2. How much interest is earned on a principal of $200 invested at an interest rate of 9% for eight
years?
Answer:

(i) The coordinates of the point Q is [tex](x, y) = (21, 0)[/tex].

(ii) The equation of the curve is [tex]y = 6\cdot \ln (2\cdot x + 1)-1.592[/tex].

(iii) The rate of increase of the y-coordinate is 1.2 units per second.

(i) By analytical geometry, we know that the slope of a line normal of a curve ([tex]m_{\perp}[/tex]) by the following expression:

[tex]m_{\perp} = - \frac{1}{\frac{dy}{dx} }[/tex] (1)

Where [tex]\frac{dy}{dx}[/tex] is the slope of the line tangent to the curve.

If we know that [tex]x = 1[/tex], then the slope of the normal to the curve is:

[tex]\frac{dy}{dx} = \frac{12}{2\cdot (1)+1}[/tex]

[tex]\frac{dy}{dx} = 4[/tex]

And the slope of a line normal of a curve is:

[tex]m_{\perp} = -\frac{1}{4}[/tex]

By definition of secant curve we calculate the remaining coordinate of the point Q:

[tex]m_{\perp} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}[/tex] (2)

Where:

If we know that [tex](x_{P}, y_{P}) = (1, 5)[/tex], [tex](x_{Q}, y_{Q}) = (x, 0)[/tex] and [tex]m_{\perp} = -\frac{1}{4}[/tex], then the remaining coordinate of point Q is:

[tex]-\frac{1}{4} = \frac{0-5}{x-1}[/tex]

[tex]-\frac{1}{4}\cdot (x-1) = -5[/tex]

[tex]-\frac{1}{4}\cdot x +\frac{1}{4} = -5[/tex]

[tex]\frac{1}{4}\cdot x = \frac{21}{4}[/tex]

[tex]x = 21[/tex]

The coordinates of the point Q is [tex](x, y) = (21, 0)[/tex].

(ii) The equation of the curve is derived by separating the variables and integrating the resulting expression:

[tex]dy = \frac{12}{2\cdot x + 1}\,dx[/tex]

[tex]\int\, dy = 6\int {\frac{2\,dx}{2\cdot x + 1} }[/tex]

[tex]\int \, dy = 6\int {\frac{du}{u} }[/tex]

[tex]y = 6\cdot \ln u[/tex]

[tex]y = 6\cdot \ln (2\cdot x + 1)+C[/tex]

And the integration constant is found for [tex](x,y) = (1, 5)[/tex]:

[tex]5 = 6\cdot \ln(2\cdot 1 + 1) + C[/tex]

[tex]C = -1.592[/tex]

The equation of the curve is [tex]y = 6\cdot \ln (2\cdot x + 1)-1.592[/tex].

(iii) The rate of increase of the y-coordinate by using the differential equation presented in statement and the definition of rate of change:

[tex]\frac{dy}{dt} = \left(\frac{12}{2\cdot x +1}\right)\cdot \frac{dx}{dt}[/tex] (3)

If we know that [tex]\frac{dx}{dt} = 0.3[/tex] and [tex]x = 1[/tex], then the rate of increase of the y-coordinate is:

[tex]\frac{dy}{dt} = \left[\frac{12}{2\cdot (1)+1} \right]\cdot (0.3)[/tex]

[tex]\frac{dy}{dt} = 1.2[/tex]

The rate of increase of the y-coordinate is 1.2 units per second.

To learn more on differential equations, we kindly invite to check this verified question: https://brainly.com/question/25731911

i). The coordinates of Q is equal to:

[tex](x,y) = (21, 0)[/tex]

ii). The equation of the curve is:

[tex]y = 6. In(2.x + 1) - 1.592[/tex]

iii). The rate of increase for y-coordinate when x = 1:

[tex]1.2 units[/tex] per second

i). Using analytical geometry,

[tex]xp[/tex] and [tex]xq[/tex] are the P and Q's x-coordinates.

[tex]yp[/tex] and [tex]yq[/tex] are the P and Q's y-coordinates.

Since ([tex]xp[/tex], [tex]yp[/tex]) = (1,5) and ( [tex]xq[/tex], [tex]yq[/tex]) = [tex](x, 0)[/tex] and m⊥ = - 1/4, the left coordinate of Q's point:-

-1/4 = (0-5)/(x - 1)

∵[tex]x = 21[/tex]

Thus, the coordinates of y = (21, 0)

ii). Through isolating the variables and employing integration:-

[tex]dy = \frac{12}{(2.x + 1)} dx[/tex]

by integration and integration constant (1,5), the equation is:

[tex]y = 6. In(2.x + 1) - 1.592[/tex]

iii). The rate of increase for y-coordinate:

[tex]dy/dt[/tex] = [tex]\frac{(12)}{(2.1 + 1)} .0.3[/tex]

∵ [tex]dy/dt[/tex] [tex]= 1.2[/tex]

Thus, the rate of increase for y-coordinate when x = 1 is 1.2 units per second.

