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
HELP MEEEEEE PICKING BRAINLIEST!!!
Answers
Answer:
2 kg cashews
6 kg pecans
Step-by-step explanation:
System of Equations:
c + p = 8
8c + 7p = 8(7.25)
let c = 8-p
8(8-p) + 7p = 58
64 - 8p + 7p = 58
-p = -6
p = 6
The graph shows depth of water in a tank over time.
Calculate the rate at which the depth is decreasing.
Give your answer as a decimal.
PLEASE HELP ASAP!!!
Answers
x+10> 20 or x+12< 3. Help please!!!
Answers
Answer:
x < -9 or x > 10.
Step-by-step explanation:
x + 10 > 20
x > 10.
x + 12 < 3
x < -9.
Amjed has 223 cards in his trading card collection. Latif has
8.741 cards in his trading card collection. Using the orders of
magnitude, about how many times more trading cards does Latif
have than Amjed?
Answers
Answer:
The orders of magnitude are numbers of the form:
10^n
where n can be any integer number.
So we can write something like:
"A is n orders of magnitude above B
Now we have the quantities:
Amjed cards = 223
Latif cards = 8741
We want to find how many times more trading cards does Latif have than Amjed.
Then we need to look at the quotient between the number of cards of Latif and Amjed.
8741/223 = 39.2
Now we need to approximate this to the nearest 10^n number.
(..., 0.1, 1, 10, 100, 1000, ...)
The nearest one to 39.2 is 10.
So we can say that Latif's collection is 10.
and 10 = 10^1
then n = 1
Then we can say that Latif's collection is one order of magnitude above Amjed's collection.
The area of a rectangular room is 240 square feet. The width is 12 feet. What is the length?
Answers
Answer:
20 ft
A=wl
l=A/W=240/12=20ft
If using the method of completing the square to solve the quadratic equation
x²-10x – 15 = 0, which number would have to be added to "complete the
square"?
Answers
Answer:
For quadratic equations that cannot be solved by factorising, we use a method which can solve ALL quadratic equations called completing the square. We use this later when studying circles in plane analytic geometry.
Completing the square comes from considering the special formulas that we met in Square of a sum and square of a difference earlier:
(x + y)2 = x2 + 2xy + y2 (Square of a sum)
(x − y)2 = x2 − 2xy + y2 (Square of a difference)
To find the roots of a quadratic equation in the form:
\displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax
2
+bx+c=0,
follow these steps:
(i) If a does not equal \displaystyle{1}1, divide each side by a (so that the coefficient of the x2 is \displaystyle{1}1).
(ii) Rewrite the equation with the constant term on the right side.
(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.
(iv) Write the left side as a square and simplify the right side.
(v) Equate and solve.
Example 1
Find the roots of x2 + 10x − 4 = 0 using completing the square method.
Answer
Example 2
Solve 4x2 + x = 3 by completing the square.
Answer
Exercises
Solve the following quadratic equations by completing the square
Q1. \displaystyle{2}{s}^{2}+{5}{s}={3}2s
2
+5s=3Answer
Q2. \displaystyle{3}{x}^{2}={3}-{4}{x}3x
2
=3−4xAnswer
Q3. \displaystyle{9}{v}^{2}-{6}{v}-{2}={0}9v
2
−6v−2=0Answer
Q4. \displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax
2
+bx+c=0Answer
1. Solving Quadratic Equations by Factoring
3. The Quadratic Formula
x² -10x = 15
x² - 10x + 25 = 15 + 25
(x-5)² = 40
x = -2√(10) + 5
x = 2√(10) + 5
The radius of a circle is 2 inches. What is the circle's area?
r=2 in
Use 3.14 for a
square inches
Answers
Answer:
12.56 in.
Step-by-step explanation:
A=Pi*R to the 2nd power
A=3.14*2 to the 2nd power
A=3.14*4
A=12.56
Let me know if im wrong
Area of the circle is 12.56 square units which has radius 2 inches.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that radius of a circle is 2 inches.
We need to find the area of circle.
Radius= 2 inches.
π=3.14
We know that area of circle=πr²
Area of circle=3.142×2²
=3.142×4
=12.56 square inches.
Hence, area of the circle is 12.56 square units which has radius 2 inches.
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5.12 = 5w, what is W
Answers
Answer:
The answer is 1.024
Step-by-step explanation:
5.12 divided by 5 = 1.024
Hope this helps.
24x^2 + 26x - 104 solve for x
Answers
Answer: 24x2+26x−104 or -104
Step-by-step explanation:
I need help?!?!
I think it’s 9 ??!!
Answers
Answer:
C. 14
iedujdd
Step-by-step explanation:
i think i searched
Answer:
9
Step-by-step explanation:
Triangle DCE and ACD are similar (they share the angle at A, and since DE║CB, ∠D=∠C and ∠E=∠B (corresponding angles))
That means the side lengths are in ratio:
12/(8+12)=?/(6+?)
0.6(6+?)=?
3.6+0.6?=?
0.4?=3.6
?=9
No question, just whoever needs free answers.
Answer this and get free answers for a bit.
Now what's 2+2?
Answers
Answer:
4 lol
Step-by-step explanation:
Answer:
Step-by-step explanation:
Your family has a second car that takes 1 gallon per 25 miles and has 10 gallons to start. Write an equation, identify the y intercept and slope. Please help !
Answers
Answer:
Let's use the slope-intercept form of the equation of a line describe the slope and the y-intercept:
y = mx + b where m=slope and b=y-intercept
y = 25x + 10
write a polynomial in standard form that represents the area of the shaded region
Answers
Answer:
x^2-3x+36
Step-by-step explanation:
THE ANSWER IS: x^2 - 3x + 36
Find the distance between
(5 , 1 ) and ( 3 ,6)
Answers
Answer:
Step-by-step explanation:
[tex]\sqrt{(6-1)^{2}+(3-5)^{2} }[/tex]=[tex]\sqrt{29}[/tex]
=5.39(correct to nearest hundredth)
In the figure, shown, AD, CE, and FB intersect at point F. Find the value of x.
Answers
Answer:
8
Step-by-step explanation:
∡AB + ∡BC + ∡CD = 180°
∡CD = ∡AE
∡AB + ∡BC + ∡AE = 180°
(8x + 6)° + (6x + 2)° + (7x + 4)° = 180°
8x + 6 + 6x + 2 + 7x + 4 = 180
21x + 12 = 180
21x = 180 - 12
21x = 168
x = 8
The compound interest on a sum of money in
2 years and 4 years are Rs 5,460 and Rs 12,066.60
respectively. Find the difference between principal
and compound interest of 3 years.
Answers
Answer:
The difference between the principal and the compound interest in three years is Rs 17,994
Step-by-step explanation:
The compound interest is given according to the following formula;
[tex]C.I. = P \cdot \left ( 1 + \dfrac{r}{n} \right ) ^{n\cdot t} - P[/tex]
The given amount of the compound after 2 years = Rs 5,460
The given amount of the compound after 4 years = Rs 12,066.60
Therefore, we have;
[tex]5,460 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{2} - P[/tex]...(1)
[tex]12,066.60 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{4} - P[/tex] ...(2)
Dividing equation (2) by (1), we have;
[tex]\dfrac{12,066.60}{5,460} = \dfrac{P \cdot \left ( \left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1\right )}{P \cdot \left (\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 \right ) } =\dfrac{\left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1}{\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 }[/tex]
[tex]Let \ \left ( 1 + \dfrac{r}{100} \right ) ^{2} = x, we \ get;[/tex]
[tex]\dfrac{12,066.60}{5,460} =\dfrac{\left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1}{\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 } = \dfrac{x^2 - 1}{x - 1}[/tex]
∴ 12,066.60 × (x - 1) = 5,460 × (x² - 1) = 5,460 × (x - 1) ×(x + 1)
∴ 12,066.60 × (x - 1)/(x - 1) = 5,460 × (x + 1)
12,066.60/5,460 = x + 1
x = 12,066.60/5,460 - 1 = 1.21 = 121/100
x = 121/100
[tex]\left ( 1 + \dfrac{r}{100} \right ) ^{2} = x = \dfrac{121}{100}[/tex]
[tex]1 + \dfrac{r}{100} =\sqrt{ \dfrac{121}{100}} = \dfrac{11}{10}[/tex]
We get
[tex]\dfrac{12,066.60}{5,460} =\dfrac{221}{100}[/tex]
[tex]\therefore \dfrac{12,066.60}{5,460} =\dfrac{221}{100} = \left ( 1 + \dfrac{r}{100} \right ) ^{2}[/tex]
[tex]1 + \dfrac{r}{100} = \sqrt{ \dfrac{221}{100} } = \dfrac{\sqrt{221} }{10}[/tex]
[tex]\dfrac{r}{100} = \dfrac{\sqrt{221} }{10} - 1[/tex]
[tex]\dfrac{r}{100} = \dfrac{11}{10} - 1 = \dfrac{1}{10} = 0.1[/tex]
r = 100 × 0.1 = 10%
r = 10%
Therefore, we have;
[tex]5,460 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{2} - P = P \times \left ( 1 + 0.1\right ) ^{2} - P[/tex]
[tex]5,460 = P \times \left ( 1 + 0.1\right ) ^{2} - P = P \times \left (\left ( 1 + 0.1\right ) ^{2} - 1\right) = P \times \dfrac{21}{100}[/tex]
[tex]P = \dfrac{100}{21} \times 5,460 = 26,000[/tex]
The principal = Rs. 26,000
The compound interest in 3 years is therefore;
[tex]CI_3 = 26,000 \times \left ( 1 + \dfrac{10}{100} \right ) ^{3} - 26,000= 8606[/tex]
The difference, 'd', between the principal and the compound interest in three years, is given as follows;
d = P - CI₃
d = 26,600 - 8606 = 17994
The difference between the principal and the compound interest in three years, d = Rs 17,994.
what's HCF/GCD of 144 and 0 ?
Answers
Answer:
144 =4
=>144=2×2×2×3×3
OK
OK i know this only
enjoy your day
What percent is 50% of 50% of x? Please help.
Answers
25% is 50% of 50.
Explaination is on the picture.
50% of 100 is 50.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
Let x be a number such that
50% of x is 50
This forms an equation in one variable which can be solved by transposition.
[tex]50/100\times x = 50[/tex]
x/2=50
On multiplying 2 both sides,
[tex]X/2\times 2 =50\times 2[/tex]
X=100
Thus, 50% of 100 is 50.
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Correct question:
50% of what is 50.
Ian's car can go 93 miles on 3 gallons of gas. During a drive, last weekend, Ian used 8 gallons of gas. How far did Ian drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas used.
Answers
Answer:248
Step-by-step explanation:
First you need to find the unit rate by dividing 93 by 3 which would be 31 then take that number (which is how many miles for one gallon) and multiply it by 8 which would get you 248( if you need this as an equation here 93\3= 31 31*8 = 248). If they gave you the distance instead you would have had to divide by 31 instead of using multiplication. Hope this helps!
Complete the equation of the line whose slope is 5 and y- intercept is (0,4)
y?
Answers
Answer:
y = 5x + 4
Step-by-step explanation:
y - 4 = 5(x - 0)
That is point-slope form. I'm not sure if you want it in slope intercept form, but slope intercept form of the equation is y = 5x + 4
Answer:
y=5x+4
Step-by-step explanation:
y=mx+b
Donna packs 14 pounds of nuts in bags . Each bag has 1/4 pound of nuts Which equation shows the number of bags Donna packed with all the nuts
Answers
Answer:
Step-by-step explanation:
Where are the equations to choose from?
14 pounds × (1 bag)/(¼ pound) = 56 bags
30 POINTS!!!!! What is the domain for each function below?
Picture included below!
-For the 1st equation, the options are the greater than/equal to symbol and the less than/equal to symbol, and then 3, -3, and 0.
-For the 2nd equation, the options are the greater than/equal to symbol and the less than/equal to symbol, and 0 and 3.
Answers
The domain is the set of input values for which the function is real and defined.
Find non negative values for the radicals.
For y = sqrt(3-x) if x is greater than the 3 the value under the square root would be negative which would result in a non real number.
The answer needs to be x <= 3 ( less than or equal to)
For y = sqrt(3x), if x is less than 0, the number under the sqrt root would be negative resulting in a non real number.
The answer is x >= 0 ( greater than or equal to)
40 kişinin katıldığı bir davete 5 evli çift daha
katılırsa, davete katılan erkeklerin sayısı, ka-
dınların sayısının 2 katından 13 eksik oluyor.
Buna göre, son durumda davete kaç erkek-
katılmıştır?
a) 30 D) 29 C) 26
D) 24
Answers
sen türksün be ne işin var senin burada
A machine paints 360 toy boats in 45 MINUTES. Write the expression that represents the unit rate per HOUR
Answers
Answer:
480 toy boats per hour
Step-by-step explanation:
1. Divide 360 by 45 to find unit rate per MINUTE.
360 / 45 = 8
2. One hour = 60 minutes, so multiply 8 and 60.
8 * 60 = 480
Find the slope for the line that runs through points (2, 5) and (-3, 7)
Answers
Answer:
-0.4
Step-by-step explanation:
to solve use the formula m=y2-y1/x2-x1
The composite score range for the ACT is:
A. 20 to 85
B. 1 to 98
C. 1 to 50
D. 1 to 36.
Answers
The composite score range for the ACT is D) 1 to 36.
The composite score range for the ACT (American College Testing) is the total score achieved by an individual after taking all four sections of the ACT, which include English, math, reading, and science. The composite score ranges from 1 to 36, with 36 being the highest possible score.
The ACT score is used by colleges and universities in the United States to assess the readiness of a student to enter college. A high composite score indicates that the student has the skills and knowledge needed to succeed in college-level courses. Therefore, the correct answer is D) 1 to 36.
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solve 1.9(2x + 1) = 22x + 13
Answers
the answer is: x= -111/182
Answer:
x= -0.60989010989
Step-by-step explanation:
Which expression is equivalent to 1 1/2 plus 1 6/7 I NEED HELP HURRY
Answers
Answer: is this correct
Step-by-step explanation:
Write two integers that are closest to the number in the middle to complete the statement.
Answers
4 and 5
finally that is closest to the number in the middle to complete the statement
The ratio of coretta's weight to Justin's weight is 3:4. If corretta gains 5 pounds the ratio of their weights will be 4:5. How much does Justin weigh?
Answers
Answer:
100 pounds
Step-by-step explanation: