Interval 0 to 10.5 f(x) dx = 9, interval 0 to 3.5 f(x) dx = 2, and interval 7 to 10.5 f(x) dx = 3, how do I find interval 3.5 to 7 (5f(x)-3) dx?
Answers
a. The value of the definite integral [tex]\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]
b. The value of the definite integral [tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]
To answer the question, we need to know what definite integrals are.
What are definite integrals?These are integrals which are evaluated between two values of the variable.
a. Integral of [tex]\int\limits^7_{3.5} {f(x)} \, dx[/tex][tex]\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]
Given that [tex]\int\limits^{10.5}_0 {f(x)} \, dx = 9, \int\limits^{3.5}_0 {f(x)} \, dx = 7 and \int\limits^{10.5}_7 {f(x)} \, dx = 3[/tex]
We require [tex]\int\limits^7_{3.5} {f(x)} \, dx[/tex]
So, [tex]\int\limits^{10.5}_0 {f(x)} \, dx = \int\limits^{3.5}_0 {f(x)} \, dx + \int\limits^7_{3.5} {f(x)} \, dx + \int\limits^{10.5}_7 {f(x)} \,dx[/tex]
So, [tex]\int\limits^7_{3.5} {f(x)} \, dx = \int\limits^{10.5}_0 {f(x)} \, dx - \int\limits^{3.5}_0 {f(x)} \, dx - \int\limits^{10.5}_7 {f(x)} \,dx[/tex]
Substituting the values of the variables into the equation, we have
So, [tex]\int\limits^7_{3.5} {f(x)} \, dx = \int\limits^{10.5}_0 {f(x)} \, dx - \int\limits^{3.5}_0 {f(x)} \, dx - \int\limits^{10.5}_7 {f(x)} \,dx[/tex]
[tex]\int\limits^7_{3.5} {f(x)} \, dx = 9 - 7 - 3\\\int\limits^7_{3.5} {f(x)} \, dx = 2 - 3\\\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]
So, [tex]\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]
b. Integral of [tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx[/tex][tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]
[tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = \int\limits^7_{3.5} 5{f(x)}\, dx - \int\limits^7_{3.5} 3\, dx\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = 5\int\limits^7_{3.5} {f(x)}\, dx - 3(7.5 - 3)\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx= 5 X (-1 ) - 3 X 4.5 \\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx= -5 - 13.5\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]
So, [tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]
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Related Questions
Rachel was pouring milk into an 8-inch-tall cylindrical container. She used the formula
V = #r?h to calculate the cylinder's volume which Rachel found to be 231 cubic inches of liquid.
What would be the most accurate measurement for the radius of the container of milk?
O 3 inches
O 5 inches
O 9 inches
O 10 inches
Answers
The volume of the cylinder container is the amount of milk in it
The most accurate measurement for the radius is 3 inches
How to determine the accurate radius?The given parameters are:
Volume = 231Height = 8 inchThe volume of a cylinder is:
V = πr²h
So, we have:
πr² * 8 = 231
Divide both sides by 8π
r² = 9.19
Take the square root of both sides
r = 3.03
Approximate
r = 3
Hence, the most accurate measurement for the radius is 3 inches
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NO LINKS!! Please help me with this problem
Answers
#GH
[tex]\\ \rm\Rrightarrow \dfrac{GH}{FG}=\dfrac{TS}{TU}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{GH}{36}=\dfrac{42}{28}=\dfrac{3}{2}[/tex]
[tex]\\ \rm\Rrightarrow GH=108/2=54[/tex]
#UV
[tex]\\ \rm\Rrightarrow \dfrac{UV}{TU}=\dfrac{JF}{FG}[/tex]
[tex]\\ \rm\Rrightarrow\dfrac{ UV}{28}=\dfrac{63}{36}=\dfrac{21}{12}=\dfrac{7}{4}[/tex]
[tex]\\ \rm\Rrightarrow UV=7(28)/4=7(7)=49[/tex]
#VW
[tex]\\ \rm\Rrightarrow \dfrac{VW}{SW}=\dfrac{IJ}{IH}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{VW}{35}=\dfrac{27}{45}=\dfrac{3}{5}[/tex]
[tex]\\ \rm\Rrightarrow VW=3(35)/5=3(7)=21[/tex]
FGHIJ ≅ UTSWV
making proportional equations
GH/FG = TS/UTGH/36 = 42/28GH = 54FJ/FG = UV/UT63/36 = UV/28UV = 49IJ/FG = VW/UT27/36 = VW/28VW = 21What is 2/3 - 5/6 divided by 3/4
Answers
Decimal form: -0.4
C
7
24
What is the measure of C
Answers
someone pls help me i will give brainliest to the first to answer
Answers
Answer:
21 and 35
Step-by-step explanation:
21 for the first box, when it is in parenthesis you multiply each, so then 35 for the second box
7 times 3 then 7 times 5
For Halloween, Gwen received 4*10 pounds of candy in the first hour and another 43/5 pounds the second hour. How much
candy did she get total?
Answers
Answer:
4*10 = 40
43/5 = 8.6
40 + 8.6 = 48.6 candy in total.
Find the particular solution of the differential equation that satisfies the initial condition f'(x) 4x, f(0) = 5 f(x) =
Answers
Answer: [tex]f(x)=2x^2+5[/tex]
Step-by-step explanation:
First integrate f'(x) so we can find the funtion f(x):
[tex]4\int\limits {x} \, dx =4[\frac{1}{2} x^2]=2x^2+C=f(x)[/tex]
The initial conditions say that when x = 0, the function equals 5. Let's write that down:
[tex]f(0)=5=2(0^2)+C=C[/tex]
Therefore, the integration constant 'C' must equal 5. This means that our function is:
[tex]f(x)=2x^2+5[/tex]
Let x1 = 36, y1 = −6, and y2 = 8, and let y vary inversely as x. Find x2.
Answers
Answer:
-30
Step-by-step explanation:
Using 'y' is vary inversely to 'x', the value of x₂ = -27.
What is inverse?The word inverse in mathematics "a function or operation which reverses the order or operation of another function or operation".
According to the question,
x₁ = 36, y₁ = -6, y₂ = 8 and x₁ is inversely proportional to y₁ which mean
(x₁) (y₁) = k
(36)(-6) = -216.
Formula for inverse is x = k([tex]\frac{1}{y}[/tex]).
In order to find x₂, x₂ = -216(1/8)
x₂ = -27
Hence, the value of x₂ = -27.
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solve for x: x^3 + x^2 + x = 3
Answers
What is the IQR for 79 85 98 125 140
Answers
Hi there!
We have the numbers:
79 85 98 125 140
From the data, we can see that '98' is the median value as it is exactly in the middle. We can then split the data into equal groups on both sides of the median.
79 85
125 140
Since there are only two numbers, we can find the median of EACH sub-group (Q1 and Q3 respectively) by taking the average.
Q1 = (79 + 85)/2 = 82
Q3 = (140 + 125)/2 = 132.5
The IQR is simply the difference between Q3 and Q1, so:
IQR = 132.5 - 82 = 50.5
What is the following product?
30 10
O 2010
O 3 V10
4./10
o 10/3
What is the following product?
Square root 30 and square root 10
Answers
Answer:
10 sqrt 3
Step-by-step explanation:
sqrt (30) * sqrt (10) = sqrt (300) = sqrt ( 4 * 25 * 3) = 10 sqrt 3
You work with 3 other students on a project for science class. Your group
zarns 329 points, or 94%, of the total possible points. How many points are
possible for the project?
Answers
Answer:
350 points are possible
Step-by-step explanation:
You take 329 divided by 94% or .94 to get 350.
100% of 350 is 350
To double check, 94% of 350 is 329 & 6% of 350 is 21. 329 +21 = 350
Find the surface area
Answers
Answer:
Area of a sphere
Radius
15 m
Diameter
30 m
Volume
14,137 m³
Surface to volume ratio
0.2 1/m
Surface area
2,827.4 m²
Step-by-step explanation:
Write 0.000299 in scientific notation
Answers
Answer:
0.000299 in scientific notation
2.99 × 10-4
Step-by-step explanation:
To convert 0.000299 into scientific notation also known as standard form, follow these steps:
Move the decimal 4 times to right in the number so that the resulting number, m = 2.99, is greater than or equal to 1 but less than 10
Since we moved the decimal to the right the exponent n is negative
n = -4
Write in the scientific notation form, m × 10n
= 2.99 × 10-4
Answer:
0.000299
2.99 × 10^-4.
Step-by-step explanation:
1=5-4+3-2-1 pls help me i need to turn this and
Answers
Answer:
The answer would be true
Step-by-step explanation:
[tex]1=5-4+3-2-1[/tex]
[tex]1=1+1-1[/tex]
[tex]1=2-1[/tex]
[tex]1=1[/tex]
You have two part-time jobs making $11 an hour mowing lawns and $8 an hour washing cars. You want to make at least $150 a week but work less than 20 hours per week. Write a system to represent this situation..
