Answer:
[tex]\displaystyle \int\limits^8_1 {\frac{3}{x}} \, dx = 9 \ln 2[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \frac{3}{x} \\\left[ 1 ,\ 8 \right][/tex]
Step 2: Integrate
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle \int\limits^8_1 {\frac{3}{x}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 3 \int\limits^8_1 {\frac{1}{x}} \, dx[/tex][Integral] Logarithmic Integration: [tex]\displaystyle 3 \int\limits^8_1 {\frac{1}{x}} \, dx = 3 \ln \big| x \big| \bigg| \limits^8_1[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle 3 \int\limits^8_1 {\frac{1}{x}} \, dx = 3 \ln 8[/tex]Simplify: [tex]\displaystyle \int\limits^8_1 {\frac{3}{x}} \, dx = 9 \ln 2[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
A scientist teacher murdered $3980 worth of microscopes and dissension kits for the new science lab a total of 38 microscopes and 47 dissension kids were ordered a microscope cost four times as much as a Ascension kit write a system of linear equations that represents the situation what is the cost of each item
Answer:
dang
Step-by-step explanation:
._.
HURRY PLEASE?!
Determined to finish her milkshake before Diego, Lin now drinks her 12 ounce milkshake at a rate of 13 an ounce per second. Diego starts with his usual 20 ounce milkshake and drinks at the same rate as before, 23 an ounce per second.
Below is a graph of this system.
After how many seconds do both Diego and Lin have the same amount of milkshake left?
[ Select ]
How many ounces do both Diego and Lin have left of their milkshakes at that point?
[ Select ]
Answer: 24 seconds
4 ounces
Answer:
24 seconds and 4 ounces
Step-by-step explanation:
The point where both lines meet is the point where they are both equal.
The point where both lines meet is (24,4)
Since the x-axis represents seconds the x-coordinate will represent the number of seconds it takes for them to be equal which is 24.
Since the y-axis represents ounces the y-coordinate will represent the number of ounces they have when they are equal which is 4.
which relations represent functions?
2 divided by 1/3 pls
Answer:
6
Step-by-step explanation:
2/ 1/3= 6
Answer:
= 6
Step-by-step explanation:
you can do the keep, switch, flip strategy
keep 2/1, switch division to multiplication, and flip 1/3 to 3
2 x 3 = 6
will name brainiest please help thank u
Answer:
C
This was one of the questions on my test.
please please help me!
Answer:
Option 4
Step-by-step explanation:
It has a negative slope of -[tex]\frac{1}{5}[/tex] (move down one and to the right 5)
What is the value of 4+ y if y = 18?
Answer:
22
Step-by-step explanation:
4+18 = 22
Some marbles in a bag are red and the rest are blue. If one red marble is removed,
then one-seventh of the remaining marbles are red. If two blue marbles are removed
instead of one red, then one-fifth of the remaining marbles are red. How many
marbles were in the bag original
Pls give EXPLANATION
Answer:
22
Step-by-step explanation:
Let r be red and b be blue
1/7(r-1+b)=r-1
1/5(r+b-2)=r
r-1+b=7(r-1)
r+b-2=5r
r-1+b=7r-7
1=7r-7-5r
8=2r
r=4
1/5(4+b-2)=4
2+b=20
b=18
18+4=22
3) 15x + 4 = 106
Can someone show me the steps ? Pls :)
1) Subtract 4 from both sides to get 15x = 102
2) Divide by 15 on both sides to get x = 6.8
Answer:
x=6.8
Step-by-step explanation:
15x + 4 = 106
subtract 4 from both sides
15x=102
divide both sides by 15
x=6.8
A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month is given by C=0.3X^2+8,000. How fast is the cost per month changing when production is changing at the rate of 14 units per month and the production level is 70 UNITS?
Costs are ___ at the rate of $___ per month at this production level.
Answer:
Costs are changing at the rate of $588 per month at this production level.
Step-by-step explanation:
From the question, we have:
C = 0.3X^2 + 8,000 ........................ (1)
Differentiating equation (1) with respect to time, t, we have:
dC/dt = (0.3 * 2) X (dX/dt)....................... (2)
Where;
X = 70
dX/dt = 14
Substituting this into equation (2), we have:
dC/dt = (0.3 * 2) * 70 * 14
dC/dt = 588
This implies that costs are changing at the rate of $588 per month at this production level.
Write an recursive rule for the sequence 7,14,21,28
sharice is putting jars of jam into boxes. she puts 8 jars into each box, and she has a total of 144 jars. sharice wants to know how many boxes she needs.
she needs 18 boxes.
What is factoring?A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.
Given
Based on the given conditions, formulate: 8 x = 144
Divide both sides of the equation by the coefficient of variable: x = 144/8 out the common factor: x = 18
To know more about factoring refer to :
https://brainly.com/question/25829061
#SPJ2
find the value of 5^-3 x 2^-1
Answer:
Step-by-step explanation:
5^-3 = 1/(5*5*5) = 1/125
2^-1 = 1/2
1/125 * 1/2 = 1/250
That could be the answer
So could 0.004
For any positive number b not equal to 1 and any number or variable n, evaluate the following expression. log.(b") = O A. no O B. n O c. b Б OD. "
Answer:
a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
What is the midpoint of line segment
A (-3,-5)
B (1,-9)
‾
start overline, A, B, end overline?
Hi!
Find the approximate area of the shaded region of the figure below.
Thank you!
(P.S, Please ignore the “Below” in the picture! Sorry!)
Which of the following coordinate points have an x-value of 4? Select all that apply.
A) (2, 4)
B) (4, 5)
C) (4,0)
D) (4,3)
Answer:
it b
Step-by-step explanation:
Can someone help pls !
Answer:
(B). [tex]A_{y}[/tex] = [tex]\left[\begin{array}{cc}12&7\\17&-51\end{array}\right][/tex]
Step-by-step explanation:
12x - 13y = 7
17x - 22y = - 51
A = [tex]\left[\begin{array}{cc}12&-13\\17&-22\end{array}\right][/tex]
[tex]A_{x}[/tex] = [tex]\left[\begin{array}{cc}7&-13\\-51&-22\end{array}\right][/tex]
[tex]A_{y}[/tex] = [tex]\left[\begin{array}{cc}12&7\\17&-51\end{array}\right][/tex]
29. The population of Minnesota is about 5.577 million people. Write Minnesota's population in standard notation (as a number).
Answer:
5,577,000
Step-by-step explanation:
The sum of 2 times p and 2 is 48. What is p?
Answer:
p = 23
Step-by-step explanation:
2p + 2 = 48
-2 -2
2p = 46
/2 /2
p = 23
Hope this helps and I hope u have an Amazing day!!
what is the equation of the line through (2,-1) and (0,5)
A. y= -3x + 5
B. y= 3x - 5
C. y= -3x - 5
D. y= 3x + 5
Find g(-7) for g(x) = -8x+1
Answer:
Step-by-step explanation:
if we have g(x)=- 8x+1
we will replace x with -7
g(-7)=56+1=57
Write the ratio as a fraction lowest terms 7 days to 13 days
Answer:
The answer is: [tex]\mathbf{Ratio \ as \ fraction =\frac{7}{13}}[/tex]
Step-by-step explanation:
We need to write ratio as a fraction lowest terms 7 days to 13 days
Ratio as fraction is written as: [tex]\frac{a}{b}[/tex] if we have a to b
So, in our case 7 days to 13 days
a= 7, b= 13
Writing ratio as fraction:
[tex]Ratio \ as \ fraction =\frac{7}{13}[/tex]
The fraction cannot be further simplified as already in lowest form so, the answer is: [tex]\mathbf{Ratio \ as \ fraction =\frac{7}{13}}[/tex]
Multiply 1 by 5 152 x 61 =
Answer:
5
Step-by-step explanation:
1*5=5
2/3 x 4/5 plz help me
Multiple choice! Pls help :) i really need help!
Answer:
A and D
Step-by-step explanation:
What basic geometric shape is always created by an actual snowflakes?
Answer:
A regular hexagon. Search up pictures of snowflakes and you can see by the symmetry.
Answer:hexagon
Step-by-step explanation:
There are 18 fish in a pond. 9 carp, 8 koi,
and 1 trout. what is the probability of picking a koi if you pick a fish at random?
Answer:18/5
Step-by-step explanation:
Select the correct answer.
Find the sum of 2 1/9 + (-2/9) + 3 5/9
OA. -5
OB. 5
OC. 5 2/9
OD. 5 4/9
O E. 5 5/9
Answer:
5 4/9
Step-by-step explanation:
Convert a mixed number 2 19
to a improper fraction: 2 1/9 = 2 19 = 2 · 9 + 19 = 18 + 19 = 199
To find new numerator:
a) Multiply the whole number 2 by the denominator 9. Whole number 2 equally 2 * 99 = 189
b) Add the answer from previous step 18 to the numerator 1. New numerator is 18 + 1 = 19
c) Write a previous answer (new numerator 19) over the denominator 9.
Two and one ninth is nineteen ninths
Add: 19
9+ (-29) = 19 + (-2)9= 179
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(9, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 9 = 81. In the next intermediate step the fraction result cannot be further simplified by canceling.
In words - nineteen ninths plus minus two ninths = seventeen ninths.
Conversion a mixed number 3 59
to a improper fraction: 3 5/9 = 3 59= 3 · 9 + 59= 27 + 51 = 329
To find new numerator:
a) Multiply the whole number 3 by the denominator 9. Whole number 3 equally 3 * 99 = 279
b) Add the answer from previous step 27 to the numerator 5. New numerator is 27 + 5 = 32
c) Write a previous answer (new numerator 32) over the denominator 9.
Three and five ninths is thirty-two ninths
Add: the result of step No. 2 + 32
9= 179+ 329 = 17 + 329 = 499
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(9, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 9 = 81. In the next intermediate step the fraction result cannot be further simplified by canceling.
In words - seventeen ninths plus thirty-two ninths = forty-nine ninths.
Answer:
D. 5 4/9
I hope this helps
Machine A makes 12.75 ounces of popcorn in 3 minutes. Machine B makes 18 ounces of popcorn in 4 minutes.
If each machine makes popcorn for 10 minutes, will there be enough popcorn for eight 9-ounce bags? Explain.
Answer:
Machine A makes popcorn at a rate of 4.25 ozs per minute (12.75oz/3min).
Machine B makes popcorn at a rate of 4.5 ozs per minute (18oz/4min).
Machine A will make 4.25oz/min * 10minutes = 42.5oz of popcorn after 10 minutes
Machine B will make 4.5oz/min * 10 minutes = 45oz of popcorn after 10 minutes
After 10 minutes there will be a total of 42.5oz (Machine A) +45oz (Machine B) = 87.5oz.
So the answer is: Yes there will be (more than) enough popcorn if both machines make popcorn for 10 minutes.
If the question is wondering how many 9oz bags they can fill: 87.5oz/9oz per bag = 9.7222 bags. The machines can fill 9, 9oz, bags with some popcorn leftover.
Step-by-step explanation:
Machine A makes popcorn at a rate of 4.25 ozs per minute (12.75oz/3min).
Machine B makes popcorn at a rate of 4.5 ozs per minute (18oz/4min).
Machine A will make 4.25oz/min * 10minutes = 42.5oz of popcorn after 10 minutes
Machine B will make 4.5oz/min * 10 minutes = 45oz of popcorn after 10 minutes
After 10 minutes there will be a total of 42.5oz (Machine A) +45oz (Machine B) = 87.5oz.
So the answer is: Yes there will be (more than) enough popcorn if both machines make popcorn for 10 minutes.
If the question is wondering how many 9oz bags they can fill: 87.5oz/9oz per bag = 9.7222 bags. The machines can fill 9, 9oz, bags with some popcorn leftover.
Answer:
Yes
Step-by-step explanation:
Divide 12.75 by 3 to get the amount Machine A makes in 1 minute, 4.25 ounces.
Divide 18 by 4 to get the amount Machine B makes in 1 minute, 4.5 ounces
Multiply 4.25 by 10 for a total from Machine A, 42.5 ounces.
Multiply 4.5 by 10 for a total from Machine B, 45 ounces.
Add 42.5 to 45 totalling 87.5
Eight 9-ounce bags require 72 ounces of popcorn. So if both Machines made a total of 87.5 ounces they would have enough popcorn.