Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers to four decimal places.) (8.99)3 using differentials

Answers

Answer 1

Answer:

726.572699

Step-by-step explanation:

According to differentials

(x+Δx)³ = x³ + 3x²Δx + 3x(Δx)² + (Δx)³ (Using binomial expansion)

Using this formula to solve (8.99)³, this can also be written as;

(8.99)³ =  (9-0.01)³ where

x = 9

Δx = -0.01

Substitute this vales into the differential expression above

(9+(-0.01))³ = 9³ + 3(9)²(-0.01) + 3(9)(-0.01)² + (-0.01)³

(9+(-0.01))³ = 729 + (243)(-0.01) + 27(0.0001) + (-0.000001)

(9+(-0.01))³ = 729-2.43+0.0027-0.000001

(9+(-0.01))³ = 729-2.43+0.0027-0.000001

(9+(-0.01))³  = 726.572699

Hence 8.99³ = 726.572699 (Using differential)

Using calculator;

8.99³ = 726.572699


Related Questions

Last week Carlos spent 3 1/2 hours practicing piano. This was 1/3 the amount of time he spent reading. How long did Carlos spend reading last week?

Answers

Answer:

3 1/2 = 210 minutes

1/3 * 210 = 70 minutes = 1 hour and 10 minutes

Thank you and please rate me as brainliest as it will help me to level up

On solving the linear equation 3.5 = x/3 , we get that the time Carlos spent on reading last week was x= 10.5 hours

What is an linear equation in one variable?

Linear equation is an equation containing one unknown variable with power one and constants.

The standard form of an linear equation in one variable x is :

ax + b = 0 , where a, b are constants

x= -b/ a is solution if this equation or we can solve this equation by adding or subtracting , multiplying or dividing by same number to both sides.

Let Carlos spent x hours reading last week

Given that last week the time that Carlos spent practicing piano for 3 1/2 hours = 7/2 hours = 3.5 hours

Time spent on practicing piano = 1/3 ( time spent on reading)

3.5 = (1/3) x

Multiply both sides by 3

⇒ 3.5 ×3 =3×(1/3)x

⇒10.5 = x

Therefore, the time spent by Carlos on reading last week is 10.5 hours.

Also, learn more about linear equation from the link below:

https://brainly.com/question/24145091

#SPJ2

PLEASE HELP!!!

DUE IN AN HOUR!!!

Answers

Answer:

Don't cheat u cheater...

Lae bought grapes for $1.50 per pound.

Answers

Answer:

Where is the question or is that it?

1.Use the numbers in the table to create

Ordered pairs

2.Pounds are graphed on the x - axis

3.Plot the ordered pairs on the graph

4.Draw a straight line that starts at the origin and connects all the points

Leila bought 3 bananas, which weighed a total of 3/4 of a pound . if each banana weighed the same amount , what is the weight of each banana ?​

Answers

Answer:

1/4

Step-by-step explanation:

3/4 (total weight)

3 bananas

(3/4)/3=1/4

PLS GIVE BRAINLIEST

Which of the following functions has the function rule y=x+4? (-2, 2), (-1,-5), (3.7)} {(-3, 1), (0.4), (2. 6)) (12.6). (-3.-7), (0.4) (0.2).(-2,-6). (1.5))​

Answers

Answer:

b. {(-3, 1), (0, 4), (2, 6)}

Step-by-step explanation:

I suck at math I need help

Answers

Answer:

74° is the answer

In the triangle

112°+33°+a=180. (sum of angles of triangle)

a=180-145

a=35°

a+b+71°=180. (linear pair)

35°+b+71°=180

b=180-106

{b= 74°}

You may use any notes from class or past assignments on this assessment. You may also use a
calculator. You may not look up any answers on the internet or use anyone else's work.
1.
The equation m=40g gives the distance in miles, m, that a car can travel using g gallons
of gas.
a. If the car has gone 140 miles, how much gas was used?
b. Write an equation that represents the inverse function: the gallons of gas as a
function of distance in miles.
Function C is defined by the equation cov) = 50 + 4y It mives the month con

Answers

Part a is 3.5 gallons

What is the surface area in square inches of a cube with a side 7 inches long? HEL0 QUICK​

Answers

Answer: a = 294 square inches

Use the formula: A = 6a^2

Answer:

294

Step-by-step explanation:

A=6x²

A=6*7²

A=6*49

A=294

Rudy has been paying an annual homeowners insurance premium of $1,106.30 ($0.37 per $100 of value) since

he first purchased his house. For the past six months, Rudy has completed some major improvements to his

house to improve its overall value. If Rudy successfully adds $50,000 to the value of his house, what will his new

annual homeowners insurance premium be?

a. $185.00

b. $315.00

c. $1,291.30

d. $1.351.14

Please select the best answer from the choices provided

Answers

Answer:

c. $1,291.30

Step-by-step explanation:

Calculation what will his new annual homeowners insurance premium be

Insurance premium= [$1,106.30+ ($0.37/ $100*$50,000)]

Insurance premium=$1,106.30+$185

Insurance premium=$1,291.30

Therefore what his new annual homeowners insurance premium will be is $1,291.30

Answer:

c

Step-by-step explanation:

edge 2021

Diego lives 1/2 miles from school.What is 50% of 1/2

Answers

Answer:

0.25

Step-by-step explanation:

Does this graph show a function? Explain how you know.

A. No, there are yvalues that have more than one x-value.

B. Yes, there are no yvalues that have more than one x-value

C. Yes, the graph passes the vertical line test. PREVIOUS

D. no the graph fails the vertical line test

Answers

Answer:

D. no the graph fails the vertical line test

[solved] These Cylinders are similar. Find the volume of the smaller cylinder. Round to the nearest tenth. (the answer is 84.9 cm^3)

Answers

Answer:

84.9 cm³

Step-by-step explanation:

Height of the bigger Cylinder = 5 cm

Volume of the bigger Cylinder = 393 cm³

Height of the smaller cylinder = 3 cm

Volume of the smaller cylinder = x cm³

Since they are similar, therefore: the cube of their ratio would equal the ratio of their volume.

Thus:

[tex] (\frac{5}{3})^3 = \frac{393}{x} [/tex]

[tex] \frac{125}{27} = \frac{393}{x} [/tex]

Cross multiply

[tex] 125*x = 393*27 [/tex]

[tex] 125x = 10,611 [/tex]

Divide both sides by 125

[tex] \frac{125x}{125} = \frac{10,611}{125} [/tex]

[tex] x = 84.888 [/tex]

Volume of the smaller cylinder = 84.9 cm³ (to nearest tenth?

Jose uses 1/5 cup of red paint for every 3/5 cup of blue paint to make purple paint. Enter the number of cups of red paint Evelyn uses for 1 cup of blue paint.
Please help this is due tomorrow!!

Answers

1/3 red cups in order to use 1 blue cup of paint

write -90 in simplest radical form
please help or i’ll failll

Answers


Search Results
Featured snippet from the web

Simplest radical form means simplifying the radical such that there are no square roots ,cube roots ,etc to find. When simplifying a fraction, if there is a radical, should it always be a numerator?

Find the equation of the line.
6
The line is parallel to y =--x + 1 and passes through the point (-7, -3).
7
The equation of the line is

Answers

Answer:

y = - x - 10

Step-by-step explanation:

y - (- 3) = - (x + 7)

y = - x - 10

A scientist is filling beakers of water for an experiment. He begins with 3 liters of water in a large container and each beaker holds 2/5 of a liter of water. How many beakers can the scientist fill?

Answers

Answer:

just looking for free point..

Step-by-step explanation:

For homework, a student had to complete 54 problems total. If she finished 9 problems in
class, what is the ratio of problems she still needs to complete to problems that she's
already finished?

Answers

Answer:

10

Step-by-step explanation:

Answer:

45:9

Step-by-step explanation:

5
y=2x+5y, equals, 2, x, plus, 5
Complete the missing value in the solution to the equation.
(
2
,

Answers

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

[tex]y = f(x) = 2x + 5[/tex]

[tex]f(2) = 2(2) + 5[/tex]

[tex]f(2) = 4 + 5[/tex]

[tex]f(2) = 9[/tex]

Thus ;

[tex]( \: 2 \: , \: 9 \: )[/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

9

Step-by-step explanation:

chen is baking muffins and banana bread for brunch buffet. he needs 3 1/5 cups of flour to make the muffins and 3 2/3 cups of flour to make the banana bread. which is the best estimate of the number of cups of flour needed​

Answers

Answer:

I think 7 would be the estimate if im wrong this is the specific number 6 13/15

Step-by-step explanation:

Answer:

She will need aproximately 7 cups

Step-by-step explanation:

First, you add 3 1/5 and 3 2/3 which is 6.86666666667

Just round that answer up and that'll give you seven

The length of the rectangle is 3ft less than twice the width,and the area of the rectangle is 27ft^2,find the diameter

Answers

Answer:

The dimensions of rectangle are:

width = w = 4.5 ftlength = l = 6 ft

Step-by-step explanation:

Let 'l' be the length and 'w' be the width of the rectangle

The length 'l' of the rectangle is 3ft less than twice the width 'w'.

so

[tex]l=2w-3[/tex]

Also, the area of the rectangle is 27ft^2.

[tex]A=27\:ft^2[/tex]

As the area of the rectangle has the formula:

[tex]\:A\:=\:l\times w[/tex]

so

[tex]27=\:l\times w[/tex]

so the equation becomes

[tex]27=\left(2w-3\right)\times \:w[/tex]

[tex]27=2w^2-3w[/tex]

[tex]2w^2-3w-27=0[/tex]

[tex]\left(w+3\right)\left(2w-9\right)=0[/tex]

if   [tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]

[tex]w+3=0\quad \mathrm{or}\quad \:2w-9=0[/tex]

[tex]w=-3,\:w=\frac{9}{2}[/tex]

as the width can not be negative, so

[tex]w=\frac{9}{2}=4.5[/tex] ft

As

[tex]l=2w-3[/tex]

[tex]l=2\left(4.5\right)-3[/tex]

[tex]l=9-3[/tex]

[tex]l=6[/tex]

So the dimensions of rectangle are:

width = w = 4.5 ftlength = l = 6 ft

80% of teenagers have access to some social media . If you do a random survey of 400 teenagers, what is the probability that between 300 and 340 of them will patronize it.

Answers

Answer:

P(300 < p^ < 340) = 0.9876 or 98.76%

Step-by-step explanation:

We are given;

Population proportion; p = 80% = 0.8

Sample proportion; p1^ = 300/400 = 0.75 and p2^ = 340/400 = 0.85

Sample size: n = 400

z-score formula for sample proportion is;

z = (p^ - p)/(√(p(1 - p)/n)

Thus;

z1 = (0.75 - 0.8)/(√(0.8(1 - 0.8)/400)

z1 = -0.05/0.02

z1 = -2.5

z2 = (0.85 - 0.8)/(√(0.8(1 - 0.8)/400)

z2 = 0.05/0.02

z2 = 2.5

From online calculator of probability between 2 z-scores, we have;

P(-2.5 < z > 2.5) ≈ 0.9876

Find the m ULE in the triangle below.
L

109
RU

E49

Find the m ULE. Plzzzzz help hurry

Answers

m ULE is 60 degrees.
The sum of the angles inside a triangle is 180 degrees. Also don’t forget that the sum of supplementary angles is 180.

Twice the sum of a number and 6 is
more than 84.

Answers

Answer:

Step-by-step explanation:

yth ok

What is the sum of -2/3 and -4/6?
A. -4/3
B. -2/3
C. 2/3
D. 4/3

Answers

Answer:

A

Step-by-step explanation:

-2/3 = -4/6, -4/6 + -4/6 = -8/6 = -4/3

Answer: D. -4/3

Step-by-step explanation:

-2/3 + -4/6

make the denominators the same

so -2 * 2 and 3 * 2 = -4/6

-4/6 + -4/6 = -8/6 = -4/3

please someone help me out on this

Answers

Answer:

Step-by-step explanation:

28

Answer:

27⁰

Step-by-step explanation:

angles on a straight line add up to 180⁰

180-(39+86+28)=YVZ

three less than the sum of a number and
twelve

Answers

Answer:

(x + 12) - 3

Step-by-step explanation:

I used x for "a number".

Hope this helps and pls do mark me brainliest:)

Mitchell walked 5/12 of a mile in 1/2 of an hour. At this rate, how far could Mitchell walk in 1 hour?

Answers

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[tex]2 \times \frac{1}{2} hour = 1hour \\ [/tex]

Thus ;

[tex]2 \times \frac{5}{12} \: \: miles = \frac{10}{12} \: \: miles = \frac{5}{6} \: \: miles \\ [/tex]

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I think the answer is 5/6

[(15 x 3) + 3] = (12-6) = N​

Answers

Answer:

45+3 = 6=N

48_6= N

42= N

:. N= 42

Step-by-step explanation:

:. N= 42

Answer:

did you mean to put 2 equal signs in this?

Step-by-step explanation:

that would make this false because the first part equals 48 and the second equals 6 and since 48 doesn't equal 6 this is a false statement

There are stars to circle there are 4 stars and 2 circles how much is the ratio

Answers

Answer:

2:1

Step-by-step explanation:

The original ratio is 4:2. Divide both sides by 2. Then you get 2:1.

Answer:2 stars for every one circle

Step-by-step explanation:

hope you get what i mean if not sorry my friend

x - -13 = 11 PLEASE HELP

Answers

Answer:

the answer is -2 because -(-13) translates to 13 and -2+13=11

(can I get brainliest)

Answer:

The answer is x = -2!

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