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ANTONII [103]
3 years ago
8

Total amount = P (1 + i)t Ryan has an eight–year loan for $6,000. He is being charged an interest rate of 5 percent, compounded

annually. Calculate the total amount that he will pay. A. $7,657.69 B. $8,815.97 C. $8,864.73
Mathematics
1 answer:
IceJOKER [234]3 years ago
8 0

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Total amount = P(1+i)^t

Number of years = 8

Loan amount = $ 6000

Rate of interest = 5%

So, Total amount is given by

6000(1+0.05)^8\\\\=6000(1.05)^8\\\\=\$8864.73

Hence, Option 'c' is correct.

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Help with 30 please. thanks.​
Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

\displaystyle  y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}

And we want to show that:

\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}

Instead of differentiating directly, we can first square both sides:

\displaystyle y^2 = 3e^{2x} -4x + 1

We can find the first derivative through implicit differentiation:

\displaystyle 2y \frac{dy}{dx}  = 6e^{2x} -4

Hence:

\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}

And we can find the second derivative by using the quotient rule:

\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}

Substitute:

\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}

Simplify:

\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}

Combine fractions:

\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}

Simplify:

\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}

Simplify:

6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}

Q.E.D.

6 0
2 years ago
Write an equation of the line perpendicular to the x-axis and passes through (4,-3)
Firdavs [7]

Step-by-step explanation:

The equation of the line is x = 4.

4 0
2 years ago
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PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS PLS ASAP
ollegr [7]

Answer:

The bottom one

Step-by-step explanation:

the lowest dot is on -3 so that's the y-intercept

the other is at 2 x and -1 y

4 0
2 years ago
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Evaluate 2/3 - 1/6<br><br> A. 1/6<br> B. 1<br> C. 1/2<br> D. 5/6
Zina [86]

Answer:

1/2

Step-by-step explanation:

2/3-1/6

=4/6-1/6

=3/6

=1/2

8 0
3 years ago
The ratio of boys to girls in Coach Sheppard's class is 3 to 5. There are 20 girls in the
kondaur [170]

Answer:

32 Students

Step-by-step explanation:

3/5 = 12/20

This means you add the boys and girls to get 32.

8 0
2 years ago
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