Learn more about "Co-ordinates" here:

brainly.com/question/21902081

Answer:

I think x= 5

Step-by-step explanation:

because u put 2 where x is supposed to go so it would be -2(2)+9 and -2(2)=-4 and then add 9 and that =5

Answer:

I think d = 6 because 24 + 6 = 30

Answer:

d=6

Step-by-step explanation:

Answer:

because AC and BD bis => AX = XC; BX = XD

ΔAXD ≅ ΔCXB (SAS) because: AX = CX

                                                    DX = BX

                                                    m∠AXD = m∠BXC ( 2 opposing angles)

because ΔAXD ≅ ΔCXB (SAS)

=> AD = BC and m∠DAX = m∠BCX

because m∠DAX = m∠BCX => AD//BC

ABCD has AD = BC and AD//BC => ABCD is a parallelogram

Step-by-step explanation:

Answer:

translation

Step-by-step explanation:

Sliding: moving a shape without rotating or flipping it.

Answer:

bruh 4 days duh

Step-by-step explanation:

Answer:

35.8

Step-by-step explanation:

                [tex]\frac{340.1}{9.5}[/tex]  = 358

 We know that our answer can never be greater than 358 since the dividend

is 340.1 and the divisor is 9.5;

  Also,

  Both values are to one decimal places and we can use this to solve the problem;

  9 can divide 340 in about 37 place with a remainder of 7,

    So, it is appropriate to make the solution 35.8

Answer:

its 10 with the remainder of 38

Step-by-step explanation:

The result of the division is remainder = 38 and quotient = 10

Division is the opposite of multiplying. When we know a multiplication fact, we can find a division fact: Example: 3 × 5 = 15, so 15 / 5 = 3. Also, 15 / 3 = 5.

Given that, 708 divided by 67

When dividing 708 by 67 will get 10 as quotient and 38 remainder

Hence, the result of the division is remainder = 38 and quotient = 10

Learn more about division, click;

https://brainly.com/question/21416852

#SPJ2

Answer:

C. There is one solution, because the coefficients of the variables on both sides of the equation are different.

Step-by-step explanation:

The solution is m = 1

~theLocoCoco

Answer:

add 2 zeros at the end of all of them

Step-by-step explanation:

Answer:

1. $539

2. $300

3. C

Step-by-step explanation:

May I have brainliest?

Answer:

4x+12

Step-by-step explanation:

A 5 inch × 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame?

(5+2x)+(7+2x)

The perimeter would be 4x+12

Hope I helped!

Please mark Brainliest!!!

Answer:

The answer is A. 4x+12

Step-by-step explanation:

Just took the test on edge 2020 :D

Answer: the variable is p=6 .

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable

Answer:

p = 6

Step-by-step explanation:

Step 1: Simplify both sides.

3 + 2p − 4 = 11

3 + 2p + −4 = 11

(2p) + (3+−4) = 11 (Combine Like Terms)

2p + −1 = 11

2p − 1 = 11

Step 2: Add 1 to both sides.

2p − 1 + 1 = 11 + 1

2p = 12

Step 3: Divide both sides by 2.

2p/2 = 12/2

p=6

Answer:

3=k

Answer:

option 1 or should be

Step-by-step explanation:

4/1.5 is 2.6 and 2/3 as a fraction is 66666 so yeah

Answer:

x=20

Step-by-step explanation:

7+0.20x=5+0.30x              

then take the 7 and subtracet the 2 from it, then take the 0.30 and subtract the 0.20 from it then you should get 2=0.10x      

then to get rid of the 0.10 you take it and divide it from the 2 which gives you 20 then you have 20=x and thats your answer

Answer:

it's x=50 hope this helps

Answer:

[tex]\frac{50}{5}[/tex] is the answer

Step-by-step explanation:

you would times 10 by 5 and you have your answer

Answer: I think its Consine

Step-by-step explanation:

Answer: The answer should be 1.5.

Step-by-step explanation:

$6 divided by 12 is .5... Multiply .5 by 3, seeing as 1 pound = $.5

Answer:

$.5

Step-by-step explanation:

hope this helps y'all

Answer:

I hope this helps!

Step-by-step explanation:

1. M is .25

b is 20

so

y= .25x+20

2. y= 3x+2

Answer:26.85 miles

Step-by-step explanation: 7.25+12.3+7.3=26.85

Answer:

-2

Step-by-step explanation:

-2-4/3-0=-2

you basically take the y value of the first point subtract it from the y value of the 2nd point. you do the same for the x values

Answer:

-2

Step-by-step explanation:

You can use the equation rise over run, which is basically y2-y1 over x2-x1

Y2 is -2 and y4 is 4, x2 is 3  x1 is 0

-2-4 over 3-0=-6/3=-2

Answer:

1200 because 12*60 is 1200

Answer:

that's a lot of clients

Answer:

4

Step-by-step explanation:

8/12 simplifies to 4/6. so x needs to be 4 for it to work

Answer:

(

y

−

4

)

=

2

⋅

(

x

+

3

)

y

−

4

=

2

x

+

6

y

=

2

x

+

6

+

4

We get the equation of the line as :

y

=

2

x

+

10

The graph will look like this:

graph{y=2x+10 [-10, 10, -5, 5]

Step-by-step explanation: