For f(x) =1/x^2-3

find:

(a) f(3) (3 points)

(b) f(2+h) (3 points)

Answers

Answer 1

Answer:

[tex]f(3) = \frac{-26}{9}[/tex]

[tex]f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{1}{x^2} - 3[/tex]

Required

Find f(3) and f(2 + h)

Solving f(3)

Substitute 3 for x in [tex]f(x) = \frac{1}{x^2} - 3[/tex]

[tex]f(3) = \frac{1}{3^2} - 3[/tex]

[tex]f(3) = \frac{1}{9} - 3[/tex]

Take LCM

[tex]f(3) = \frac{1 - 27}{9}[/tex]

[tex]f(3) = \frac{-26}{9}[/tex]

Solving f(2 + h)

Substitute 2 + h for x in [tex]f(x) = \frac{1}{x^2} - 3[/tex]

[tex]f(2 + h) = \frac{1}{(2 + h)^2} - 3[/tex]

[tex]f(2 + h) = \frac{1}{(2 + h)(2 + h)} - 3[/tex]

[tex]f(2 + h) = \frac{1}{4 + 2h + 2h + h^2} - 3[/tex]

[tex]f(2 + h) = \frac{1}{4 + 4h + h^2} - 3[/tex]

Take LCM

[tex]f(2 + h) = \frac{1- 3(4 + 4h + h^2)}{4 + 4h + h^2}[/tex]

[tex]f(2 + h) = \frac{1- 12 - 12h - 12^2}{4 + 4h + h^2}[/tex]

[tex]f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}[/tex]


Related Questions

Find the product 822x9=

Answers

Answer:

7398

Step-by-step explanation:

Answer:

7398

I mean, this is the answer. You COULD just use a calculator, but here.

Glad I can help. :)

Please need help thank

Answers

Answer:

35 balloons

Step-by-step explanation:

If wrong srry...hope this helps

Answer:

35 bunches

Step-by-step explanation:

25*7=175 balloons

5 balloons in each bunch=175/5

=35

2. What number is equal to five units + three tenths? Circle the correct answer.
0.53
0.35
5.3
3.5
53
35

Answers

Answer:

35

Step-by-step explanation:

5*1+3*10

5+30 = 35

Complete each ordered pair so that it is a solution of the given linear equation.
x-3y = -2;( ,1). (-8, )

Answers

Answer: (1, 1), (-8, -2)

Step-by-step explanation:

Let’s start with the first solution: ( , 1)

We know that the y-coordinate for this solution is 1, so we can plug that in to find the x-coordinate.

x - 3y = -2

x - 3(1) = -2

x - 3 = -2

x = -2 + 3

x = 1

Therefore, for this solution x = 1, so our final solution is (1, 1).

Now let’s work on the second solution: (-8, ).

We know that the x-coordinate for this solution is -8, so we can plug that in.

x - 3y = -2

-8 - 3y = -2

-3y = -2 + 8

-3y = 6

y = -2

Therefore, for this solution y = -2, so our final solution (-8, -2).

How can I figure out my screentime password.
100 points to whoever can tell me exactly how to do it and maybe even brainless if it works and it has to be an actual answer not just a random one!!!

Answers

Answer:

Screen record as your parent puts the password in or wipe off your screen and give the parent your phone to put the password in then look at the fingerprint circles and that where each number is, then try all the possible combinations

Step-by-step explanation:

What is the domain of the relation [(x,y):y=x(x-3)/(x+4)(x-7)

Answers

Answer:

i think its b

Step-by-step explanation:

What is the equation for the line that passes through (3, 2) and has a slope
equal to 12
3

Answers

Answer:

Step-by-step explanation:

Remark

I'm not sure I know what you intend for the slope. I will take it as 12/3 = 4

If that is the case then what you have so far is

Solution

y = 4x + b

The given point determines b

Givens

x = 3

y  = 2

Given point

2 = 4*3 + b

2 = 12 + b

b = 2 - 12

b = -10

The equation is y = 4x - 10

I NEED THE ANSWER QUICK

Answers

9514 1404 393

Answer:

  4^0

Step-by-step explanation:

The rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)/(a^c) = a^(b-c)

So, your expression simplifies to ...

