AP Calc BC help!
Can someone explain how to do these problems? I care more about the explanation than the actual answer! My course never taught me how to do these kinds of problems.
Thank you!!
Answers
Answer:
Question 1) 72
Question 2) 40
Question 3) Both C and D.
Question 4) Both A and C.
Step-by-step explanation:
Question 1)
We are given that:
[tex]\displaystyle \int_1^5f(x)\, dx=8\text{ and we want to find} \int_1^5xf'(x)\, dx[/tex]
We will use integration by parts, given by:
[tex]\displaystyle \int_a^b u\, dv=uv-\int_a^b v\, du[/tex]
We will let:
[tex]u=x\Rightarrow du=dx\text{ and } dv=f'(x)\, dx \Rightarrow v=f(x)[/tex]
Therefore:
[tex]\displaystyle \int_1^5xf'(x)\, dx=xf(x)\Big|_1^5-\int_1^5f(x)\, dx[/tex]
Substitute:
[tex]\displaystyle \int_1^5xf'(x)\, dx=(5(f(5))-(1(f(1))-(8)[/tex]
Evaluate:
[tex]\displaystyle \int_1^5xf'(x)\, dx=75-(-5)-8=72[/tex]
Question 2)
Similarly, we will let:
[tex]\displaystyle u=x\Rightarrow du=dx\text{ and } dv=f'(x)\, dx \text{ so } v=f(x)[/tex]
Hence:
[tex]\displaystyle \int_0^3 xf'(x)\, dx=xf(x)\Big|_0^3-\int_0^3f(x)\, dx[/tex]
Evaluate:
[tex]\displaystyle \int_0^3 xf'(x)\, dx=(3f(3))-(0(f(0))-(2)[/tex]
Thus:
[tex]\displaystyle \int_0^3 xf'(x)\, dx=3(14)-2=40[/tex]
Question 3)
We are given:
[tex]\displaystyle g(x)=\int_4^xf(x)\, dx[/tex]
By the Fundamental Theorem of Calculus:
[tex]g'(x)=f(x)>0[/tex]
The derivative of g is always positive. So, the values of g are always increasing.
The tables that reflect this are C and D.
And there are, as I understand it, no way to determine their exact values. Both C and D are correct.
Question 4)
Similarly, we are given:
[tex]\displaystyle g(x)=\int_{-2}^xf(x)\, dx[/tex]
By the FTC:
[tex]g'(x)=f(x)<0[/tex]
So, g should be decreasing for all x.
The tables that reflect this are A and C.
So, both A and C are correct.
Related Questions
Please answer for kind of a lot of points :D
Answers
= 6d +8
Answer:
(5.5d + 8) miles27.5 milesStep-by-step explanation:
Lyndsay ⇒ 3d + 5Seth ⇒ 2.5d + 3a) Together they run:
3d + 5 + 2.5d + 3 = (5.5d + 8) milesb) They run 5 days Monday through Friday last week:
5.5*5 = 27.5 milesplzz write with formula and explanation plzzzzzzzz
Answers
Given:
[tex]-\dfrac{33}{16}[/tex] should be divided by a number to get [tex]-\dfrac{11}{4}[/tex].
To find:
The unknown number.
Solution:
Let [tex]-\dfrac{33}{16}[/tex] should be divided by x to get [tex]-\dfrac{11}{4}[/tex].
[tex]\dfrac{-\dfrac{33}{16}}{x}=-\dfrac{11}{4}[/tex]
[tex]-\dfrac{33}{16}=-\dfrac{11}{4}x[/tex]
Multiply both sides by 16.
[tex]-33=-44x[/tex]
Divide both sides by -44.
[tex]\dfrac{-33}{-44}=x[/tex]
[tex]\dfrac{3}{4}=x[/tex]
Therefore, the unknown number is [tex]\dfrac{3}{4}[/tex].
Quadrilateral JKLM has vertices at J(0,0), K(0,6), L(9,12), and M(12,0). Find the vertices of the quadrilateral after a dilation with scale factor 2/3.
Answer choices
J'(0, 0), K'(0, 9), L'(27/2, 18), and M'(18, 0)
J'(0, 0), K'(0, 4), L'(6, 8), and M'(8, 0)
J'(0, 0), K'(0, −4), L'(−6, −4), and M'(−8, 0)
J'(2/3, 2/3), K'(2/3, 20/3), L'(9/3, 38/3), and M'(38/3, 2/3)
Answers
Answer:
The vertices of the quadrilateral after a dilation with scale factor [tex]\frac{2}{3}[/tex] are [tex]J'(x,y) = (0,0)[/tex], [tex]K'(x,y) = (0,4)[/tex], [tex]L'(x,y) = (6, 8)[/tex] and [tex]M'(x,y) = (8,0)[/tex].
Step-by-step explanation:
Let suppose that center of dilation is located at origin, that is [tex]O(x,y) = (0,0)[/tex]. Vectorially speaking, dilation is described by following expression:
[tex]D'(x,y) = O(x,y) + r\cdot [D(x,y)-O(x,y)][/tex] (1)
Where:
[tex]O(x,y)[/tex] - Center of dilation.
[tex]D(x,y)[/tex] - Original point.
[tex]D'(x,y)[/tex] - Dilated point.
[tex]r[/tex] - Dilation factor.
If we know that [tex]O(x,y) = (0,0)[/tex], [tex]r = \frac{2}{3}[/tex], [tex]J(x,y) = (0,0)[/tex], [tex]K(x,y) = (0,6)[/tex], [tex]L(x,y) = (9,12)[/tex] and [tex]M(x,y) = (12,0)[/tex], then the dilated points are, respectively:
[tex]J'(x,y) = O(x,y) + r\cdot [J(x,y)-O(x,y)][/tex]
[tex]J'(x,y) = (0,0) +\frac{2}{3}\cdot [(0,0)-(0,0)][/tex]
[tex]J'(x,y) = (0,0)[/tex]
[tex]K'(x,y) = O(x,y) + r\cdot [K(x,y)-O(x,y)][/tex]
[tex]K'(x,y) = (0,0)+\frac{2}{3}\cdot [(0,6)-(0,0)][/tex]
[tex]K'(x,y) = (0,4)[/tex]
[tex]L'(x,y) = O(x,y) +r\cdot [L(x,y)-O(x,y)][/tex]
[tex]L'(x,y) = (0,0) + \frac{2}{3}\cdot [(9,12)-(0,0)][/tex]
[tex]L'(x,y) = (6, 8)[/tex]
[tex]M'(x,y) = O(x,y) +r\cdot [M(x,y)-O(x,y)][/tex]
[tex]M'(x,y) = (0,0) +\frac{2}{3}\cdot [(12,0)-(0,0)][/tex]
[tex]M'(x,y) = (8,0)[/tex]
The vertices of the quadrilateral after a dilation with scale factor [tex]\frac{2}{3}[/tex] are [tex]J'(x,y) = (0,0)[/tex], [tex]K'(x,y) = (0,4)[/tex], [tex]L'(x,y) = (6, 8)[/tex] and [tex]M'(x,y) = (8,0)[/tex].
Option B will be the correct option.
Dilation of a point about the origin by a scale factor 'k',If a point (a, b) is dilated by a scale factor 'k' about the origin, coordinates of the image point will be,
(a, b) → (ka, kb)
Following the rule for dilation,
If a quadrilateral J(0, 0), K(0, 6), L(9, 12) and M(12, 0) is dilated by a scale factor [tex]\frac{2}{3}[/tex], coordinates of the image points will be,
[tex]J(0,0)\rightarrow J'(0, 0)[/tex]
[tex]K(0,4)\rightarrow K'(0, 4)[/tex]
[tex]L(9,12)\rightarrow L'(6,8)[/tex]
[tex]M(12,0)\rightarrow M'(8,0)[/tex]
Therefore, Option B will be the correct option.
Learn more about the rule of dilation here,
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A car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours.
A. True
O
B. False
Answers
A car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours is true.
What is Speed?Speed is the time rate at which an object is moving along a path,
Given that car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours.
We have to check whether the statement is true or false.
To check, we can use the formula:
distance = rate x time
Substituting the given values, we get:
distance = 60 x 4.5 = 270 miles
Therefore, the statement is true.
Hence, A car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours is true.
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Sara says, "If you subtract 17 from my number and multiply the difference by - 2,
the result is - 22." What is Sara's number?
Answers
Answer: 28
28 - 17 = 11
11 * -2 = -22
(x-17)/2=-22
Multiply 2 by both sides
x-17=-44
Add 17 to both sides
x=-27
what times what equals 168 besides 84 times 2?
Answers
Answer:
12 & 14
Step-by-step explanation:
Zoltan read 15 pages of his book in 6 minutes. At this rate, how many pages can he read in 10 minutes?
Answers
Answer:
25 pages in 10 minutes.
write an equation of the line perpendicular to the given line that contains P in point slope form? P (4,8) y=4x-7
Answers
Answer:
y - 8 = -1/4(x - 4)Step-by-step explanation:
Perpendicular lines have negative-reciprocal slopes.
The line contains point P(4, 8)
Point slope form:
y - y₁ = m(x - x₁)Given line:
y = 4x - 7The slope of the perpendicular line is m = -1/4.
The line in point-slope form is:
y - 8 = -1/4(x - 4)Answer:
y - 8 = -1/4(x - 4)
Step-by-step explanation:
If two lines are perpendicular to each other, they have opposite slopes.
The first line is y = 4x - 7. Its slope is 4. A line perpendicular to this one will have a slope of -1/4, the reciprocal (opposite) of the given equation.
Plug this value (-1/4) into your standard point-slope equation of y - y₁ = m(x - x₁)
y - y₁ = -1/4(x - x₁)
To find x₁ and y₁, we want to plug in a value that we know is on this line: in this case, it is P (4, 8). Plug in the x and y values into the x₁ and y₁ of the standard equation.
y - 8 = -1/4(x - 4)
This equation is perpendicular to your given equation (y = 4x - 7) and contains point P (4, 8)
Hope this helps!
tysmmmmmmmmmmmmmmmmmmmmmm
Answers
Answer:
The answer is 10
Step-by-step explanation:
To get this you will make the improper fraction into a fraction and then turn that into decimal form
[tex]4 \frac{1}{8} = 4[/tex]
and
[tex]5 \frac{6}{10} = 6[/tex]
That is how you find the estimated answer
Hope this Helped
how to solve for mamath
Answers
Answer:
2
Step-by-step explanation:
Answer:
X= 20
Step-by-step explanation:
To find x you need to know what are the dimensions
48 divided by 12 = 4
5 x 4 = 20
x = 20
hope this helps
Meena cuts a 287-in. long ribbon into 2 pieces in the ratio 3 : 4. What is the length of the longer piece of ribbon? (ASAP)
Answers
Answer:
164 inches
Step-by-step explanation:
First, add 3 and 4
3+4= 7
Then divide 287 by 7
287/7= 41
Then, multiply 4 (from the ratio) by 41
4*41= 164
To get the length of the shorter piece, subtract 164 from 287
287-164= 123
Check your work:
123+164= 287
Hope this helps!
Enter the number that belongs in the green box
Answers
The reason for this is because the image shows that ALL the sides are EQUAL. Therefore, all the angles must be equal.
So, we know that a triangle equals a total of 180°. If we simply divide that total by 3 we get 60°.
Equilateral triangles are triangles whose all sides and angles are equal.
Since the above given triangle has 3 equal sides it is an equilateral triangle.
So, the three angles of this triangle can be 3x.
Which means :
[tex] =\tt 3x = 180[/tex]
[tex] =\tt x = \frac{180}{3} [/tex]
[tex]\hookrightarrow \tt \color{plum}x = 60°[/tex]
▪︎Therefore, x = 60°
Find the measure of Angles A, C, D
Answers
Answer:
A= 65 C= 65 and D= 115
Step-by-step explanation:
given a parallelogram .
interior angles sum is 360 degree.
sum of adjacent angles is 180degree.
opposite angles are congruent (B=D).
A + B + C + D = 360
(A + D) + C + 115 = 360 since A and D are adjacent angles .
180 + 115 + C = 360
295 + C = 360
C = 360 - 295
C = 65
D = 115
A = 65
a+b+c+d=360
65 + 65 + 115 + 115 = 360
130 + 230 = 360
360 = 360
PLS PLS PLS PLS HELP ME
Exponents work the same way on bases that are _[blank A]_ as they do on bases that are numbers.
When a variable has an exponent, the exponent tells you how many times the variable is _[blank B]_ by itself.
In order to make a negative exponent positive, you must take the _[blank C]_ of the base.
A variable raised to the power of _[blank D]_ is always equal to 1.
Match each blank with the correct item that fills in that blank.
multiplied
0
exponents
reciprocal
1
added
variables
opposite
Answers
A - variables
B - multiplied
C - reciprocal?
D - 0
//
I'm not too sure about C. it can either be the reciprocal or the opposite.
Johnisha paid $144 for 36 ice cream cones. She incorrectly calculates the cost per cone
to be $0.25 each.
Which statement identifies the error Johnisha most likely made in determining the cost per
cone and describes the correct method for determining the cost per cone?
Answers
144/36=4
Which inequalities have -0.5, 2.5, and 4 as part of the solution set? Select all that apply.
z > -3
z < 5
z < 4
z Less-than-or-equal-to 4
z > 0
Answers
Z>-3
Z<5
Z< or = 4
These 3 above have the 3 numbers in the solution set!
You just have to test each number in each inequality, and when all 3 of them work, the inequality is a part of the solution set!
Also Thanks for the 50 Points!
The inequalities are z ≤ 4 and z < 5 that have -0.5, 2.5, and 4 as part of the solution set.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
If the inequality have -0.5, 2.5, and 4 as part of the solution set.
That means, the required value has to be less than or equal to 4.
So, the inequalities are z ≤ 4 and z < 5.
Therefore, the inequalities are z ≤ 4 and z < 5.
To learn more about the inequality;
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1. The number of customers in a restaurant during the peak hour of each day for a month varied
significantly from day to day. Here are pieces of the data on the number of customers served
during the peak hour of each business day:
3 Lowest
25, 32, 37
Q1
45
Mean
48
Median
50
Q3
58
3 highest
69, 70, 75
(a) Are there any outliers in the data set? Justify your answer numerically
Answers
Step-by-step explanation:
First we must calculate the interquartile range (IQR), using this equation:
[tex]IQR = Q_{3} - Q_{1}[/tex]
Based on the information provided we fill in:
[tex]IQR = 58 - 45[/tex]
[tex]IQR = 13[/tex]
In order to find what the range for the data set is we need to use the Interquartile Rule:
[tex]Q_{1}-1.5[/tex] × [tex]IQR\\[/tex]
[tex]Q_{3}+1.5[/tex] × [tex]IQR\\[/tex]
[tex]1.5[/tex] × [tex]13 = 19.5[/tex]
Now we plugin in:
[tex]45 - 19.5 = 25.5\\[/tex]
[tex]58 + 19.5 = 77.5[/tex]
Any number below 25.5 is a possible outlier and any number above 77.5 is a possible outlier.
Answer:
Based on the results of the calculations, 25 could be a possible outlier in the data set.
Identify the shape that is graphed from the points:
A (4, 6)
B (4, 7)
C (8, 6)
D (8, 7)
Answers
Answer:
Rectangle
Step-by-step explanation:
It's a rectangle because opposite sides are parallel as you can see , it has 4 right angles , and it has 4 sides .. it's not a square because in a square all sides are equal
the question is: The endpoints of ST are S(2,-2) and T(4,2) what are the coordinates of midpoint of ST?
Answers
Answer:
(3,0)
Step-by-step explanation:
If you use a graphing calculator and connect the two points then you would get (3,0) :))
is a rectangle a plane shape
Answers
Answer:
A plane shape with four straight sides and four right angles for corners is called a rectangle.
Step-by-step explanation:
Is A PQR-AXYZ? If so, name which similarity postulate or
theorem applies.
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
D. Cannot be determined
Answers
Answer:
D. Cannot be determined
Step-by-step explanation:
Similarly between given triangles can not be determined because given information are insufficient.
The correct option for the given triangles is D. Cannot be determined
What are similar triangles?Any two triangles will be considered as similar as they have congruent corresponding angles and the corresponding sides are in equal ratios.
Two shapes are Similar when one can become the other after a resize, flip, slide or turn.
Given are two triangle PWR and XYZ we need to determine whether they are similar or not,
So, we only have measurement of a pair of sides and measurement of an angle,
We have some similarity rules by which we can prove two triangles to be similar, they are :-
AA rule, Side Angle Side (SAS), Side Side Side (SSS) and Right-angle Hypotenuse Side (RHS)
Since, we do not enough information to conclude our discussion.
Hence, the correct option is D. Cannot be determined
Learn more about similar triangles, click;
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What is the y-intercept of the line shown?
−1
0
0.5
1
Answers
Answer:
-1
Step-by-step explanation:
It crosses the y axis at negative 1, the y axis is the vertical line
A recipe uses 2 cups of milk to make 4 servings. If the same amount of milk is used for each serving, how many servings can be made from three pints?
Answers
Answer:
12 servings
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
a cow is tied to a pole fixed at the mid-point of a side of a square field of side 40m by means of a 14m long rope find the area that cow can graze pls explain
Answers
Step-by-step explanation:
The area that cow can graze is in the form of semicircle.
Radius of semicircle
Length of rope =14 m
Required area = 1/2 ×πr
=1/2×22/7×r^2
=1/2×22/7×14×14
=308m2
help pls ;;-;; ye thxs
Answers
Answer:
You still need help? :P
Step-by-step explanation:
I really need help with this one or I fail
Answers
2. x-intercept — c. (-5,0),(1,0),(3,0)
3. y-intercept — a. (0,-1.5)
4. ...positive infinity — b. positive infinity
5. ..negative infinity — d.negative infinity
6. Local maximum — e. (2.1,0.7)
Hope it helps!
Mark me brainliest, please
Mr. Villa bought 91.25 inches of plastic
labeling tape. He will make labels 1.25 inches long
each. How many labels can he make?
1. What is asked in the problem?
A. the measurement of the tape
B. the labels can he make to the tape
C. inches of plastic labeling tape
D. Mr. Villas tape
2. What is the answer?
A. he can make 69 labels
B. he can make 70 labels
C. he can make 72 labels
D. he can make 73 labels
Answers
Answer:
1) B. the labels can he make to the tape
2) D. he can make 73 labels
Step-by-step explanation:
1) We are told that He will make labels 1.25 inches long each. We are asked the number of labels he can make.
Thus, correct answer is option B.
2) He wants to make labels 1.25 inches long out of 91.25 inches of plastic.
Thus, number of labels he can make = 91.25/1.25 = 73 labels
can some one help me please....
by step by step explanation......
Answers
x * 5 * 25 * 4 ÷ 5, if x = 813 simplified form please
Answers
Answer:
81,300
Step-by-step explanation:
if you can help me i’ll make brainliest
Answers
Answer:
help me
Step-by-step explanationok so
Answer:
pts
Step-by-step explanation:
