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3 years ago

15

Graph the function. y=5 (x+1) ^2 -3

1 answer:

ra1l [238]3 years ago

8 0

Answer:

Step-by-step explanation:

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Match each differential equation to a function which is a solution.

inessss [21]

Answer: 1 - C

2 - E

3 - no answer

4 - B

Step-by-step explanation:

A. $y = 3x+x^2$

$y' = 3 + 2x\\y'' = 2$

Replace in 1:

$y'' + y = 0$

$2 + 3x + x^2 \neq 0$

So, A is not an answer for 1

Replace in 2:

$y' = 3y$

$3+2x = 3(3x + x^2)$

So, A is not an answer for 2

Replace in 3

$2x^2y'' + 3xy'= y$

$2x^2(2) + 3x(3 + 2x) = 4x^2 + 9x + 6x^2 \neq 3x+x^2$

So, A is not an answer for 3

Replace in 4

$y'' + 6y' + 8y = 0$

$2 + 6(3+2x)+8(3x + x^2) = 2+18+12x+24x+8x^2 \neq 0$

So, A is not an answer for 4

B. $y = e^{-4x}$

$y' = -4e^{-4x}$

$y'' = 16e^{-4x}$

Replace in 1

$y'' + y = 0$

$16e^{-4x} -4e^{-4x} = 12e^{-4x} \neq 0$

So, B is not an answer for 1

Replace in 2

$y' = 3y$

$-4e^{-4x} \neq 3e^{-4x}$

So, B is not an answer for 2

Replace in 3

$2x^2y'' + 3xy' = y$

$2x^2(16e^{-4x}) +3x(-4e^{-4x}) \neq e^{-4x}$

So, B is not an answer for 3

Replace in 4

$y'' + 6y' +8y = 0$

$16e^{-4x} + 6(-4e^{-4x}) + 8e^{-4x} = e^{-4x}(16-24+8) = 0$

So, B is an answer for 4

C. $y = sin(x)$

$y' = cos(x)$

$y'' = -sin(x)$

Replace in 1

$y'' + y = 0$

$-sin(x) + sin(x) = 0$

So, C is an answer for 1

We jump to

D. $y = x^{12}$

$y' = 12x^{11}$

$y'' = 132 x^{10}$

Replace in 2

$y' = 3y$

$12x^{11} \neq 3x^{12}$

So, D is not an answer for 2

Replace in 3

$2x^2y'' + 3xy' = y$

$2x^2(132x^{10}) + 3x(12x^{11}) = 300x^{12} \neq x^{12}$

So, D is not an answer for 3

E. $y = 6e^{3x}$

$y' = 18e^{3x}$

$y'' = 54e^{3x}$

Replace in 2

$y' = 3y$

$18e^{3x} = 3(6e^{3x}) = 18e^{3x}$

So, E is an answer for 2

3 0

3 years ago

Write the equation for the following relation.

krok68 [10]

Y= 1/2x plus three
This works for all of the ordered pairs so will most likely be correct

5 0

3 years ago

HELP ASAP PLEASE I WILL GIVE BRAINLIEST..........

nexus9112 [7]

Use that math app where you take pictures of the problem and it gives you the answers and all the work to solve it.

4 0

3 years ago

Calculate the a) future value of the annuity due, and b) total interest earned. (From Example 2)

vredina [299]

Answer:

value: $66,184.15
interest: $6,184.15

Step-by-step explanation:

The future value can be computed using the formula for an annuity due. It can also be found using any of a variety of calculators, apps, or spreadsheets.

__

<h3>formula</h3>

The formula for the value of an annuity due with payment P, interest rate r, compounded n times per year for t years is ...

FV = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)

FV = 5000(1 +0.06/4)((1 +0.06/4)^(4·3) -1)/(0.06/4) ≈ 66,184.148

FV ≈ 66,184.15

<h3>calculator</h3>

The attached calculator screenshot shows the same result. The calculator needs to have the begin/end flag set to "begin" for the annuity due calculation.

__

<h3>a) </h3>

The future value of the annuity due is $66,184.15.

<h3>b)</h3>

The total interest earned is the difference between the total of deposits and the future value:

$66,184.15 -(12)(5000) = 6,184.15

A total of $6,184.15 in interest was earned by the annuity.

3 0

2 years ago

Which word MOST affects the tone of this sentence?

LuckyWell [14K]

I would say gaudy , it’s pretty descriptive

3 0

3 years ago

Read 2 more answers