The table above gives selected values of twice-differentiable functions f and g, as well as the first two derivatives of g. If f′ (x)=3 for all values of x, what is the value of [tex]\begin{equation}\int_{2}^{4} f(x) g^{\prime \prime}(x) d x\end{equation}[/tex]
Answers
Answer:
63
Step-by-step explanation:
∫₂⁴ f(x) g"(x) dx
Integrate by parts.
If u = f(x), then du = f'(x) dx.
If dv = g"(x) dx, then v = g'(x).
∫ u dv = uv − ∫ v du
= f(x) g'(x) − ∫ g'(x) f'(x) dx
f'(x) is constant at 3, so:
= f(x) g'(x) − ∫ 3 g'(x) dx
= f(x) g'(x) − 3 g(x)
Evaluate from x=2 to x=4.
[f(4) g'(4) − 3 g(4)] − [f(2) g'(2) − 3 g(2)]
[(13) (7) − 3 (9)] − [(7) (1) − 3 (2)]
64 − 1
63
The required value of [tex]\int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex] is 63.
Given that,
The table above gives selected values of twice-differentiable functions f and g,
The first two derivatives of g. If f′ (x) = 3 for all values of x.
We have to determine,
What is the value of [tex]\int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex].
According to the question,
To obtain the value of given function, integrating the function,
[tex]= \int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex]
Integrating by using by-parts.
[tex]= \int\limits^4_2 {f(x)g"(x)} \, dx (1)\\\\if\ u = f(x), \ then \ du = f'(x)dx\\\\if \ dv = g"(x)dx, \ then \ v = g'(x)\\\\[/tex]
Then,
[tex]\int u\ dv = uv\ - \ \int v \ du\\\\= f(x) \ g'(x) - \int g'(x) f'(x) \ dx\\[/tex]
if f'(x) is constant at 3,
Then,
[tex]= f(x) g'(x) - \int g'(x)\dx\\\\= f(x) g'(x) -3g(x)[/tex]
Substitute from x = 2 to x = 4 then evaluate,
[tex]= [f(4)\ g'(4) - 3 \ g (4)]- [f(2)\ g'(2) - 3 \ g (2)]\\\\= [(13).(7) - 3.(9)] - [7.(1)- 3.(2)]\\\\= [91-27} - {7-6}\\\\= 64-1\\\\= 63[/tex]
Hence, The required value of [tex]\int\limits^4_2 {f(x)g"(x)} \, dx (1)[/tex] is 63.
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Related Questions
Solve 0.5y+y/3=0.25y+7
please answer this question
Answers
Answer:
y = 28
Step-by-step explanation:
0.5y + y/ 3 = 0.25y + 7
1.5y / 3 = 0.25y + 7
y/2 = 0.25y + 7
y = ( 0.25y + 7)*2
y = 0.5y + 14
y - 0.5y = 14
0.5y = 14
y = 14/0.5
y = 28
1. Evaluate f(x) = 3x - 1 at f(2) 2. Evaluate f(x) at f(-5) -6 f(x) 3 4 -5 -4 -5 3 3 Evaluate f(x) at (0)
Answers
Answer:
5
Step-by-step explanation:
3(2)-1
6-1
5
Answer:
5
Step-by-step explanation:
3(2)-1
6-1
5
as a fraction:
(i) 48%
(ii) 220%
(iii) 2.5%
Answers
Answer:
48% = 48/ 100 = 12/25220% = 220/100=11/52.5% = 25/1000 = 1/40i. 48%
ii. 220%
iii. 2.5%
To Convert:The given percentage into fractions.
Answer:[tex] \large \purple {\tt {i. \: 48\% = \frac{48}{100} = \frac{12}{25}}} [/tex]
[tex] \large \pink {\tt {ii. \: 220\% = \frac{220}{100} = \frac{11}{5}}} [/tex]
[tex] \large \blue {\tt {iii. \: 2.5\% = \frac{2.5}{100} = \frac{1}{40}}} [/tex]
Simplify the expression. Write your answer as a complex number.
2 times the square root of 25 plus the square root of negative 16
Answers
Answer:
d
Step-by-step explanation:
You are using a 9 inch paint roller to paint a wall of your bedroom. The roller has a dimension of 1 5/8 inches and a nap thickness of 1/4 inch, as shown
Answers
Answer:
21.38 square inches
Step-by-step explanation:
Given that You are using a 9 inch paint roller to paint a wall of your bedroom. The roller has a dimension of 1 5/8 inches as diameter and a nap thickness of 1/4 inch, as shown
The nap is the fuzzy materials on the surface roller. How much area does the roller cover in one full revelation
The parameters to be considered are:
Diameter = 15/8 inches
Thickness = 1/4 inches
After one revolution rolling, the dimensions of the length will be:
L = 1/4 + 15/8 + 1/4
L = 19/8 inches.
Let the width be equal to 9 inches
The area covered = L × W
Substitute L and W into the formula
Area = 19/8 × 9
Area = 21.38 square inches
Therefore, the area covered by the roller in one full revelation is 21.38 square inches
What is 18=3(3x-6) algebra 1
Answers
Answer:
x=4 i believe
Step-by-step explanation:
1st. move terms
-3x+6=-6
2nd. calculate the difference
-3x=-12
3rd. divide both side to get x alone
x= 4
what is the value of y?
Answers
Answer:
y +43⁰ +123⁰ =180⁰
=) y +160⁰ =180⁰
=) y = 20⁰
Answer:
Y = 34
Step-by-step explanation:
y + 43 + 123 = 180
y + 146 = 180
180 - 146. = y = 34
Y = 34
A car travels 100 meters in 5 seconds. Whats is the speed of the car
Answers
Answer:
20m/s
Step-by-step explanation:
[tex]Speed=Distance\div Time[/tex]
[tex]Speed=100m \div 5s[/tex]
[tex]Speed = 20m/s[/tex]
The price of an item has been reduced by 55%. The original price was $53. what is the price now
Answers
Answer:
$29.15
Step-by-step explanation:
Step 1:
$53 × 55%
Step 2:
53 × 0.53
Answer:
29.15
Hope This Helps :)
The GCF of 24 and 32 is...
Answers
Answer:
The GCF is 8 there is your anwser
Point O is between points Mand N on line segment MN. O is the midpoint of line segment MN if
ON = NM
OM = NM
ON + OM = MN
ON = OM
Answers
M------------O-------------N
................. ^ midpoint
Obviously if O is the *mid*point, then it is exactly halfway between M and N. That also means it has bisected the segment into two equal parts.
On one side you have MO (or OM, if you like)
On the other side you have ON.
In order for O to be the midpoint:
ON = OM
What are the values of a and b on the number line?
Answers
Answer:
B is the answer
Step-by-step explanation:
P Mar
1 The table shows pairs of figures that are related to each other in the same way.
Figure 1 Figure 2
Oo
Which conjecture best describes how the second figure in each set is related to the first?
A) Figure 2 is always a horizontal reflection of Figure 1.
B) Figure 2 is always a vertical reflection of Figure 1.
C) Figure 2 is always a 90° clockwise rotation of Figure 1.
D) Figure 2 is always a 180° rotation of Figure 1.
Answers
What is 4 divided by 348?
Answers
Answer:
4/348 = 0.01149425287
348/4 = 87
Step-by-step explanation:
348 divided by 4 is 87
4 divided by 348 is 0.01149425287
Hope this helps you :)
Use elimination to solve and match each system of equations to the correct solution . I’ll mark u brainliest
-3x+8y=73
X-7y=-46
Answers
Answer:
Step-by-step explanation:
Let's solve for x.
−3x+8y=73
Step 1: Add -8y to both sides.
−3x+8y+−8y=73+−8y
−3x=−8y+73
Step 2: Divide both sides by -3.
−3x
−3
=
−8y+73
−3
x=
8
3
y+
−73
3
Answer:
x=
8
3
y+
−73
3
x−7y=−46
Step 1: Add 7y to both sides.
x−7y+7y=−46+7y
x=7y−46
Answer:
x=7y−46
-4(4x + 4) + 7(1 + 9x)
Answers
Answer:
47x - 9
Step-by-step explanation:
-4(4x + 4) + 7(1 + 9x)
-16x -16 + 7 + 63x
47x -9
You can find what x = because there is no = sign. This is in simplest form.
Answer:
47x -9
Step-by-step explanation:
[tex]-4(4x + 4) + 7(1 + 9x)\\\\\mathrm{Expand}\:-4\left(4x+4\right):\quad -16x-16\\=-16x-16+7\left(1+9x\right)\\\\\mathrm{Expand}\:7\left(1+9x\right):\quad 7+63x\\=-16x-16+7+63x\\\\\mathrm{Simplify}\:-16x-16+7+63x:\\\quad 47x-9[/tex]
How many solutions does y=-x^2-4x+7 have
Answers
Answer:
x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2
Step-by-step explanation:
Solve for x:
y = -x^2 - 4 x + 7
y = -x^2 - 4 x + 7 is equivalent to -x^2 - 4 x + 7 = y:
-x^2 - 4 x + 7 = y
Multiply both sides by -1:
x^2 + 4 x - 7 = -y
Add 7 to both sides:
x^2 + 4 x = 7 - y
Add 4 to both sides:
x^2 + 4 x + 4 = 11 - y
Write the left hand side as a square:
(x + 2)^2 = 11 - y
Take the square root of both sides:
x + 2 = sqrt(11 - y) or x + 2 = -sqrt(11 - y)
Subtract 2 from both sides:
x = sqrt(11 - y) - 2 or x + 2 = -sqrt(11 - y)
Subtract 2 from both sides:
Answer: x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2
Using the statements: If it is Friday, then I will get paid. It is Friday. Write the conclusion
Answers
HELPPP PLEASE!!!
The store has 61 guppies divided into 8 aquarium tanks, and a small display aquarium on
the sales counter. Each of the 8 tanks has an even number in them with the remaining
guppies in the display aquarium. How many guppies are in each aquarium and in the
display aquarium?
Answers
Answer:
5 in display, 7 in each aquarium.
Step-by-step explanation:
Evaluate each expression if a = 4, b = 6, and c = 2.
Answers
Answer:
26
Step-by-step explanation:
ab+c
plug in #s
4(6)+2
start to solve
24+2
26
Which problem is the same as 4 + 5
Answers
Answer:
6+3
Step-by-step explanation:
Simplify. 4−8÷2+3
i need help with it
Answers
Answer:
3
Step-by-step explanation:
Using PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction), You do 8/2 first, which equals 4, then add 3 which turns 4 into a 7, then finally subtract 4 and your final answer is 3.
Answer:
3
Step-by-step explanation:
I took the test >.<
What value of q satisfies this equation?
59 + 5q = 159 - 11
Answers
Answer:
0,454
Step-by-step explanation:
= 59 + 5q = 159q - 11
= 5q - 159q = 11 + 59
= 154q = 70
= q = 70 : 154
= q = 0,454
Answer:
89/5 or 17.8
Step-by-step explanation:
The density of a substance can be found by dividing the mass of the substance by the volume of the substance. A sheet of pure iron has a mass of 500 grams and a volume of 4 in3. Write an equation of the form m=dv, where m represents the mass of a sheet of iron in grams, v represents the volume of a sheet of iron in cubic inches, and d is a constant, the density of iron in grams per cubic inch
Answers
Answer:
D=375g/cubic inch
Step-by-step explanation:
D=500 divided by 4/3
This seller must sell at least 120 newspapers each month. He sold 85 newspapers in the first three weeks of the month. How many more newspapers must he sell by the end of the month? Make an inequality to show this scenario as a math problem, be sure to use the correct symbols, and share your answer!
Answers
Answer:35
120-85=35
120>85
HELP ME PLEASE I NEED THIS and tell me how to solve for it
Answers
Answer:
616.6 square cm
Step-by-step explanation:
Area of a regular octagon
[tex] = 2 {a}^{2} (1 + \sqrt{2} ) \\ = 2 \times {12}^{2} (1 + 1.414) \\ = 2 \times 144 \times 2.141 \\ = 288 \times 2.141 \\ = 616.608 \\ = 616.6 \: {cm}^{2} [/tex]
WILL MARK BRAINLIEST NEED IT ASAP
Answers
Answer:
8
Step-by-step explanation:
6 x 9=54. 54+10=64. the square root of 64 = 8
Answer:
ANSWER IS 8
Step-by-step explanation:
18 is 2/3 of what number
Answers
Hope this helps!
The number 18 is 2/3 of the number 27.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that 18 is 2/3 rd of the number. The value of the unknown number will be calculated as,
2 / 3 x = 18
x = ( 18 x 3 ) / 2
x = 9 x 3
x = 27
Therefore, the unknown number will be 27.
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Jill made 20 muffins. She puts them into 3 boxes and has two muffins left. How many are in each box if they all contain the same amount of muffins?
Answers
Answer:
it would be 6 muffins each and muffins sounds so good right now TwT
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
20-2=18
18÷3=6
Therefore there are 6 muffins in each box
Help how do i do these
Answers
Answer:
Step-by-step explanation: What I would do is make the triangle into a square and what ever is mirroring it i would put that for my answer and then I would round it. I used to do this i don't exactly remember. Sorry if this doesn't help.