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rusak2 [61]
3 years ago
13

Jamie purchased a condo in Naples, Florida, for $699,000. She put 20% down and financed the rest at

Mathematics
1 answer:
ololo11 [35]3 years ago
6 0

By applying the formulas of present and future values of annuity we can solve this problem. In this mortgage problem, first we have to find loan amount after the down payment. It is 699,000 - 699,000 * 0.2 = 559,200$. We have to set it as PV (Present Value) of annuity. Using the PV formula PV = A \frac{[1- \frac{1}{(1+r)^{N}}]}{r}, we first find A, which is an annual payment. Exact calculation with mortgage calculator gives us A = 33,866.56$. After finding it, plugging this number into FV (Future Value) formula FV = A\frac{[(1+r)^{N}-1]}{r}, we find the value of the future value and it is 1,185,329.66$. And the total financial charge is 1,185,329.66 - 559,200 = 626,129.66$

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Determine the singular points of the given differential equation. Classify each singular point as regular or irregular. (Enter y
ludmilkaskok [199]

Answer:

Step-by-step explanation:

Given that:

The differential equation; (x^2-4)^2y'' + (x + 2)y' + 7y = 0

The above equation can be better expressed as:

y'' + \dfrac{(x+2)}{(x^2-4)^2} \ y'+ \dfrac{7}{(x^2- 4)^2} \ y=0

The pattern of the normalized differential equation can be represented as:

y'' + p(x)y' + q(x) y = 0

This implies that:

p(x) = \dfrac{(x+2)}{(x^2-4)^2} \

p(x) = \dfrac{(x+2)}{(x+2)^2 (x-2)^2} \

p(x) = \dfrac{1}{(x+2)(x-2)^2}

Also;

q(x) = \dfrac{7}{(x^2-4)^2}

q(x) = \dfrac{7}{(x+2)^2(x-2)^2}

From p(x) and q(x); we will realize that the zeroes of (x+2)(x-2)² = ±2

When x = - 2

\lim \limits_{x \to-2} (x+ 2) p(x) =  \lim \limits_{x \to2} (x+ 2) \dfrac{1}{(x+2)(x-2)^2}

\implies  \lim \limits_{x \to2}  \dfrac{1}{(x-2)^2}

\implies \dfrac{1}{16}

\lim \limits_{x \to-2} (x+ 2)^2 q(x) =  \lim \limits_{x \to2} (x+ 2)^2 \dfrac{7}{(x+2)^2(x-2)^2}

\implies  \lim \limits_{x \to2}  \dfrac{7}{(x-2)^2}

\implies \dfrac{7}{16}

Hence, one (1) of them is non-analytical at x = 2.

Thus, x = 2 is an irregular singular point.

5 0
3 years ago
Simplify x^3y^4/3y^4
yan [13]
The given expression is:
(x^3 * y^4) / (3y^4)

We can notice that the term y^4 is a common term found in both the numerator and the denominator of the given expression, therefore, we can cancel this term from the both numerator and denominator (as if you divided both numerator and denominator by y^4).

Doing this, we will have the simplified form of the expression as follows:
(x^3) / (3)
4 0
3 years ago
Read 2 more answers
What is 1,099 rounded to the nearest ten
Elena-2011 [213]
1,099= 1,100

HOPE THIS HELPS!!!
5 0
3 years ago
On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a verte
statuscvo [17]

Answer:

Option 4.

Step-by-step explanation:

The vertex form of a parabola is

g(x)=a(x-h)^2+k                    ... (1)

where, a is a constant (h,k) is vertex.

The given function is

f(x)=x^2

The vertex of the function is (0,0) and it goes through (-2, 4) and (2, 4).

It is given that the vertex of function g(x) is at (5,2).

Substitute h=5 and k=2 in equation.

g(x)=a(x-5)^2+2

g(x) is passes through (3, 6).

6=a(3-5)^2+2             .... (2)

6-2=4a

4=4a

Divide both sides by 4.

a=1

Substitute a=1 in equation (2).

g(x)=1(x-5)^2+2

g(x)=(x-5)^2+2

The function g(x) is g(x)=(x-5)^2+2.

Therefor, the correct option is 4.

3 0
3 years ago
Read 2 more answers
Will give brainlist
Cloud [144]

72 = 6*12  = 3*2 * 4*3  = 3*2*2*2*3

72 = 2*2*2*3*3

72=2^3 * 3^2

You can check your answer by multiplying out the factors

2*2*2*3*3

2*2 is 4

4*2 is 8

8*3 is 24

24*3 is 72

checks

4 0
3 years ago
Read 2 more answers
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