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m_a_m_a [10]
3 years ago
11

Lucas took out a car loan for $14,475 that has a 0% APR for the first 16

Mathematics
1 answer:
Fiesta28 [93]3 years ago
7 0

Answer:

The answer is 44 months.

Step-by-step explanation:12*5=60

60 months - 16 months = 44

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Solve the following differential equation: y" + y' = 8x^2
PtichkaEL [24]

Answer:

y=y_p+y_h = \frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}

Step-by-step explanation:

Let's  find a particular solution. We need a function of the form y= ax^3+bx^2+cx+d such that

y'= 3ax^2+2bx+c and

y''= 6ax+2b

y'+y''= 3ax^2+2bx+c+6ax+2b = 3ax^2+x(2b+6a)+(c+2b) = 8x^2

then, 3a= 8, 2b+6a =0 and c+2b = 0. With the first equation we obtain

a =  8/3 and replacing in the second equation 2b+6(8/3) = 2b + 16 = 0. Then, b = -8. Finally, c = -2(-8) = 16.

So, our particular solution is  y_p= \frac{8}{3}x^3-8x^2+16x.

Now, let's find the solution y_p of the homogeneus equation y''+y'=0 with the method of constants coefficients. Let y=e^{\lambda x}

y'=\lambda e^{\lambda x}

y''=\lambda^2e^{\lambda x}

then \lambda e^{\lambda x}+\lambda^2 e^{\lambda x} = 0

e^{\lambda x}(\lambda +\lambda^2)= 0

(\lambda +\lambda^2)= 0

\lambda (1+\lambda)= 0

\lambda =0 and \lambda)= -1.

So, y_h = C_1 + C_2e^{-x} and the solution is

y=y_p+y_h =\frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}.

5 0
2 years ago
Need help with perfect square! 40 points
andriy [413]
The value of C would be 25
6 0
3 years ago
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Suppose that a large number of samples are taken from a population. Which of the following sample sizes will be most likely to r
Montano1993 [528]

If you use a large enough statistical sample size, you can apply the Central Limit Theorem (CLT) to a sample proportion for categorical data to find its sampling distribution. The population proportion, p, is the proportion of individuals in the population who have a certain characteristic of interest (for example, the proportion of all Americans who are registered voters, or the proportion of all teenagers who own cellphones). The sample proportion, denoted

6 0
3 years ago
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The numbers a,b,c,d are four consecutive terms of an arithmetic sequence and a+b+c+d=12
likoan [24]

The smallest possible product of these four numbers is 59.0625

<h3>How to find the smallest possible product of these four numbers?</h3>

The equation is given as:

a + b + c + d = 12

The numbers are consecutive numbers.

So, we have:

a + a + 1 + a + 2 + a + 3 = 12

Evaluate the like terms

4a = 6

Divide by 4

a = 1.5

The smallest possible product of these four numbers is represented as:

Product = a * (a + 1) * (a + 2) * (a + 3)

This gives

Product = 1.5 * (1.5 + 1) * (1.5 + 2) * (1.5 + 3)

Evaluate

Product = 59.0625

Hence, the smallest possible product of these four numbers is 59.0625

Read more about consecutive numbers at:

brainly.com/question/10853762

#SPJ1

6 0
1 year ago
Which line intersects the parabola y = x^2 + 6x-2 at two points?
schepotkina [342]

Answer:

C

Step-by-step explanation:

You find y-intercept x=0

3 0
3 years ago
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