Given k > 3 and
( +
2x+2) dx = 10k
show that k3 – 10k2 + ak + b = 0
where a and bare constants to be found.
Answers
Answer:
See Below.
Step-by-step explanation:
We are given that:
[tex]\displaystyle \int_3^k\left(2x+\frac{6}{x^2}\right)\, dx = 10k, k>3[/tex]
And we want to show that:
[tex]k^3-10k^2+ak+b=0[/tex]
Integrate the definite integral:
[tex]\displaystyle x^2-\frac{6}{x}\Big|_{3}^{k}=10k[/tex]
Evaluate:
[tex]\displaystyle \left(k^2-\frac{6}{k}\right)-((9)-(2))\right)=10k[/tex]
Simplify:
[tex]\displaystyle k^2-\frac{6}{k}-7=10k[/tex]
Multiply both sides by k:
[tex]k^3-6-7k=10k^2[/tex]
Rewrite:
[tex]k^3-10k^2-7k-6=0[/tex]
Hence, a = -7 and b = -6.
Related Questions
Mr. Carr is hiring a plumber to repair his sink. The cost of Plumber T is shown in the table.
A table titled Plumber T Costs is shown. It has three columns and two rows. Row one is labeled Hours, h. Row two is labeled Cost, c. One hour, one hundred twenty-eight dollars. Two hours, two hundred fifteen dollars. Three hours, three hundred two dollars.
Part A. What is the initial cost and hourly rate of Plumber T?
Part B. Write an equation to represent the function shown in the table.
Part C. Plumber W charges $95 per hour and an additional $32 for the parts needed. What is the difference in cost between Plumber W and Plumber T if the repair Mr. Carr needs takes 5 hours?
Enter the correct answers in the boxes.
A. Initial cost: $
Rate per hour: $
B. Equation:
C. Difference in cost: $
Answers
The hourly rate of plumber T is $87 per hour and have an initial cost of $41.
Linear equationLinear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial amount.
From the table, using points (1, 128) and (2, 215):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-128=\frac{215-128}{2-1}(x-1)\\ \\y= 87x+41[/tex]
The hourly rate of plumber T is $87 per hour and have an initial cost of $41.
Find out more on Linear equation at: https://brainly.com/question/14323743
Answer:
Initial cost: $ 41
Rate per hour: $87
Equation: y=87x+41
Step-by-step explanation:
Sorry I do not know the difference in cost.
The transportation department predicts that about 800,000 cars will be registered in a certain state by year 2012. Their license plates are made using and two letters followed by and three digits from 0 to 9. Will there be enough possible arrangements?
Answers
Answer:
There won't be enough arrangement
Step-by-step explanation:
Given
[tex]Letters = 2[/tex]
[tex]Digits= 3[/tex]
[tex]Cars = 800000[/tex]
Required
Determine if the possible arrangement will be enough
The 2 letters can be selected from any of the 26 alphabets without restriction.
So, the selection of letters is:
[tex]Letters = 26 * 26[/tex]
The 3 digits can be selected from any of the 10 digits without restriction.
So, the selection of digits is:
[tex]Digits = 10*10*10[/tex]
The total arrangement is:
[tex]Total = Letters * Digits[/tex]
[tex]Total = 26*26*10*10*10[/tex]
[tex]Total = 676000[/tex]
By comparison:
[tex]Total < Cars[/tex]
i.e.
[tex]676000 < 800000[/tex]
Hence, the arrangement will not be enough
If on a triangle, angle A is 5x, B is 4X, and C is
3x, what is the measurement for each angle.
Answers
Answer:
A=75, B=60, C=45
Step-by-step explanation:
5x+4x+3x=180
12x=180
x=15
plug them in and get
A=5(15)=75
B=4(15)=60
C=3(15)=45
What is the following product of the cube root of 16 X to the seventh times the cube root of 12 X to the ninth
Answers
Answer:
7
Step-by-step explanation:
hi I don't know what to do
How do I find the angles
Answers
Answer:
if there smaller than 90 degrees then it's acute if the angle is bigger then 90 degrees it's obtuse
Step-by-step explanation:
convert 8m 32 cm into centimeters
Answers
Answer:
832 cm one meter us equal to 100 cm so 8 multiply 100 plus 32 is equal to 832
What is the graph of y = x2 + 6x + 13 ?
What does the graph look like
Answers
Answer:
If I entered it in correctly it would look something like this,,
Type the correct answer in the box. Round your answer to the thousandth place.
The board of directors of a company knows that the probability that carbon emissions from the company’s factory exceed the permissible level is 35%. They hire a consultant who uses a carbon footprint calculator to test the emissions level. The accuracy of the test is 85%.
The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is
.
Answers
Answer:
The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place)
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Probability that carbon emissions from the company’s factory exceed the permissible level = 35% = 0.35
Accuracy of the test of emissions level = 85% = 0.85
2. The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is?
These two events, carbon emissions from the company’s factory and the accuracy of the test are independent events, therefore:
Probability that carbon emissions from the factory are within the permissible level = 1 - 0.35 = 0.65
Probability that the test predicts the opposite to be true = 0..35 * 0.85 = 0.2975 (The opposite is that the carbon emissions from the company exceed the permissible level)
Probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is:
0.65 * 0.2975 = 0.193375
The probability that carbon emissions from the factory are within the permissible level and the test predicts the opposite to be true is 19.338% (Rounding to the next thousandth place
MARK BRAINLIEST PLS
Solve the problem and enter your solution for the variable below. Do not include units in your answer. The scale below shows the weight, in grams, of two identical blocks. How many grams does one of the blocks weigh?
Answers
Answer:
1) 100+10+10 = 120
2) 120 : 2 = 60
1 block — 60
Answer by 11:59 today!!!
Answers
Answer:
x = 30
Step-by-step explanation:
These angles are all supplementary (they all add up to 180) so:
x + 3x + 2x = 180
6x = 180
x = 30
Gulliver tossed a coin 100 times and got 43 heads. What percent of the tosses where tails?
Answers
Answer:
53 %
Step-by-step explanation:
you have the percentage of 43% for heads and you subtract 43 from one hundred and you get 57%
Answer: 57%
Dont ask how but it is 57%
Im just like dat
What is the wall height for H??
Answers
Answer:
Step-by-step explanation:
Side "h" ( wall height ) is 35
The height of the wall "h".
Solution:-[tex]{\boxed{\mathcal{\red{The\:height\:of\:the\:wall\:"h"\:is\:35.71\:ft.}}}}[/tex]
Step-by-step explanation:[tex]\sf\purple{Using\:Pythagoras \:theorem, \:we\:have}[/tex]
[tex]( {Perpendicular})^{2} + ( {Base})^{2} = ( {Hypotenuse})^{2} \\ ➡ \: {h}^{2} + ({35 \: ft})^{2} = ({50 \: ft})^{2} \\ ➡ \: {h}^{2} + 1225 \: {ft}^{2} = 2500 \: {ft}^{2} \\ ➡ \: {h}^{2} = 2500 {ft}^{2} - 1225 \: {ft}^{2} \\ ➡ \: {h}^{2} = 1275 \: {ft}^{2} \\ ➡ \: h \: = \sqrt{1275 \: {ft}^{2} } \\ ➡ \: h = 35.707\: ft \: \\ ➡ \: h = 35.71\: ft[/tex]
[tex]\sf\red{Therefore\:the\:height\:of\:the\:wall\:"h"\:is\:35.71\:ft.}[/tex]
To verify :-[tex]( {35.71 \: ft})^{2} + ( {35 \: ft})^{2} = ({50 \: ft})^{2} \\ ✒ \: 1275 \: {ft}^{2} + 1225 \: {ft}^{2} \: = 2500 \: {ft}^{2} \\ ✒ \: 2500 \: {ft}^{2} = 2500 \: {ft}^{2} \\ ✒ \: L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
A camera shop purchases a camera for $56.98 and sells it for $102.56. What is the percent of markup?
180%
120%
80%
20%
Answers
Answer:
180%
Step-by-step explanation:
Set up an equation:
Variable x = percent of markup
102.56/56.98 = x/100
Cross multiply
102.56 × 100 = 56.98 × x
10,256 = 56.98x
Divide both sides by 56.98:
179.99297.... = x
Round to nearest whole number:
180 = x
Check your work:
56.98 × 180%
Convert the percentage into a decimal:
56.98 × 1.80
102.564
Round to nearest cent:
102.56
Correct!
u don’t have to explain
Answers
Answer:
6
Step-by-step explanation:
RQ=x
x/9=4/6
x=(9*4)/6
x=6
A box of Pop-tarts costs $3.00 for 8. How much per pop-tart?