  [tex]4^5\times4^{-7}\div4^{-2}=4^{5-7-(-2)}=\boxed{4^0}[/tex]

How do you do this question?

Answers

Answer:

(a) >, decreasing

(b) 0, horizontal

Step-by-step explanation:

(a) dy/dt = eᵗ (y − 1)²

eᵗ is always positive, and (y − 1)² is always positive.  So dy/dt is always positive.  Meaning the graph of the solution can never be decreasing.

(b) When y = 1, dy/dt = e¹ (1 − 1)² = 0.  However, this graph does not have a horizontal tangent line at y=1, so this is not the solution of the differential equation.

Which ordered pair would form a proportional relationship with the point graphed below?

(10.-20)
(-30, 20)
(-10,5)
(35, -20

Answers

The third option but can also be the first option, The would proportionate properly.

PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!

Find the slope of the line that passes through the points (–2, 4) and (5, 4).

Answers

Answer:

slope is 0

Step-by-step explanation:

Answer:

slope is 0

Step-by-step explanation:

I used another app to find the awnser for you

I need help please : )

Answers

Answer:

i think the answer is 10x^3-12^2-198x-40

Please help me!!!!!​

Answers

Answer:

The answer is A.

Step-by-step explanation:

The ratio is 1 second/2 centimeters, but since they're asking for a unit ratio, you need to divide the top and bottom by 2 which gives you a unit ratio of ½ second/1 centimeter.

Answer:

Perhaps, B or A

Step-by-step explanation:

An asteroid and a planet are 383 000 km apart.
The asteroid then travels 99 500 km towards the planet.
How far does the asteroid have left to travel before
it reaches the planet? Work it out in your head.

Answers

Answer:

283500

Step-by-step explanation:

Your answer is

[tex]383000-99500[/tex]

Which is 283500

Hope this helps Please hit the crown :D

The asteroid are separated by 383,000 km.

The asteroid moves 99,500 km toward the planet.

Let F = how far does the asteroid need to travel before reaching the planet.

F = 383,000 km - 99,0m500 km

F = 283,500 km

Got it?

The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of

Answers

Answer:

Answer and Explanation:

We have:

Population mean,

μ

=

3

,

000

hours

Population standard deviation,

σ

=

696

hours

Sample size,

n

=

36

1) The standard deviation of the sampling distribution:

σ

¯

x

=

σ

n

=

696

36

=

116

2) As per the central limit theorem, the expected value of the sampling distribution is equal to the population mean.

Therefore:

The expected value of the sampling distribution is equal to the population mean,

μ

¯

x

=

μ

=

3

,

000

The standard deviation of the sampling distribution,

σ

¯

x

=

116

The shape of the sampling distribution of

¯

x

is approximately normal. As the sample size is more than

30

.

3) The probability that the average life in the sample will be between

2670.56

and

2809.76

hours:

P

(

2670.56

<

x

<

2809.76

)

=

P

(

2670.56

3000

116

<

z

<

2809.76

3000

116

)

=

P

(

2.84

<

z

<

1.64

)

=

P

(

z

<

1.64

)

P

(

z

<

2.84

)

=

0.0482

Using Excel: =NORMSDIST(-1.64)-NORMSDIST(-2.84)

4) The probability that the average life in the sample will be greater than

3219.24

hours:

P

(

x

>

3219.24

)

=

P

(

z

>

3219.24

3000

116

)

=

P

(

z

>

1.89

)

=

0.0294

Using Excel: =NORMSDIST(-1.89)

5) The probability that the average life in the sample will be less than

3180.96

hours:

P

(

x

<

3180.96

)

=

P

(

z

<

3180.96

3000

116

)

=

P

(

z

<

1.56

)

=

0.9406

The expected value, standard deviation, and shape of the sampling distribution of will be 116.

What is Standard deviation?

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that;

The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.

And, A simple random sample of 36 bulbs is taken.

Now,

Since, The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.

And, A simple random sample of 36 bulbs is taken.

Hence, The expected value, standard deviation, and shape of the sampling distribution of is,

⇒ Standard error = 696 / √ 36

                            = 696 / 6

                            = 116

Thus, The expected value, standard deviation, and shape of the sampling distribution of = 116.

