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omeli [17]
4 years ago
11

Diane borrowed 8000 at a rate of 7%, compounded semiannually. Assuming she makes no payments, how much will she owe after 6 year

s?
Do not round any intermediate computations, and round your answer to the nearest cent.​
Mathematics
1 answer:
dmitriy555 [2]4 years ago
7 0

Answer: $12088.55

Step-by-step explanation:

A = p(1+r/n)^nt

A = 8000(1+0.07/2)^2*6

A = 12088.54926

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A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordin
Anit [1.1K]

Answer:

y=5e^{2x}

Step-by-step explanation:

Let (x,y) represents a point P on the curve,

So, the slope of the curve at point P = \frac{dy}{dx}

According to the question,

\frac{dy}{dx}=2y

\frac{1}{y}dy=2dx

Integrating both sides,

\int \frac{dy}{y}=2dx

ln y=2x+ln C

ln y-ln C = 2x

ln(\frac{y}{C})=2x

\frac{y}{C}=e^{2x}

\implies y=Ce^{2x}

Since, the curve is passing through the point (0, 5),

5=Ce^{0}\implies C=5

Hence, the required equation of the curve is,

y=5e^{2x}

7 0
4 years ago
What is the slope of the line that passes through the points<br> (1, -3) and (4, 2)?
Vitek1552 [10]

in this situation it would be the last one or d.

6 0
3 years ago
Point p(a,b) is in the first quadrant on the graph of the line x+y=4. A triangular region is shown on the diagram. What is the m
Gala2k [10]

Answer:

The maximum area of the triangular region is 2 square units

Step-by-step explanation:

we know that

The area of the triangular region is equal to

A=\frac{1}{2}(x)(y) -----> equation A

where

x is the x-coordinate of point P

y is the y-coordinate of point P

we have

The equation of the graph of the line is

x+y=4

y=-x+4 -----> equation B

substitute equation B in equation A

A=\frac{1}{2}(x)(-x+4)

A=-\frac{1}{2}x^2+2x

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The y-coordinate of the vertex represent the maximum area of the triangular region

Find the vertex

Convert the quadratic equation in vertex form

Factor -1/2

A=-\frac{1}{2}(x^2-4x)

Complete the square

A=-\frac{1}{2}(x^2-4x+4)+2

Rewrite as perfect squares

A=-\frac{1}{2}(x-2)^2+2

The vertex is the point (2,2)

so

The maximum area is the y-coordinate of the vertex

The maximum area of the triangular region is 2 square units

Find the coordinates of point P for the maximum area

x=2 (x-coordinate of the vertex)

Find the y-coordinate of point P

substitute in equation B

y=-2+4=2

The coordinates of point P for the maximum area is P(2,2)

3 0
4 years ago
Figure is not d
ollegr [7]

Answer:

1.5

Step-by-step explanation:

the feet in perimeter is going to be the same

7 0
4 years ago
Which sentence from this introduction paragraph is most clearly providing background
Damm [24]

Answer:

sentence 2?

Step-by-step explanation:

sentence 1 provides background for the question, sentence 2 provides background for the graph, and sentence 3 is the question.

If you wanted the answer to the question:

8:4 = 2:1

4 0
3 years ago
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