Ask question

Ask question

All categories

3 years ago

13

Find the difference quotient f(x+h)-f(x)/h , where, for the function below. f(x)= -6x+3 Simplify your answer as much as possible

. HELP!!! will get five-star rating the brainiest

1 answer:

VARVARA [1.3K]3 years ago

3 0

Answer:

-6.

Step-by-step explanation:

Difference coefficient

= -6(x + h) + 3 - (-6x + 3) / h

= -6x - 6h + 3 + 6x - 3 / h

= -6h / h

= -6.

You might be interested in

28 + 2A = 5A + 7<br><br> Please explain thank you!

Vinvika [58]

First you need to get x on one side of the equation and to do that subtract 2a from both sides.
28 + 2a = 5a + 7
-2a -2a
28=3a+7

Then we need to get a alone by subtracting 7 on both sides.
28=3a+7
-7 -7
21=3a

Finally divide each side by 3 and you should get a = 7. Hope this helps!

3 0

3 years ago

A store is having a sale on walnuts and chocolate chips. For 7 pounds of walnuts and 9 pounds of chocolate chips, the total cost

Jlenok [28]

Answer:

Walnuts cost $1.75, chocolate chips cost $2.75

Step-by-step explanation:

<h3>Let the costs be:</h3>

Walnuts - x
Chocolate chips - y

<h3>Set equations as per question</h3>

For 7 pounds of walnuts and 9 pounds of chocolate chips, the total cost is $37:

7x + 9y = 37

For 5 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $17:

5x + 3y = 17

<h3>Solve the system by elimination</h3>

Multiply the second equation by 3 and subtract the first equation, solve for x:

3(5x + 3y) - (7x + 9y) = 3(17) - 37
15x + 9y - 7x - 9y = 51 - 37
8x = 14
x = 14/8
x = 1.75

Find the value of y:

7*1.75 + 9y = 37
12.25 + 9y = 37
9y = 37 - 12.25
9y = 24.75
y = 24.75/9
y = 2.75

6 0

2 years ago

y = c1 cos(5x) + c2 sin(5x) is a two-parameter family of solutions of the second-order DE y'' + 25y = 0. If possible, find a sol

TEA [102]

Answer:

y = 2cos5x-9/5sin5x

Step-by-step explanation:

Given the solution to the differential equation y'' + 25y = 0 to be

y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.

According to the boundary condition y(0) = 2, it means when x = 0, y = 2

On substituting;

2 = c1cos(5(0)) + c2sin(5(0))

2 = c1cos0+c2sin0

2 = c1 + 0

c1 = 2

Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given

y(x) = c1cos5x + c2sin5x

y'(x) = -5c1sin5x + 5c2cos5x

If y'(π) = 9, this means when x = π, y'(x) = 9

On substituting;

9 = -5c1sin5π + 5c2cos5π

9 = -5c1(0) + 5c2(-1)

9 = 0-5c2

-5c2 = 9

c2 = -9/5

Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation

y = c1 cos(5x) + c2 sin(5x) will give

y = 2cos5x-9/5sin5x

The final expression gives the required solution to the differential equation.

3 0

3 years ago

A credit card company charges 18.6% percent per year interest. Compute the effective annual rate if they compound, (a) annualy,

Darina [25.2K]

Answer:

a) Effective annual rate: 18.6%

b) Effective annual rate: 20.27%

c) Effective annual rate: 20.43%

d) Effective annual rate: 20.44%

Step-by-step explanation:

The effective annual interest rate, if it is not compounded continuously, is given by the formula

$I=C(1+\frac{r}{n})^{nt}-C$

where

<em>C = Amount of the credit granted </em>

<em>r = nominal interest per year </em>

<em>n = compounding frequency </em>

<em>t = the length of time the interest is applied. In this case, 1 year. </em>

In the special case the interest rate is compounded continuously, the interest is given by

$I=Ce^{rt}-C$

(a) Annually

$I=C(1+\frac{0.186}{1})-C=C(1.186)-C=C(1.186-1)=C(0.186)$

The effective annual rate is 18.6%

(b) Monthly

<em>There are 12 months in a year </em>

$I=C(1+\frac{0.186}{12})^{12}-C=C(1.2027)-C=C(0.2027)$

The effective annual rate is 20.27%

(c) Daily

<em>There are 365 days in a year </em>

$I=C(1+\frac{0.186}{365})^{365}-C=C(1.2043)-C=C(0.2043)$

The effective annual rate is 20.43%

(d) Continuously

$I=Ce^{0.186}-C=C(1.2044)-C=C(0.2044)$

The effective annual rate is 20.44%

3 0

3 years ago

The function f(x)=5(2)^x was replaced with f(x)+k , resulting in the function graphed below. what is the value of k?

xxTIMURxx [149]

Since adding a constant to a function simply moved the graph upwards by that amount, solve f(x) for any value and see how much the graph given is different from that value of y...the simplest way in this case may be to simply find f(0) which is:

5*2^0=5

Clearly the graph at x=0 is at y=-2 so we can see that k is:

5+k=-2 so

k=-7

5 0

3 years ago