Learn more about the standard deviation visit:

https://brainly.com/question/475676

#SPJ5

Please help what is the answer

Answers

Answer:

7^12=13,841,287,201

Step-by-step explanation:

when you are putting a  power to a power, you just multiply the powers by each other

Answer:

7^12

Step-by-step explanation:

(7^6)^2

7^12

helppppp help help helppppp help help thanks

Answers

Answer:

60 percent

Step-by-step explanation:

Answer:

60% are roses

Step-by-step explanation:

1. Add all the numbers together to find the total

15+6+4= 25 total flowers

2. Put the total as the denominator, and the rose count as the numerator since we are trying to find what percentage are roses

15/25

3. Simplify fraction

15/25= 3/5

4. Divide numerator by denominator

300/5

5. Simplify

300/5= 60%

Please help I’ll mark brainliest if u give a small explanation!!!

Answers

Answer:

ut is a if you add 5 plus 4 it makes 9 do not add the 8

Which of the following graphs shows the set of points that represents the number of hours that Leah
can work in order to earn at least $120 and not work more than 20 hours per month?

Answers

Answer:

I think it’s A,C, and E

Step-by-step explanation:

I’m not for sure but if you plot those points in the shaded region for graph C, those should be correct .

Given the cos(θ) = 5/13 the ratio for sine of θ is
. Enter your answer as a fraction.

Answers

12/13 is the answer for sure

What is the value of a? Please solve this with the law of sine

Answers

Answer:

what chap is this

Step-by-step explanation:

Help please ;-; The values in the table represent a linear function.

x 1 2 3 4
f(x) −3 −1 1 3
What is the function rule?

Write the rule in function notation, using the slope-intercept form of a line.

Enter your answer in the box.

Answers

Answer:

The function rule in slope-intercept form is:

[tex]y = \frac{1}{2}x-\frac{7}{2}[/tex]

Step-by-step explanation:

The slope-intercept form of a function is given as:

[tex]y = mx+b[/tex]

Here

m is the rate of change of function and b is the y-intercept

The rate of change is calculated as:

[tex]m = \frac{difference\ in\ y}{difference\ in\ x}[/tex]

For this, any two pairs of input and output can be taken.

So using the pairs (1,-3) and (2,-1)

[tex]m=\frac{2-1}{-1+3}\\=\frac{1}{2}[/tex]

Putting the value of slope in slope-intercept form

[tex]y = \frac{1}{2}x+b[/tex]

Putting (1,-3) in the equation

[tex]-3 = \frac{1}{2}(1)+b\\-3 = \frac{1}{2}+b\\b = -3-\frac{1}{2}\\b = \frac{-6-1}{2}\\b= \frac{-7}{2}[/tex]

Putting the value of b

[tex]y = \frac{1}{2}x-\frac{7}{2}[/tex]

Hence,

The function rule in slope-intercept form is:

[tex]y = \frac{1}{2}x-\frac{7}{2}[/tex]

If a bike has a sale price of $6 what was the original price if she pays 60% off original price

Answers

Answer:$15

Step-by-step explanation:$6=30% 6/3=$1.5*10=$15

An item on sale cost 35%of the original price. The original price was $25. What was the sale price?

Answers

[tex]{\underline{\pink{\textsf{\textbf{ Answer : }}}}}[/tex]

➩ $33.75

[tex]{\underline{\purple{\textsf{\textbf{ Explanation : }}}}}[/tex]

Original price of the item is $25

As it told that it costs 35% of the original price

Therefore

➡ $25 + (35% of 25)

➡ $25 + 8.75

➡ $33.75 ans.

Answer: 8.75

Step-by-step explanation:

i got it wrong this is what the test showed as the real answer

29.9.2+ n+ 8.4 = 20.8
Please help

Answers

Answer:

n=6.42

Step-by-step explanation:

Following the steps for this equation.

Answer:

29.9.2+

Step-by-step explanation:

That should be right

A local Little league has a total of 60 players, 80% of whom are right-handed. How many right-handed players are there?
(Please answer step by step.)

