Answer:
-93
Step-by-step explanation:
This is just.a matter of using a couple of integration rules and plugging in then using order of operations.
Difference rule and constant multiple rule will be used here.
3(-17)-7(6)
-51-42
-93
Answer:
[tex]\displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx = -93[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^6_4 {f(x)} \, dx = -17[/tex]
[tex]\displaystyle \int\limits^6_4 {g(x)} \, dx = 6[/tex]
[tex]\displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx = \int\limits^6_4 {3f(x)} \, dx - \int\limits^6_4 {7g(x)} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx = 3 \int\limits^6_4 {f(x)} \, dx - 7 \int\limits^6_4 {g(x)} \, dx[/tex][Integrals] Substitute: [tex]\displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx = 3(-17) - 7(6)[/tex]Simplify: [tex]\displaystyle \int\limits^6_4 {[3f(x) - 7g(x)]} \, dx = -93[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
please help:
give an example of an undefined term and how it relates to a circle.
amusement park is 1.50$ for children and $4 for adults. on certain day 220 people entered the park, and the admission fee collected totalled 630.00. how many children and how many adults were admitted? write and use an equation to solve
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Answer:
230 children
Step-by-step explanation:
Which relation is not a function?
Answer:
A
For something to be a function every x value bust have at most 1 y value and in A 9 has 2 y values so it cant be a function
3a
[tex] \frac{3a + a {}^{2} }{a} [/tex]
Simplify.
Answer:
(3+a)
Step-by-step explanation:
3a + a^2
-------------
a
Factor out an a in the numerator
a(3+a)
-------------
a
Cancel like terms
(3+a)
Step-by-step explanation:
[tex] \frac{3a + {a}^{2} }{a} \\ = \frac{3a}{a} + \frac{ {a}^{2} }{a} \\ = 3 + a \\ thank \: you[/tex]
Which of the following statements best describes the relationship between
any point on an ellipse and each of its two foci?
A. The quotient of the distances to each focus equals a certain
constant.
B. The difference of the distances to each focus equals a certain
constant.
C. The sum of the distances to each focus equals a certain constant.
D. The product of the distances to each focus equals a certain
constant.
Answer:
C
Step-by-step explanation:
The sum of distances from any point on the ellipse to each foci equals a certain amount, no matter what point on the ellipse it starts from. The foci are on the major radius of the ellipse (the longer length of horizontal/vertical). The foci are of equal distance from the center, with one on each side.
If you wanted to find where the foci are using the major and minor radius, we can find that, representing the distance between the center and any foci as g,
g² = major radius² - minor radius². Then, the distance between the center and the foci is equal to g
Please hurry I will mark you brainliest
What is the equation of the line parallel to y = 2x - 4 and with the same x - intercept as 3x – 4y = 12?
Answer:
y=2x-8
Step-by-step explanation:
Hi there!
We want to find an equation of the line parallel to y=2x-4 but has the same x intercept as 3x-4y=12
Parallel lines have the same slope, but different y intercepts
In y=2x-4, which is written in y=mx+b form, m is the slope and b is the y intercept
2 is in the place of where the slope would be, so the slope of that line is 2
That means the slope of the line parallel to it would also have a slope of 2
Here is the equation of the parallel line so far:
y=2x+b
We need to find b, the y intercept
Typically, we'll substitute a point into the equation to solve for b, but we don't have a point, yet
We're given that the new line has the same x intercept as 3x-4y=12
The x intercept is the point where the line passes through the x axis, and so the value of y at that point is 0
Let's substitute 0 for y in 3x-4y=12 and solve for x to find the x intercept
3x-4(0)=12
Multiply
3x=12
Divide both sides by 3
x=4
So the value of the x intercept is 4. As a point, it's (4,0)
So now substitute the values of the point (4,0) into y=2x+b to find b
0=2(4)+b
Multiply
0=8+b
Subtract 8 from both sides
-8=b
Substitute -8 as b into the equation
y=2x-8
Hope this helps!
A viewfinder has a triangular lens. Some of the measurements of the lens are
shown below. Which of the following best represents the length of a?
B
26°
a
С
389
10
A
Triangle not drawn to scale
=========================================================
Explanation:
It's a bit strange why your teacher has the "26 degree" label pointing at a side length, rather than an actual angle. I'm assuming your teacher meant to aim it at angle C. In other words, I'm assuming they meant to say angle C = 26 degrees.
If that assumption is correct, then,
A+B+C = 180
38+B+26 = 180
B+64 = 180
B = 180-64
B = 116
Then we can use the law of sines like so:
a/sin(A) = b/sin(B)
a/sin(38) = 10/sin(116)
a = sin(38)*10/sin(116)
a = 6.84986152123146
a = 6.8
Side 'a' is approximately 6.8 inches long. So that's why the answer is choice A.
what is the range of the function y = 2x - 3 if the domain is 1
Answer:
1.5
Step-by-step explanation:
y=2x - 3
0 = 2x - 3
-2x = - 3 /÷(-2)
x = 3 ÷ 2
x = 1.5 3/2
please someone answer! i need it rn!
(x+4)^2 - (x-6)^2 - (x-1)*(x+1)
Answer:
-9
Step-by-step explanation:
the best way to learn math formulas
Writing down the formulas on charts and pasting it in your room,by seeing this daily it helps to memorize the formulas.
Saying the formulas louder also helps to memorize the formula.
Watching videos related to maths formulas and equations helps to remember the formulas easier.
Doing many problems regularly will helps you to remember the formulas.
lastly study to Understand The Formula not to memorize
four less than the product of a number and 7 is eight more than that number
Answer:
2
Step-by-step explanation:
Replace the number with x, then the equation would be:
7x-4=x+8
7x-x=8+4
6x=12
6x/6=12/6
x=2
8TH GRADE MATH ¯\_(ツ)_/¯
What is the fractional equivalent of the repeating decimal n = 0.1515.... ?
Answer the questions to find out.
1. How many repeating digits does the number represented by n have?
2. You need to multiply n by a power of 10 to help you find the fraction. Decide on the power of 10 to multiply by, and tell how you identified that number.
3. Write an equation where the left side is your power of 10 time n and the right side is the result of multiplying 0.1515... by that power.
4. Write the original equation, n = 0.1515... underneath your equation from question 3. Then subtract the equations. Show your work!
5. Write n as a fraction in simplest form. Show your work!
If n = 0.151515…, then 100n = 15.151515…
Then
100n - n = 15.151515… - 0.151515…
99n = 15
n = 15/99 = 5/33
A. Explain why the point (100,2) is on the graph.
B. What is the x-intercept of the graph? Explain how you know.
49
C. When will the graph meet the line y = 5? Explain how you know.
Answer:
the log function is the "inverse" function of an exponential function
by definition [tex]log_{a} b = c[/tex] then [tex]a^{c} = b[/tex]
in this problem you have [tex]log_{10} 100[/tex]
thus what x solves this ? [tex]10^{x} = 100[/tex] the answer is [tex]10^{2}[/tex]
thus (100,2)
B) the x intercept is when y = 0
[tex]10^{0} = 1[/tex]
x intercept at (1,0)
C) at 100, the curve will hit y = 5000
Step-by-step explanation:
Which is the equation of a parabola with Vertex (0,0) and focus (0, 2)?
a. ya = 8x
c. x2 = 8
b. y2 = 4x
d. x2 = 4y
Answer:
So the equation of the parabola is x2=8y i don't really know
Find the nth term of the arithmetic
sequence - 1,2,5, ....
A. 3n - 2
B. -2n + 1
C. 2n + 2
D. 3n - 4
Answer:
3n -4
Step-by-step explanation:
We are adding 3 each time
-1+3 =2
2+3 = 5
The formula for an arithmetic sequence is
an = a1+d(n-1) where a1 is the first term and d is the common difference
an = -1+3(n-1)
= -1 +3n -3
= 3n -4
191+13=13+191191+13=13+191
what type of property is that
what nice question that we can understand ok
Question 11 of 25
If the point (1, 4) is on the graph of an equation, which statement
must be true?
A. There are solutions to the equation for the values x = 1 and
x = 4.
B. The values x = 1 and y = 4 are the only values that make the
equation true.
C. The values x = 4 and y= 1 make the equation true.
D. The values x = 1 and y = 4 make the equation true.
SUBMIT
Answer:
D
Step-by-step explanation:
simple : when we have a point defined as (1, 4), it means x = 1, y = 4.
and since the point is on the graph of a function/equation it means that when we use x = 1 and calculate the equation, we get 4 as result (= y). so yes, that means that both sides of the "=" sign are indeed equal for this pair of values, which makes the equation true.
but there will be usually many other pairs that do that too.
