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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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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1 The table shows pairs of figures that are related to each other in the same way.
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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.
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What value of q satisfies this equation?
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Answers
Answer:
0,454
Step-by-step explanation:
= 59 + 5q = 159q - 11
= 5q - 159q = 11 + 59
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Answer:
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Step-by-step explanation:
-4(4x + 4) + 7(1 + 9x)
Answers
Answer:
47x - 9
Step-by-step explanation:
-4(4x + 4) + 7(1 + 9x)
-16x -16 + 7 + 63x
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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]
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
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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.
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:
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Answers
Answer:
The GCF is 8 there is your anwser
what is the value of y?
Answers
Answer:
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Answer:
Y = 34
Step-by-step explanation:
y + 43 + 123 = 180
y + 146 = 180
180 - 146. = y = 34
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Answers
Answer:
$29.15
Step-by-step explanation:
Step 1:
$53 × 55%
Step 2:
53 × 0.53
Answer:
29.15
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Simplify the expression. Write your answer as a complex number.
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Answers
Answer:
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Step-by-step explanation:
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Answers
Hope this helps!
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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.
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Answers
Answer:
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Step-by-step explanation:
Answer:
6
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
3
Step-by-step explanation:
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Answers
M------------O-------------N
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On the other side you have ON.
In order for O to be the midpoint:
ON = OM
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Answers
Answer:
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ii. 220%
iii. 2.5%
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Use elimination to solve and match each system of equations to the correct solution . I’ll mark u brainliest
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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
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Answer:
x=7y−46
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
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
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y - 0.5y = 14
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Answers
Answer:
B is the answer
Step-by-step explanation:
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
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]
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
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 :)