Answers

Answer:

48 right-handed players

Step-by-step explanation:

first, make an equation

[tex]\frac{80}{100} =\frac{x}{60}[/tex]

then, cross multiply and the new equation is

[tex]100x=4800[/tex]

finally, divide by 100 on both sides to isolate the x and you get

x=48

Hailey is going to use a computer at a Internet cafe. The cafe charges $1.50 for every minute using a computer on top of an initial charge of $4. Make a table of values and then write an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the Internet cafe.

Answers

Answer:

The equation is C(t) = 1.50t + 4.00 and the data table is below.

Step-by-step explanation:

We are given that a cafe charges $1.50 for every minute that someone uses the internet. The cafe also charges an initial $4 fee to use the internet.

We need to find a function, in terms of t, that will find these values.

We can treat this as a linear equation. If we initially pay $4, this is acquired before we pay the fee every minute. Therefore, this would be our y-intercept at x = 0. Our first coordinate is (0, 4).

Secondly, if we are charged every minute, this would be a recurring payment and therefore we would spend $1.50 after each minute elapses. This gives us our slope: 1.50 or [tex]\frac{3}{2}[/tex].

Therefore, we can set up our function.

C is the total cost and t is the time, in minutes, that internet is used at the cafe. Our equation can be set up as [tex]C(t) = 1.50t + 4.00[/tex].

Now, we can create a table of values for t = 0 to t = 5 to determine what C(t) is at each of these prime intervals.

[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{C} & \textbf{t} \\ \cline{1-2} a & 0 \\ \cline{1-2} b & 1 \\ \cline{1-2} c & 2 \\ \cline{1-2} d & 3 \\ \cline{1-2} e & 4 \\ \cline{1-2} f & 5 \\ \cline{1-2} \end{array}[/tex]

This is what our table looks like, but we need to fill the C column. Therefore, we can use substitution of our t-values into the equation and solve for C.

[tex]\bullet \ \text{For t = 0,}[/tex]

[tex]C(0) = 1.50(0) + 4\\\\C(0) = 0 + 4\\\\C(0) = 4.00[/tex]

[tex]\bullet \ \text{For t = 1,}[/tex]

[tex]C(1) = 1.50(1) +4\\\\C(1) = 1.50 + 4\\\\C(1) = 5.50[/tex]

[tex]\bullet \ \text{For t = 2,}[/tex]

[tex]C(2) = 1.50(2) + 4\\\\C(2) = 3.00 + 4\\\\C(2) = 7.00[/tex]

[tex]\bullet \ \text{For t = 3,}[/tex]

[tex]C(3) = 1.50(3) + 4\\\\C(3) = 4.50 + 4\\\\C(3) = 8.50[/tex]

[tex]\bullet \ \text{For t = 4,}[/tex]

[tex]C(4) = 1.50(4) + 4\\\\C(4) = 6.00 + 4\\\\C(4) = 10.00[/tex]

[tex]\bullet \ \text{For t = 5,}[/tex]

[tex]C(5) = 1.50(5) + 4\\\\C(5) = 7.50 + 4\\\\C(5) = 11.50[/tex]

Now, we can insert these values into our table.

[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{C} & \textbf{t} \\ \cline{1-2} 4.00 & 0 \\ \cline{1-2} 5.50 & 1 \\ \cline{1-2} 7.00 & 2 \\ \cline{1-2} 8.50 & 3 \\ \cline{1-2} 10.00 & 4 \\ \cline{1-2} 11.50 & 5 \\ \cline{1-2} \end{array}[/tex]

Therefore, our equation is C(t) = 1.50t + 4.00 and our data table is above.

Find the area of the circle

Answers

If d = 12 the r = 6

3.14 * 6^2
3.14 * 36
113.04

Mrs. Garcia deposited $2500 into a new bank account. The bank pays 1.5% interest compounded annually on this account. She makes no additional deposits or withdrawals. How much is in her account at the end of 2 years?

Step-by-step explanation pls! :)

Answers

Answer:

$2575.5625

Step-by-step explanation:

2500*(1.015)^2

=$2575.5625

PLS GIVE BRAINLIEST

1st Year 2500*1.015=2537.5

2nd Year 2537.5*1.015=2575.5625

What type of sequence do these figures belong?​

Answers

Answer:

what figures? pls share the picture of the figures

Step-by-step explanation:

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