Answers
56783÷100=
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Answers
The vertex -x^2 - 2x + 8
Answers
General form of a quadratic equation: [tex]ax^2+bx+c[/tex]
⇒ since the equation: [tex]-x^2-2x+8[/tex]
⇒ so:
a = -1b = -2c = 8To calculate the x-coordinate of the vertex
⇒use x = [tex]-\frac{b}{2a}[/tex] <--- this is a property that helps you find the vertex of the
quadratic
x = [tex]-\frac{(-2)}{2*(-1)} =-1[/tex]
Since x = -1:
⇒ we can plug in this x-value into the original equation to find the y-
value
[tex]y =-(-1)^2-2(-1)+8=-1+2+8=9[/tex]
So the coordinate of the vertex: (-1,9)
Hope that helps!
add the following integers {3 +(-7)}+(-6)
Answers
Answer:
-10
Step-by-step explanation:
Answer:
-10
Step-by-step explanation:
(3+(-7))+(-6)
=3-7+-6
=3-7-6=-10
What is the volume of this figure? Enter your answer in the box.b
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Answer:
2800 ft³
Step-by-step explanation:
The required volume of given figure is 2800 ft³
I hope it helped you
Please help me with this too ,
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Answer:
Step-by-step explanation:
[tex]\sf a^{m}*a^{n} =a^{m +n}\\\\a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]
[tex]\sf a^{-n}=\dfrac{1}{a^{n}}\\\\\dfrac{a^{n}}{a^{m}}=a^{n-m}\\\\\\a^{0}=1[/tex]
[tex]\sf (a^{n})^{m} = a^{n*m}\\\\(a^{n}*b^{m})^{p}=a^{np}b^{mp}\\\\(ab)^{n}=a^{n}b^{n}[/tex]
Help help help math math math
Answers
4x + 8 > -x - 7
4x + x > - 7 - 8
5 x > - 15
x > -3
x > -3
↪explanation4x + 8 > -x - 7
4x + x > -7 - 8
5x > -15
5x ÷ 5 > -15 ÷ 5
x > -3
☆...hope this helps...☆
Pls help me with this
1. Which drink is the most preferred by your classmates?
2. Which drink is the least preferred by your classmates?
3. Compare the percentage of students who prefer juice and coffee.
4. Compare the percentage of students who prefer water and tea.
5. Compare the percentage of students who prefer chocolate drink and other drink.
Answers
Answer:
1. Choclate Drink
2. Coffee
3. 19 % difference
4. 1 % difference
5. 42% difference
Step-by-step explanation:
Math test Farley easy
Answers
Answer:
417.831823 [tex]in^{2}[/tex]
Step-by-step explanation:
surface area of cone ;
[tex]=\pi r^{2}+\pi rl\\ =\pi (7^{2}) +\pi (7)(12)=417.831823 in^{2}[/tex]
Answer:417.831823
Step-by-step explanation:
Angle 1 and angle 2 are supplementary. Angle 2 is 2 times the measurement of angle 1. What is the measurement of the larger angle?
Answers
Answer: 120 degrees
Step-by-step explanation:
Which expression equals a number that is NOT a rational number?
Please help asap
Answers
Not rational number include √2, π, e, and φ. The decimal expansion of an irrational number.
Select all ratios equivalent to 7:2.
14:4
28:8
9:1
Answers
Answer:
Step-by-step explanation:
If you multiply top and bottom of 7/2 by 2 as in (7 *2) / (2 * 2) = 14 /4
If you multiply 7/2 top and bottom by 4, you get 28/8
So 14/4 and 28/8 are both the same as 7/2
1/3(6x-3)-1/4(20x+8)=-6
Answers
Answer:
x = 1.
Step-by-step explanation:
[tex]\frac{1}{3}(6x-3)-\frac{1}{4}(20x+8)=-6\\\\[Distribute the first fraction into the parenthesis.]\\((\frac{1}{3}*6x)-(\frac{1}{3}*3))-\frac{1}{4}(20x+8)=-6\\\\2x-1-\frac{1}{4}(20x+8)=-6\\\\[Distribute the second fraction into the parenthesis.]\\2x-1-((\frac{1}{4}*20x)+(\frac{1}{4}*8))=-6\\\\2x-1-5x-2=-6\\\\[Combine like terms.]\\-3x-3=-6\\\\[Add 3 to both sides.]\\-3x=-3\\\\[Divide both sides by -3.]\\x=1[/tex]
Tickets to games of a local basketball team cost $12 for students and $16 for adults. For one game, $3700 was collected and 250 tickets were sold. How many of each kind of ticket were sold? Write and solve a system of equations.
Answers
Answer:
12x + 16y = 3700
x + y = 250
x = 75 students
y = 175 adults
Step-by-step explanation:
y = 250 - x
12x + 16(250-x) = 3700
12x + 4000 - 16x = 3700
-4x = -300
x = 75
y = 250 - 75
y = 175
For the 50 students in an art contest, there will be 1 prize for first-place, 1 prize for second-place, and 3 prizes for honorable mention. What is the probability of winning a prize?
Answers
Step-by-step explanation:
there are 50 students and 5 prizes (1 + 1 + 3).
so, already in natural language we would say "there is 1 prize for every 10 students".
formally, remember the rule of probability : desired outcomes over total possible outcomes.
this is here
5/50 = 1/10 = 0.1
your can see it also this way :
if there was only 1 prize, each student would have a chance of 1/50 of winning.
now there are 5 prizes, which gives everybody 5 times the chance of winning. which is then 5×1/50 = 5/50 = 0.1