Answers
the sum of two rational numbers is -5 if one of the number is -13/6 find the other number
Answers
Answer:
[tex]Let \ the \ number \ be = x\\sum \ of \ 2 \ rational \ numbers = -5\\\\x + \frac{-13}{6} = -5\\\\x - \frac{13}{6} = -5\\\\[/tex]
[tex]x = -5 + \frac{13}{6} = \frac{-30 + 13}{6} = -\frac{17}{6}[/tex]
The other rational number = -17/6
======================================================
Work Shown:
A = first rational number = -13/6B = second rational number = unknownA+B = -5 ... since the sum of both is -5
B = -5-A
B = -5-(-13/6)
B = -5+13/6
B = -30/6 + 13/6
B = (-30+13)/6
B = -17/6 is the answer
---------------
Extra info:
This improper fraction converts to the mixed number -2 & 5/6
In decimal form, it's approximately equal to -17/6 = -2.833
Someone please help I'm horrible at math :(
Answers
Answer:
6
Step-by-step explanation:
The verticle line in the box is the median
If Jayna's shuffler is working properly and randomizing the playlist after each song, what is the probability of playing a slow song?
ANSWER IS 33.33%
Answers
Answer:
1 song is a slow song, 2 songs are not
Step-by-step explanation:
that would give you 1/3 probability = 33.3333333333333%
The ratio of the measurement of an angle to its complement is 1: 2. Find the measurement of the angle and it’s complement.
Answers
Answer:
1.x=90 degrees
2.smaller angles =30
3.larger angles =(30×2)=60
Step-by-step explanation:
Complement angle=90 degrees
90/3 (because need to separate into 3 parts) =30 degrees
1part =30 degrees
1:2
(1×30):(2×30)
30:60
if you know how to do this pls help thankyou!
Answers
Answer : 49
I hope you understand sorry for the ugly writing
5. How many 1/2 cups can be filled with 500 milliliters of liquid?
Answers
Answer:
1/2 = 120ml
Step-by-step explanation:
500/120 = 4.16666666667 round to whole number equal 4 time
Dose anyone know how to solve this?
Answers
Answer:
Domain = [-5, -2) U (1, 3)
Range = (-3, 4]
Step-by-step explanation:
Domain is the x values
Domain = [-5, -2) U (1, 3)
Range is the y values
Range = (-3, 4]
what is 2/3 of 1/2
WILL MARK AS BRAINLIEST
Answers
Answer:
1/3
Step-by-step explanation:
2/3*1/2 =1/3
help will give brainly
Answers
Answer:
Is it 72?
Step-by-step explanation:
Find the area of the shaded sector
Answers
How do I solve this?
Answers
Answer:
25
Step-by-step explanation:
C = √a^2+b^2
√7^2+24^2
√49+576
√625
C=25
what does the following expression mean?
7!
A. 7+6+5+4+3+2+1
B. 7·6·5·4·3·2·1
Answers
Answer: B
Step-by-step explanation:
A factorial is multiplying the integer and all of the integers below it together.
The product of a whole number 'n' with every whole number until 1 is called the factorial. The correct option is B.
What is a factorial?The product of a whole number 'n' with every whole number until 1 is called the factorial. The factorial of 4 is, for example, 43221, which equals 24.
The expression 7! means 7 factorial which is expanded as,
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
Hence, the correct option is B.
Learn more about Factorial:
https://brainly.com/question/16674303
#SPJ2
Please help A.S.A.P its due today!
Answers
Answer: Ok Here you go.
Step-by-step explanation:
can y’all help me i’m taking a test
Answers
Answer:
Over time, the function is DECREASING. Cho ran at a faster rate during segment K.
Step-by-step explanation:
I NEED HELPPPPPP ¶×¶ ¶×¶
Find the RATIO and the EXACT VALUE of the given Sec A.
Answers
Answer:
Step-by-step explanation:
take angle A as reference angle
using sec rule
sec A=hypotenuse/adjacent
sec A=13/5
sec A=2.6
A=68 degree
for ratio,
sec A=13/5
expiation: