Use the Fundamental Theorem of Calculus to find the "area under curve" of
f
(
x
)
=
6
x
+
19
between
x
=
12
and
x
=
15
.
Answer:
[tex]\displaystyle A = 300[/tex]
General Formulas and Concepts:
Calculus
Integrals
Definite IntegralsArea under the curveIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration 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]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(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
f(x) = 6x + 19
Interval [12, 15]
Step 2: Find Area
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^{15}_{12} {(6x + 19)} \, dx[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle A = \int\limits^{15}_{12} {6x} \, dx + \int\limits^{15}_{12} {19} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle A = 6\int\limits^{15}_{12} {x} \, dx + 19\int\limits^{15}_{12} {} \, dx[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = 6(\frac{x^2}{2}) \bigg| \limits^{15}_{12} + 19(x) \bigg| \limits^{15}_{12}[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle A = 6(\frac{81}{2}) + 19(3)[/tex]Simplify: [tex]\displaystyle A = 300[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
The map shows the location of four places in a school. A coordinate plane is shown. There is a point at 5, 2 labeled Front office. There is a point at negative 6, 4 labeled Gym. There is a point at negative 4, negative 3 labeled Auditorium. There is a point at 6, negative 4 labeled Library. Peter's English class is located in the same quadrant as the auditorium. Which of the following could be the coordinates of the English classroom?
Answer:
its d or to be more specific its the right of the coordinate plane
Step-by-step explanation:
](6^3 - 9)/23]4
Evaluate this expression
The value of the expression is [(6^3 - 9)/23]4 = 36
How to evaluate the expression?The expression is given as:
[(6^3 - 9)/23]4
Evaluate the exponent
[(6^3 - 9)/23]4 = [(216- 9)/23]4
Evaluate the quotient and the difference
[(6^3 - 9)/23]4 = [9]4
Evaluate the product
[(6^3 - 9)/23]4 = 36
Hence, the value of the expression is [(6^3 - 9)/23]4 = 36
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Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number
of bottles she needs to sell to earn $100
Answer:
Your question isn't clear.
Step-by-step explanation:
Reading a text message takes your eyes off the road for about 4.6 seconds according
to a recent study. If you are traveling 60 mph and check a text message while you
are driving, how far do you travel (in feet) with your eyes not on the road? Round
your answer to the nearest foot.
Answer:
d = 404.8 feet
Step-by-step explanation:
We take our eyes off the road for about 4.6 seconds according to a recent study.
Speed, v = 60 mph
We need to find the distance travel by you with your eyes not on the road. Let it is d.
Speed, v = d/t
d = vt
We know that, 1 mile = 5280 feet
[tex]d=\dfrac{60\times 5280\ \text{feet}}{3600\ s}\times 4.6\ s\\\\=404.8\ \text{feet}[/tex]
Hence, the required distance is 404.8 feet.
help me with this 4 2/7÷1 1/4
9514 1404 393
Answer:
3 3/7
Step-by-step explanation:
Invert the denominator and multiply. It can help to cancel common factors from numerator and denominator.
(4 2/7) ÷ (1 1/4) = (30/7) ÷ (5/4) = (30/7)×(4/5)
= (30×4)/(7×5) = (6×4)/7 = 24/7
= 3 3/7
#3
Michael brings 6 toy cars to his friends house. These cars represent 20% of
his toy car collection.What is the total number of cars in Michael's toy car
collection?
Double number line:
double number line into the slide. Then, type your answer in the textbox. Make sure you write in a complete math sentence.
1) Shanika can run 5 miles for every 30 minutes she runs. How many minutes will it take her to run 13 miles? Explain how you solved the problem.
Answer: 78
Step-by-step explanation: multiply 13 x 30 which gives you 390 then divide that by 5 giving you 78 minutes.
Each number in a list of numbers is 3 more than the number before it. The first number in the list is -4. What is the fifth number?
A 8
B. 7
C. 6
D. 5
Answer: it’s A
Step-by-step explanation: Because you add three each time, so starting from -4 you go to -1 and then 2 and then 5 and then the fourth number 8
The fifth number in the list of numbers is 8.
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The first number in the list is -4.
Each number is 3 more than the number before it.
This means,
Second number = -4 + 3 = -1
Third number = -1 + 3 = 2
Fourth number = 2 + 3 = 5
Fifth number = 5 + 3 = 8
Thus,
The fifth number is 8.
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What is the area, in square yards of joe’s new property
A - 120
B - 134
C - 140
D - 204
Answer:
the answer is 204 because that's the area of Joe's new property
The sale price of every item in a store is 85% of its usual price.
a. The usual price of a backpack is $30, what is its sale price? $
25.5
b. The usual price of a sweatshirt is $18, what is its sale price? $
Answer
a. The backpack is $4.50
b. The sweatshirt is $2.70
Step-by-step explanation:
a. 30 x 0.15 = 4.50 (The 0.15 is from the price you are actually paying for the item. Because the item is 85% off, you are paying for 15% of the usual price. 15% as a decimal is 0.15 so you multiply that to the original price to find the amount u will pay.)
b. 18 x 0.15 = 2.70
Describe how to select a stratified random sample of 36 people hired by ETS to score the AP Statistics Exams. Explain your choice of strata.
