Answer:
A) [tex]\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx[/tex]
General Formulas and Concepts:
Calculus
Discontinuities
Removable (Hole) Jump Infinite (Asymptote)Integration
IntegralsDefinite IntegralsIntegration Constant CImproper IntegralsStep-by-step explanation:
Let's define our answer choices:
A) [tex]\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx[/tex]
B) [tex]\displaystyle \int\limits^3_1 {\frac{x + 1}{3x - 2}} \, dx[/tex]
C) [tex]\displaystyle \int\limits^0_{-1} {\frac{x + 1}{3x - 2}} \, dx[/tex]
D) None of these
We can see that we would have a infinite discontinuity if x = 2/3, as it would make the denominator 0 and we cannot divide by 0. Therefore, any interval that includes the value 2/3 would have to be rewritten and evaluated as an improper integral.
Of all the answer choices, we can see that A's bounds of integration (interval) includes x = 2/3.
∴ our answer is A.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Can someone please explain to me how I would do this, I cannot figure out how to do this equation at all!!
Answer:
First, do 4x*4x. then,16x*16x. next, 64x*64x. and,256x*256x. answer:1024x. Divide 1024x by 8x. answer to that is 128.
Answer:
The expression in simplified form:
[tex]\frac{4x^5}{8x}=\frac{x^4}{2}[/tex]
Step-by-step explanation:
Given the expression
[tex]\frac{4x^5}{8x}[/tex]
We need to simplify the expression.
Simplifying the expression
[tex]\frac{4x^5}{8x}[/tex]
Cancel the common factor: 4
[tex]=\frac{x^5}{2x}[/tex]
Cancel the common factor
[tex]=\frac{x^4}{2}[/tex]
Therefore, the expression in simplified form:
[tex]\frac{4x^5}{8x}=\frac{x^4}{2}[/tex]
share $180 between anna and barry so that Anna share to barry share is in the ratio 4:5
Answer:
Anna: $80
Barry: $100
Step-by-step explanation:
total of 9 shares
each 20 dollars
4(20) = 80
5(20) = 100
What is the slope of the line with equation y - 3= -1/2(x - 2)
Answer:
-1/2
Step-by-step explanation:
according to what I learnt, the general form of every equation is y=mx+c where y is the y value, x is the x value, m is the slope and c is the y-intercept so the equation y-3= -1/2(x - 2) in the general form wil be :
y= -x/2+4 and so m= -x/2 ,that is -1/2
Consider two people where one person is 25% taller than the other but proportion in exactly the same way That the taller person looks like a lager version of the shorter person Suppose the shorter person has a 36%-inch waist what size is the the taller person's waist?
Answer:
46.8 inches
Step-by-step explanation:
Taller person = 30% more than height of shorter individual
Waist size of shorter person = 36 inches
Since they are proportioned in the same way:
Waist size of the taller person will be 30% larger than the waist size of the shorter person :
30% increase in size 36
(100 + 30)% of 36
130% of 36
(130 / 100) * 36
1.3 * 36
= 46.8 inches
Please help me with this question!!
Step-by-step explanation:
according to pythagoras theorem
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
therefore,
x2 = (4)2 + (4)2
x2 = 16 + 16
x2 = 32
x = √32
hence, x = 4√2
△RST ~ △RYX by the SSS similarity theorem.
Which ratio is also equal to StartFraction R T Over R X EndFraction and StartFraction R S Over R Y EndFraction?
StartFraction X Y Over T S EndFraction
StartFraction S Y Over R Y EndFraction
StartFraction R X Over X T EndFraction
StartFraction S T Over Y X EndFraction
Answer:
Answer would most likely be option D. StartFraction S T Over Y X EndFraction
Explanation:
Take care..
Mini made a recipe that yields 4 and 1 over 2 cups. If each serving is 1 over 2 cup, which expression will help Mini determine the number of servings her recipe will yield?
Answer:
1/2x = 4 1/2
Where x = Number of servings = 9 servings
Step-by-step explanation:
Mini made a recipe that yields 4 and 1 over 2 cups.
1 recipe = 4 1/2 cups
1 serving = 1/2 cups
1/2 cups = 1 servings
4 1/2 cups = x servings
Cross Multiply
1/2 × x = 4 1/2
x = 4 1/2 ÷ 1/2
x = 9/2 ÷ 1/2
x = 9/2 × 2
x = 9 servings.
Therefore, the expression tha will help Mini to determine the number of servings her recipe will yield is
1/2x = 4 1/2
Where x = Number of servings = 9 servings
Subract the sum of 3a^4b-4b^3+c^2 & 6a^4b+3b^3-6c^2 from the sum of 6a^4b-4b^3-4c^2 & 2a^4b+4b^3+7c^
Answer:
-a^4b + b^3 - 8c^2
Step-by-step explanation:
Sum of
3a^4b-4b^3+c^2 + 6a^4b+3b^3-6c^2
= 3a^4b + 6a^4b - 4b^3 + 3b^3 + c^2 - 6c^2
= 9a^4b - b^3 - 5c^2
Sum of
6a^4b-4b^3-4c^2 + 2a^4b+4b^3+7c^
= 6a^4b + 2a^4b - 4b^3 + 4b^3 - 4c^2 + 7c^2
= 8a^4b + 3c^2
Subtract
8a^4b + 3c^2 - (9a^4b - b^3 - 5c^2)
= 8a^4b + 3c^2 - 9a^4b + b^3 + 5c^2
= 8a^4b - 9a^4b + b^3 + 3c^2 + 5c^2
= -a^4b + b^3 - 8c^2
3 (m+6) +7 (m-2)
7(6x + 5) - 8
4(3x + 5) - 13
Answer:SAME SIGNS 1. Add.
2. Sum is positive if both are positive; negative if both are negative.
5 + 8 = 13 –5 + (–8) = –13
DIFFERENT SIGNS
1. Subtract the absolute values.
2. Answer is sign of the integer with the greater absolute value.
5 + (–8) = –3 –5 + 8 = 3
Find each sum. 1. –4 + (–8)
–12
4. –16 + 11 –5
7. –49 + (–32)
–49 –81 –32 –81
2. 14 + 16 30
5. 28 +(–42) –14
8. 23 + (–23) 0
3. –43 + (–12) –55
6. 75 + (–5) 70
9. 86 + (–18)
86 68–18 68
Integers
Multiplying & Dividing
RULE
EXAMPLES
1. Multiply or divide.
2. The answer is positive if the signs are the same (both positive or both negative); negative if the signs are different (one positive and one negative).
–5 x(–8) = 40 40 4 = 10
16 x(–3) = –48 –20 10 = –2
Find each product or quotient.
1. –3 x (–8) 24
4. 0 x (–121)
0 5 –13
2. –5 x (–5) 25
3. –15 x 3 –45
5. –35 (–7)
6. –65 5
7. 240 (–4) 8. 36 12 9. (–49 7) x 8 –7 x 8
–60 3
–56
Step-by-step explanation:
make x the subject. 4x-5=t(x+m)
Answer:
x= tm+5/4-t
Step-by-step explanation:
4x-5=t(x+5)
4x-5-=tx+tm distributive
4x-5-tx=tm substract tx from both sides
4x-tx=tm+5 add 5 to both sides
x * 4+ x(-t) =tm+5 factor x out 4x-tx
x(4-t)=tm+5 factor x out x*4 + x(-t)
x(4-t)/4-t= tm/4-t+ 5/4-t divide each term in 4-t
x= tm/4-t + 5/4-t combine the numerators over the common denominator
x=tm+5/4-t
Help me out with this, homes
Answer:
2
Step-by-step explanation:
2
Consider the volume of a rectangular pyramid, one whose base is not square. Does changing one of the three variables (length, width, or helght)
by a given fraction have a greater effect on the volume of the pyramid than changing either of the other two variables? That is, which variable, if
any, has the largest influence on the volume? Assume that the other two variables remain constant. Explain your answer.
Answer:
dobt worry il heñp il solve
43 decreased by a number B
Answer:
43 - B = x
Step-by-step explanation:
When decreasing, you are subtracting, so the equation for this problem would be 43 minus B equals whatever quantity you were given as a solution.
i dont know plz help
Pleaseee help this is urgent!!! I need it in English! Please show all the work ! 14 points
Answer:
width = 40 feet, length = 90 feet
Step-by-step explanation:
length = 2w + 10
width = w
Perimeter = 260
Perimeter of rectangle = 2length + 2width
Sub the values into that equation:
260 = 2(2w + 10) + 2(w)
260 = 4w + 20 + 2w
260 = 6w + 20
260 - 20 = 6w
240 = 6w
w = 240/6
w = 40
So now we know the width of the garden is 40 feet.
To find the length, substitute the width into the length equation:
length = 2w + 10
length = 2(40) + 10
length = 90 feet
length = 90 feet, width = 40 feet
The equation of a curve is
[tex]y = 4x {}^{3} + 4px {}^{2} + 16x - 9[/tex]
Find the range of values of p such that y is an increasing function.
Let's solve for p.
[tex]y=4x3+4px2+16x−9[/tex]
Step 1: Flip the equation.
[tex]4px2+4x3+16x−9=y[/tex]
Step 2: Add -4x^3 to both sides.
[tex]4px2+4x3+16x−9+−4x3=y+−4x3[/tex]
[tex]4px2+16x−9=−4x3+y[/tex]
Step 3: Add -16x to both sides.
[tex]4px2+16x−9+−16x=−4x3+y+−16x[/tex]
[tex]4px2−9=−4x3−16x+y[/tex]
Step 4: Add 9 to both sides.
[tex]4px2−9+9=−4x3−16x+y+9[/tex]
[tex]4px2=−4x3−16x+y+9[/tex]
Step 5: Divide both sides by 4x^2.
4px² / 4x² = −4x³ − 16x + y + 9 / 4x²
Answer:
p = −4x³ − 16x + y + 9 / 4x²
Can y’all help me with this
Answer:
24.45cm squared
Step-by-step explanation:
(9 x 12) - ((6 x 3.14) / 2)
A is what percent of B? Pls help???
Answer:
If you want to know what percent A is of B, you simple divide A by B, then take that number and move the decimal place two spaces to the right. That's your percentage!
Step-by-step explanation: There is no exact answer and it would be null. You didn't even give an image
Find the Values of y
Y ² = 169
Answer:
Y= 13,-13
Step-by-step explanation:
In the chemical formula 2SO2, how many total atoms of oxygen (O) are there?
Answer:
4
Step-by-step explanation:
2 molecules of SO2
each molecule contains 2 atoms of Oxygen
Answer:
Step-by-step explanation:
Convert the following repeating decimal to a fraction in simplest form.
.6
Answer:
2/3
Step-by-step explanation:
Answer:
7/10
Step-by-step explanation:
0.6 is a repeating decimal in this case, so you can round it to .7
From there, you simply put it over ten because you cant break seven down any more than that in a simple fraction.
I REALLY NEED HELP ON THIS!!!!!! I WILL MARK BRAINLIEST
Answer:
y = 2,500x + 5,000
Rate of change = $2500 a year
Initial value = $5000
Step-by-step explanation:
We have 3 values to figure what is the function here, the rate of change, and the initial value.
To find the initial value, find where y is located where x is 0. In this case it's $5000, so that's the initial value.
Now the rate of change. Find y where x is 1. That is $7,500. Subtract $5000 from to get the rate of change, since it's the same. It's constant because of a straight diagonal line.
$7,500 - $5,000 = +$2,500/year
Now the equation. This is not proportional, because y's starting point is not 0. It's greater than that, so an addition sign is in the equation. Do you remember our initial value? That's right! It was $5,000, so put that after the addition sign.
y = ????x + 5,000
You also need to remember the rate of change, which was 2,500. Put that on the left of the addition sign and there's your equation!
y = 2,500x + 5,000
Answer:
y=2500x + 5000
2500
5000
Step-by-step explanation:
A video game is on sale for $55. If the discount was
14%, what was the original price?
Answer:
$77
Step-by-step explanation:
i just take 55 x 0.14 which is 7.7 then i moved the decimal 1 place to the right.
Answer:
I believe the answer it 62.70
although I am not completely sure
Step-by-step explanation:
14% of 55 = 7.7
7.7 + 55 = 62.7
= $62.70
HELP I NEED HELP ASAP
Taxi Driver A(x)=1.50x+5 and Taxi Driver B charges B(x)=1.25x+8 where x is the number of miles driven. After how many miles will the cost be the same for each taxi driver?
Answer:
12 miles
Step-by-step explanation:
1.25x + 8 =1.5x+5
1.25x-1.5x=5-8
-0.25x=-3
-0.25x/-0.25x=-3/-0.25
x= 12
Please help!!
How do I rewrite this expression into radical form??
You have 42 coins with a total value of $3.00. Some of the coins are dimes, and the rest are quarters.
Select the two equations that would create the best system of equations to represent this scenario.
Answer:
1. $3.00+42=$3.42
2. 4 Dimes , 2 Pennies
Step-by-step explanation:
2. 4 Dimes = 40 cents , 2 pennies = 2 cents
1. Add up 3.00+42 and that is how you could get the answer for number 1 .
Find the slope of the line through each pair of points
(-20,-4), (-12,-10)
Answer:
is it just the slope of those points? if so -3/4
Step-by-step explanation:
i think. if not correct me
Answer:
[tex]-\frac{3}{4}[/tex]
Step-by-step explanation:
The slope of a line is given by:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, the slope of the line that passes through these points is:
[tex]m=\frac{-10-(-4)}{-12-(-20)}=\frac{-6}{8}=\fbox{$-\frac{3}{4}$}[/tex].
PLEASE HELP MEEEE!!!!!!!
Answer:
its a black picture...?
Step-by-step explanation:
Albert, bill, claire, and David are all siblings. Bill was born 2 years after Albert. Claire's favourite colour is orange and she is currently half the age of Albert. David enjoys golf and swimming and he is 3 times older than Bill.
The total of their age is 113 using algebraic methods find out their exact age
what is their exact age
Answer:
Albert = 22
Bill = 22 - 2 = 20
Claire = 22/2 = 11
David = 3(20) = 60
Step-by-step explanation:
Let Albert's age = x
Bill = x - 2
Claire = x/2
David = 3(x - 2)
Total sum of their ages = 113
x + x - 2 + 0.5x + 3(x - 2) = 113
x + x - 2 + 0.5x + 3x - 6 = 113
x + x + 3x + 0.5x -2 - 6 = 113
5.5x - 8 = 113
5.5x = 113 + 8
5.5x = 121
x = 121 / 5.5
x = 22
Albert = 22
Bill = 22 - 2 = 20
Claire = 22/2 = 11
David = 3(20) = 60
if the mean of 6 7 13 and 10 is 8 find the range
Answer:
hope this hlo u
Step-by-step explanation:
range =highest observation-lowest observation
range=10-6
=4