Use the following graph to estimate the rate of change of the function at x=0.6 using the points (0,0) and (1,−0.5)

Use The Following Graph To Estimate The Rate Of Change Of The Function At X=0.6 Using The Points (0,0)

Answers

Answer 1

Answer:

The rate of change of the function at x = 0.6 is approximately -0.72

Step-by-step explanation:

The given information from the graph are;

Points (0, 0) and (1, -0.5)

We have that the graph is that of a cubic function, therefore;

f(x) = ax³ + bx² + cx + d

At f'(x) at  (0, 0) and (1, -0.5) = 0 gives;

3ax² + 2bx + c = 0

∴ c = 0

Also

ax³ + bx² + cx + d = 0

d = 0

We have

3a(1)² + 2b(1) + 0 = 0

3·a + 2·b = 0..............(1)

a(1)³ + b(1)² + c(1) + d = -0.5

a + b + 0×(1) + 0 = -0.5

a + b = -0.5..........(2)

Multiplying equation (2) by 2 and subtracting it from equation (1) gives;

2 × (a + b = -0.5) = 2·a + 2·b = -1

3·a + 2·b - (2·a + 2·b) = 0 - (-1) = 0 + 1 = 1

a = 1

From

a + b = -0.5, we have;

1 + b = -0.5 = 0

b = -0.5 - 1 = -1.5

The equation becomes

f(x) = x³ - 1.5·x²

The rate of change of the function at x = 0.6 is therefore given as follows;

f'(x) = 3 × x² - 2 × (1.5)·x = 3·x² - 3·x

At x = 0.6, we have;

f'(0.6) = 3·(0.6)² - 3·(0.6)

f'(0.6) = 3×0.6² - 3×0.6 = -0.72

The rate of change of the function at x = 0.6 ≈ -0.72


Related Questions

Is this statement true or false?
4 [3(5 + 2)] = 95 – 4.3
true
false

Answers

Answer:

The answer is false it’s supposed to be 84

Step-by-step explanation:

This would be false because the a swear is 63 and 95 minus 4.5 is 90.5

What is -2(x + 3 ) = -2x-6

Answers

Answer:

0 = 0 (infinite solutions)

Step-by-step explanation:

-2(x+ 3) = -2x - 6

Multiply -2 to x and 3

-2x -6 = -2x - 6

Add 2x on one side to get zero, and add 6 to the other side to get 0

0 = 0

There are infinite solutions

25 more than 8 times a number is the same as 50 less than the product of -5 and the number.

Answers

Answer:

-5x-50=8x+25 solve that

13x= -75

-5.769

Step-by-step explanation:

Your answer should be a polynomial in standard form.

(q^2-2q+5)(q^2-5)=

Answers

Answer:

q⁴ - 2q³ + 10q - 25

Step-by-step explanation:

Step 1: Write out expression

(q² - 2q + 5)(q² - 5)

Step 2: Distribute

q⁴ - 2q³ + 5q² - 5q² + 10q - 25

Step 3: Combine like terms

q⁴ - 2q³ + 10q - 25

I am doing math homework and need some assistance solving, 2(2t+4)=3/4(24-8t)

Answers

Answer:

They are equal

Step-by-step explanation:

If you do 2 plus 4 in the parentheses then that equals 6 and 6t time 2 is 12t because the t doesnt have a value therefore it sticks onto the answer and if you convert the 3/4 into .75 then you can subtract the 24 by 8t and get 16 then when you multiply the 16 by 3/4 it will take .75 off of 16 and the answer is the same therefore they are equal equations.  

3x(x+30°) i really need help asap

Answers

A13x2+390x here is the answer

Answer:

x=15

Step-by-step explanation:

Simplifying

x + 30 = 3x

Reorder the terms:

30 + x = 3x

Solving

30 + x = 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

30 + x + -3x = 3x + -3x

Combine like terms: x + -3x = -2x

30 + -2x = 3x + -3x

Combine like terms: 3x + -3x = 0

30 + -2x = 0

Add '-30' to each side of the equation.

30 + -30 + -2x = 0 + -30

Combine like terms: 30 + -30 = 0

0 + -2x = 0 + -30

-2x = 0 + -30

Combine like terms: 0 + -30 = -30

-2x = -30

Divide each side by '-2'.

x = 15

Simplifying

x = 15

f - 18 > 92

I need help fast​

Answers

Answer:

F>110

Step-by-step explanation:

how do I simplify 3⁶ x 3⁵​

Answers

Answer:

[tex]3^{11}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex] thus

[tex]3^{6}[/tex] × [tex]3^{5}[/tex] = [tex]3^{(6+5)}[/tex] = [tex]3^{11}[/tex]

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ {3}^{11} }}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ {3}^{6} \times {3}^{5} }[/tex]

Add the indices and take the same base

[tex] \dashrightarrow{ \sf{ {3}^{6 + 5} }}[/tex]

[tex] \dashrightarrow{ \boxed{ \sf{ {3}^{11} }}}[/tex]

Hope I helped!

Best regards! :D

arun had 50 rupees if he had spent 3 by 5 of his money on an alarm clock how much money is he left with him

Answers

Answer:

total money=rupees 50

3/5 of 50= rupees 30

money he spent = rupees 30

money he's left with =50-30=20

mark this as brainliest!!!!

pls follow me!!

Answer:

Step-by-step explanation:

like u told me social studis

<3

For questions 1 - 6, solve each quadratic equation.
1. (x + 5)(x - 2) = 0
2. (3x - 1)(2x + 5) = 0
3. x^2-3x -4 = 0
4.2x^2 -5x - 3 = 0
5. x^2 - 16 = 0
6.9x^2 - 25 = 0

Answers

Answer:

1. -5

2. 1/3 (1 third)

3. -3

4. -1\2 (negative one and a half)

5.-4

6. 1.66666

Step-by-step explanation:

1.  Let's solve your equation step-by-step. ( x + 5 ) ( x − 2 ) = 0 Step 1: Simplify both sides of the equation. x 2 + 3 x − 10 = 0 Step 2: Factor left side of equation. ( x − 2 ) ( x + 5 ) = 0 Step 3: Set factors equal to 0. x − 2 = 0 or x + 5 = 0 x = 2 or x = − 5.        <—— this is for the first explanation

2. Step 1: Simplify both sides of the equation. 6 x 2 + 13 x − 5 = 0 Step 2: Factor left side of equation. ( 3 x − 1 ) ( 2 x + 5 ) = 0 Step 3: Set factors equal to 0. 3 x − 1 = 0 or 2 x + 5 = 0 x = 1 3 or x = − 5 2 Answer: x = 1 3 or x = − 5 2

<———— this is for the second explanation

3.Step 1: Factor left side of equation. ( x + 1 ) ( x − 4 ) = 0 Step 2: Set factors equal to 0. x + 1 = 0 or x − 4 = 0 x = − 1 or x      

<———- this is for the third explanation

4.Step 1: Factor left side of equation. ( 2 x + 1 ) ( x − 3 ) = 0 Step 2: Set factors equal to 0. 2 x + 1 = 0 or x − 3 = 0 x = − 1 2 or x = 3

<—————- this is for the fourth explanation

5. Step 1: Add 16 to both sides. x 2 − 16 + 16 = 0 + 16 x 2 = 16 Step 2: Take square root. x = ± 16 x = 4 or x = − 4

<—————- this is for the fith explanation

6. Step 1: Add 25 to both sides. 9 x 2 − 25 + 25 = 0 + 25 9 x 2 = 25 Step 2: Divide both sides by 9. 9 x 2 9 = 25 9 x 2 = 25 9 Step 3: Take square root. x = ± 25 9 x = 1.666667 , − 1.666667

<—————- this is for the sixth explanation

Hope this helps :)

what is the probability that jenny rolls a double 1​

Answers

Answer:

1/36

Step-by-step explanation:

Assuming that there are 2 dice

There are 36 possible outcomes ( 6*6)

There is only one way to get 2 ones

P ( 1,1) =  positive outcomes / total

          =1/36

The product (x + 3y)(3x – y) =

Answers

Answer: 3x²-3y²+8xy

Step-by-step explanation:

When you multiply two factors, you want to use the FOIL method.

First

Outer

Inner

Last

(x+3y)(3x-y)                  [distribute by FOIL]

3x²-xy+9xy-3y²            [combine like terms]

3x²+8xy-3y²                 [rewrite]

3x²-3y²+8xy

Now, we know the product is 3x²-3y²+8xy.

I NEED HELP ASAP!!!

you pay 9.70 for 2.5 pounds of roasted peanuts. You buy 1.4 pounds of almonds for 8.55 per pound.

How much less do roasted peanuts cost per pound than almonds?

How much more do you spend on almonds than on roasted peanuts.

Answers

$9.70 / 2.5lbs = $3.88 / pound of roasted peanuts.

$8.55 * 1.4lbs = $11.97 / 1.4 pounds of almonds

$8.55 - $3.88 = $4.67.

Roasted peanuts cost $4.67 less per pound than almonds.

$11.97 - $9.70 = $2.27

You spend $2.27 more on almonds than you do roasted peanuts.

One week, Caroline earned $183.20 at her job when she worked for 8 hours. If she is paid the same hourly wage, how much would she make the next week if she worked 13 hours?

Answers

Answer:

$297.70

Step-by-step explanation:

First, find her hourly wage:

183.20/8

= 22.9

Then, multiply this by 13:

22.9(13)

= 297.7

So, she will make $297.70 next week

Answer:

297.70

Step-by-step explanation:

Read the pdf named "Brain"

Please help me understand
How to go from a percent to a decimal and please put an explanation and example. If you do not know the answer then don’t respond. I really need to understand this! Please

Answers

Divide a percent by 100 and remove the percent sign to convert from a percent to a decimal. The shortcut way to convert from a percentage to a decimal is by removing the percent sign and moving the decimal point 2 places to the left.

example: 3.25% = 3.25 over 100 or,
3.25%=3.25100
3.25
%
=
3.25
100
3.25 over 100 is the same as 3.25 divided by 100. Completing the division we get:

3.25 ÷ 100 = 0.0325

Therefore, we have shown that

3.25% = 0.0325

Example :When we divide 50 by 100 we get 0.5 (a decimal number). So, to convert from percent to decimal: divide by 100, and remove the "%" sign.

Jenna's retirement party will cost $9 if she invites 3 guests. If there are 5 guests, how much will Jenna's retirement party cost? Assume the relationship is directly proportional.

Answers

Answer:

$15

Step-by-step explanation:

3 guest = $9 (9/3 = 3 so each guest is $3)

so

5 guest = $15    (3 x 5 = 15)

tyrone walked 8 miles in a walkathon at a speed of 2 mph how long was he walking

Answers

Answer:

4 hours

Step-by-step explanation:

Distance / Velocity = Time

In this case, 8 / 2 = 4

pt=3x9 and tq=5x-7 because i have no idea what it is

Answers

Answer:

i have the same question on my worksheet

Step-by-step explanation: its super hard need help too

Help me plz !!!!!!!!!!!!!!!!!!!!!

Answers

I believe it is 30% decrease

Answer:

letter b. 30% decrease

Find all the zeros of the quadratic function.
y=x²-11x+18

Answers

Y= (X-9)(x+2)
X=9
X=-2

A) The sum of 5 and 2 times p is at least 11.

Answers

5 + 2p is at least 11.

Subtract 5 from both sides.

2p is at least 11.

p > 5

help‼️✌⛓✌

also please try to answer as soon as possible​

Answers

Answer:

do this then this then that and your done :D

Step-by-step explanation:

hope this helps :))

x+2/2x+3=y+1 rearrange and make x the subject

Answers

Answer:

x = y/2 - 1

Step-by-step explanation:

Solve for x:

2 x + 3 = y + 1

Hint: | Isolate terms with x to the left hand side.

Subtract 3 from both sides:

2 x = y - 2

Hint: | Solve for x.

Divide both sides by 2:

Answer: x = y/2 - 1

if Kyle's terrarium had a volume of 64 ft3 ,what would the edge length be?

Answers

Answer:

4 ft

Step-by-step explanation:

Volume of a cube = [tex]x^{3}[/tex] (where x equals the side/edge length)

V = [tex]x^{3}[/tex]

64 = [tex]x^{3}[/tex]

64 divided by 3 = 4 ft

The speed of a car traveling on a straight road increases from 63 m/s to 75
m/s in 4.2 seconds. What was the car's acceleration? m/s2 = meters per
second squared

Answers

Answer :

Initial velocity = 63m/s

Final velocity = 75m/s

Time taken = 4.2

We have to find acceleration of car[tex].[/tex]

_________________________________

◈ Acceleration is defined as the rate of change of speed.

a = (v - u) / t

It is a vector quantity having both magnitude as well as direction.

SI unit : m/s²

⇒ a = (v - u) / t

⇒ a = (75 - 63) / 4.2

⇒ a = 12/4.2

⇒ a = 2.85 m/s²
Question:

The speed of a car traveling on a straight road increases from 63 m/s to 75 m/s in 4.2 seconds. What was the car's acceleration?

Answer:

[tex] \rm\red {Given:} [/tex]

u ( initial velocity ) = 63m/s

v ( final velocity ) = 75m/s

t ( time taken ) = 4.2s

[tex] \rm\red {To \: find:} [/tex]

a ( acceleration ) =?

[tex] \rm\red {Calculation:} [/tex]

We know that,

[tex] {\huge {\boxed {\tt { a = \dfrac{v-u} {t}}}}} [/tex]

Substituting values-

[tex] \sf { \qquad \leadsto a = \dfrac{75-63}{4.2}} [/tex]

[tex] \sf { \qquad \leadsto a = \dfrac{12}{4.2}} [/tex]

[tex] \sf { \qquad \leadsto a = \dfrac{\cancel {12} {} ^{\: \: 6} \times 10}{\cancel {42} {} ^{\: \: 21} }} [/tex]

[tex] \sf { \qquad \leadsto a = \dfrac{\cancel6 {} ^{\: \: \: 2}\times 10 }{\cancel {21} {} ^{\: \: 7}}} [/tex]

[tex] \sf { \qquad \leadsto a = \dfrac{2 \times 10}{7}} [/tex]

[tex] \sf { \qquad \leadsto a = \dfrac{20}{7} = 2.85} [/tex]

[tex] \therefore [/tex] Acceleration of the car was [tex] \sf { 2.8m/{s} ^{2}} [/tex]

_________________________________

GEOMETRY HELP!!

19. What is the coordinate of the midpoint of the segment formed by the two points you found in Exercises 17 and 18?

Please explain

Answers

Answer:

0

Step-by-step explanation:

To find the coordinate of the midpoint of segment QB, first, find the distance from Q to B.

QB = |4 - 8| = |-4| = 4

The coordinate of the midpoint of QB would be at ½ the distance of QB (½*4 = 2).

Therefore, coordinate of the midpoint of QB = the coordinate of Q + 2 = 4 + 2 = 6

OR

Coordinate of B - 2 = 8 - 2 = 6

Coordinate of the midpoint of QB = 6

Coordinate of W = -8

Coordinate of A = 0

distance from W to A (WA) = |-8 - 0| = |-8| = 8

The coordinate of the midpoint of WA would be at ½ the distance of WA = ½*8 = 4.

Therefore, coordinate of the midpoint of WA = the coordinate of W + 4 = -8 + 4 = -4

Or

Coordinate of A - 4 = 0 - 4 = -4

Coordinate of the midpoint of WA = -4

Now, let's find the midpoint between the two new coordinates we have found, which are -4 and 4

Distance of the segment formed by coordinate -4 and 4 = |-4 - 4| = |-8| = 8

Midpoint = ½*8 = 4

Coordinate of the midpoint = -4 + 4 = 0

Or

4 - 4 = 0

Which of these graphs do not represent constant rates of change? Check all that apply

Answers

the first and last graph

Answer:

A and B

Step-by-step explanation:

A boy flying a kite lets out 300 feet of string. The height of the kite is 185 feet. What is the angle
formed between the string and the ground?

Answers

Answer:

The string, the height and the ground form a right triangle

The hypotenuse = 300

height =185 = opposite side

sine of the angle = 185 / 300 = 0.6166666667

arc sine (.616666666666) =

38.073 degrees

Step-by-step explanation:

A candy factory has 2 machines that make pieces of candy. Machine A makes 984 pieces of candy
every 6 hours. Machine B makes 1,296 pieces of candy every 8 hours.
Which statement best compares the machines?
Machine B makes candy faster than machine A because machine B made more candy.
Machine A makes candy faster than machine B because machine A took less time.
Machine B makes candy faster than machine A because machine B made more pieces of
candy per hour.
Machine A makes candy faster than machine B because machine A made more pieces of
candy per hour.

Answers

It would be D final answer there’s 2 machines for A so it’s easily over 1800+ candy therefore we can conclude that machine A is faster

What is the simplest form of 63/91

Answers

Answer:

Step-by-step explanation:

9/13

divide them by 7

9/17
Divide by 7., okzd
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