I am not sure. Is this right?
Answer:
14.4
Step-by-step explanation:
since the longest side is 24,find the shortest side
√20^2-12^2
√400-144
√256
=16
which means the other shortest side is 24-16
which is 8
then you have to use the 12 and 8 to find the unknown side
√12^2+8^2
144+64
√208
14.4
I hope this helps
Pls help if u only know the correct answer!! Thanks!! :))
Answer:
3.5, 4.2
Step-by-step explanation:
reflect make it not negative and its on y axis so y not affected
Solve for X. Geometry
Answer:
x=12
Step-by-step explanation:
QS=QR+RS
2x-11=7+x-6
x=12
find the missing length indicated
Answer:
192
Step-by-step explanation:
Apply the geometric mean formula to solve for x, which is the altitude of the right triangle.
The formula is:
h = √(mn)
h = x = ?
m = 144
n = 400 - 144 = 256
Substitute
h = √(256*144)
h = √36,864
h = 192
Therefore, x = 192
If the order of two matrices are different, then the addition of matrices does not exists true or false
Answer:
true
Step-by-step explanation:
A matrix can only be added/subtracted with another matrix if the two matrices have the same dimensions
A cylindrical paint can has a diameter of 12 centimeters and height of centimetrs which is closest to the volume of the paint can in cubic centimeters
Answer:
The correct answer is "1808.64 cm³".
Step-by-step explanation:
Seems that the given query is incomplete. Below find the attachment of the complete problem.
Given:
Diameter,
d = 12 cm
Radius,
r = [tex]\frac{d}{2}[/tex]
= [tex]\frac{12}{2}[/tex]
= [tex]6 \ cm[/tex]
Height,
h = 16 cm
As we know,
The volume of cylinder is:
= [tex]\pi r^2 h[/tex]
By substituting the values, we get
= [tex]3.16\times (6)^2\times 16[/tex]
= [tex]3.14\times 36\times 16[/tex]
= [tex]1808.64 \ cm^3[/tex]
Find the number in which 9 has greater value.
0.5689
5.6890
56.89
569.80
Answer:
569.80Step-by-step explanation:
Among all the choices, the digit 9 has the greatest value in number 569.80. For the reason that 9 got ones value - which are greatest than other.[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
5. There are 5,280 feet in a mile. What part of a mile, in decimal form, will you drive until you reach the exit? I NEED THIS QUICK PLZ HELP I’LL GIVE YOU 30
Answer:
5.280
Step-by-step explanation:
i did this question and got it
state the following true or false
Answer:
c. false (it should always be neg.)
d. false
Step-by-step explanation:
Answer:
(c) True, (d) False
Step-by-step explanation:
multiply
12/18×10/18
lesson name fraction.
find me out this question for answer
PLEASE HELP ASAP!!
Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest radical form.
A. 146.85 units²
B. 45+9√3 units²
C. 36+9√3 units²
D. 36+3√3 units²
The total surface area of the pyramid is 52 square units
The formula for calculating the area of the triangular based pyramid is expressed as;
[tex]TSA=Base \ Area+\frac{1}{2}ps[/tex] where;
p is the perimeter of the base
s is the slant height
Get the Base area
[tex]Base \ Area = \frac{1}{2}bh\\Base \ Area = \frac{1}{2}*6*\sqrt{5^2-3^2} \\ Base \ Area = \frac{1}{2}*6*\sqrt{25-9} \\ Base \ Area = \frac{1}{2}*6*\sqrt{16} \\ Base \ Area = \frac{1}{2}*6*4 \\ Base \ Area = \frac{24}{2} \\Base \ Area = 12 units^2[/tex]
Get the perimeter
Perimeter = 5 + 5 + 6
Perimeter = 16 units
Slant height = 5units
Substitute the given values into the formula above as shown;
[tex]TSA=12+\frac{1}{2}*16*5\\TSA=12+(8*5)\\\\TSA = 12 + 40\\TSA = 52 units ^2[/tex]
Hence the total surface area of the pyramid is 52 square units
Learn more here: https://brainly.com/question/23353623
Answer:
52squnits
Step-by-step explanation:
Put the steps In order
