,457.87](https://tex.z-dn.net/?f=PV_%7Bperpetuity%7D%3D%5B%5Cfrac%7B1%7D%7B0.1%7D%2B%5Cfrac%7B%28%5Cfrac%7B1%7D%7B0.08%7D-%5Cfrac%7B1%7D%7B0.1%7D%29%7D%7B1.1%5E%7B10%7D%7D%5D%5Ctimes%2015%2C000%2B15000%5C%5C%5C%5C%5C%5C%3D164%2C457.87%2B15%2C000%3D179%2C457.87)
#Now, we use the annuity-due present value factor to get the present values of the annuity payments, let X be the annual annuity payments;
![X[\ddot a_{10}_|_{0.10}+\frac{\ddot a_{15}|_{0.08}}{1.10^{10}}]=179,457.87\\\\\\X[6.759+\frac{9.244}{1.1^{10}}]=179457.87\\\\\\X=17384.37](https://tex.z-dn.net/?f=X%5B%5Cddot%20a_%7B10%7D_%7C_%7B0.10%7D%2B%5Cfrac%7B%5Cddot%20a_%7B15%7D%7C_%7B0.08%7D%7D%7B1.10%5E%7B10%7D%7D%5D%3D179%2C457.87%5C%5C%5C%5C%5C%5CX%5B6.759%2B%5Cfrac%7B9.244%7D%7B1.1%5E%7B10%7D%7D%5D%3D179457.87%5C%5C%5C%5C%5C%5CX%3D17384.37)
Hence, the value of X is 17,384.37
Answer:3/8 is equal to 3/4 and 4/6 is equal to 2/3.
Step-by-step explanation:
Point slope form is
in general where
m = slope
(x1,y1) = point the line goes through
In this case, m = 5 is the given slope
(x1,y1) = (1,3) is the given point the line goes through which means
x1 = 1
y1 = 3
So let's plug m = 5, x1 = 1, y1 = 3 into the general equation above to get...
---------------------------------------------------------------------------------------
So the final answer is
Answer:
usual katmai Islam Kaiserislands iStock Jericho khalidi
Answer:
y = -0.005x² + 50
Step-by-step explanation:
The diameter is 200 feet, so the parabola has roots at (-100, 0) and (100, 0). The maximum height is 50, so the vertex of the parabola is at (0, 50).
Using vertex form of a parabola:
y = a (x − h)² + k
y = a (x − 0)² + 50
y = ax² + 50
Plugging in either root:
0 = a (100)² + 50
a = -0.005
y = -0.005x² + 50