Answer:
The strata will be the category of people with at least 3 years of working experience scoring AP Statistics
Step-by-step explanation:
The strata will be the category of people with at least 3 years of working experience scoring AP Statistics Exams.
I will use this strata because it is only those with a track record of scoring AP Statistics Exams that can rightly score for ETS. People who don't have the right amount of experience of scoring AP Statistics exam may need some training because they need to understand the specifics on how to grade some questions and respective answers.
What is the percent of increase from 900,000 to 1,000,000?
Round your answer to the nearest tenth of a percent and include a percent sign (%),
Answer:
1000000/900000= 10/9= 1.1111111111*100=11.11%
Can anyone help me please
Answer:
X=1
Step-by-step explanation:
8(1)+3=11
4(1)+7=11
It is true if lines are equal.
the answer is B but idk what X=
Answer:
x= I just want free points
Which of the following statements is true?
A. All materials are good conductors of electricity.
B. Aluminum and steel are good conductors of electricity.
C. Gold and wood are poor conductors of electricity.
D. Plastic and cooper are good conductors of electricity.
(Answer it correctly and ill give you brainliest, ty <3)
Answer:
B) Aluminum and steel are good conductors of electricity.
Step-by-step explanation:
Which system of equations does the graph represent? A) y = 2x + 2 y = -3x + 4 B) y = x + 2 y = -x + 4 C) y = 2x + 4 y = -3x + 2 D) y = -x + 2 y = x + 4
Answer: I believe it’s B
Please help sorry if it’s a little blurry! I’ll mark brainliest if you tell me why you got that answer.
Answer:
Hi! Saw your comment saying you got it, congrats! I hope you are having an amazing day/night and I wish you luck with the rest of your studies! I hope you don't mind that I use this for some points! <3
What level do i have to be to choose brainliest
Answer:
any level...there just has to be 2 answers or more in your question
Step-by-step explanation:
Answer:
no level
Step-by-step explanation:
Write an equation in point-slope form, if m= 3 and passes through (4, 5).
Answer:
y - 5 = 3(x - 4)
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Slope m = 3
Point (4, 5)
Step 2: Write equation
Point-Slope Form: y - 5 = 3(x - 4)
What is the solution set for -4 x - 10 ≤ 2?
x ≤ -3
x ≥ -3
x ≤ 2
x ≥ 2
Answer:
x ≥ -3
Step-by-step explanation:
The high school has 23 teachers and 575 students what is the ratio of teachers to students
Answer:
1:25
Step-by-step explanation:
if you divide 575 by 23 you get 25, therefore there are 25 students per 1 teacher
3x+13 what is x I need help please Need a quick response
Answer:
X cannot be solved for
Step-by-step explanation:
This isn't an equation because there's no equal sign and it cannot be simplified further. X values cannot be combined with non-x values.
Evaluate the following function: *
k(t)=13t-2
k(3)=
Mr Harris owns a bubble machine that he uses for different school events
Answer:
3/8
Step-by-step explanation:
did on iready and got it right c:
Sam has 43 pencils. Abby has twice as many pencils as Sam. How many pencils do they have altogether?
Answer:
86 altogether.
Step-by-step explanation:
Since she has twice as many, you would do 43 x 2 = 86
Answer:
129
Step-by-step explanation:
Sam = 43 (s)
Abby = 2s
s + 2s = 3s
3s, when s = 43, equals 129
What’s the answer ? 54 = 5 + 7s
Answer:
s=7
Step-by-step explanation:
Answer:
y is 7
Step-by-step explanation:
First, we can isolate 7s, so we minus 5 from each side, and get 49=7y. So, y is 7.
7. In Ryan's city, it rained 2/5 of the days in September. More than 2 cm of rain fell 1/4 of those days. What fraction of the days in September had rainfall of more than 2 cm?
Answer:
1/10 of the days in September had rainfall more than 2 cm
Step-by-step explanation:
Use the information given:
2/5 of the days in September had rain1/4 of the days in September that had rain, had more then 2cm of rain1/4 of 2/5 is 2/20=1/10estimate 2/3% of $141
Answer:
0.94 cents
Step-by-step explanation:
If you multiply 0.67 with 141 you will see that you will end up with the same answer as above.
0.666 estimates to 0.67
rename fraction to similar fraction 6/8 and2/12=
Answer:
6/8=18/24
2/12 = 4/24
Step-by-step explanation:
If you want to make the fractions the same, look at the denominator.
6/8 and 2/12
what number can both 8 and 12 go into?
It goes into 24
so 6/8 would be 6*3 and 8*3 because whatever you do to the bottom, you do to the top and 8*3 is 24 so 6*3 is 18 and for 2/12 you multiply both by 2 since 12*2=24 and 2*2=4
I will do 6/8 only. You do the other fraction.
Pick a number, any number. How about 2?
Multiply the top and bottom number by 2.
6 x 2 = 12
8 x 2 = 16
We get 12/16.
Reducing 12/16 to the lowest terms we get 3/4.
Another fraction similar to 6/8 is 3/4. In fact, they are equivalent fractions.
Do the other fraction in like fashion.
Note: Each fraction given has more than one similar fraction.