Determine the area enclosed by y=2x+3, the x-axis and the ordinates x=3 and x=4
Answers
Answer:
[tex]\displaystyle \int\limits^4_3 {2x + 3} \, dx = 10[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration 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.
y = 2x + 3
x-interval [3, 4]
x-axis
See attachment for graph.
Step 2: Find Area
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^4_3 {2x + 3} \, dx[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle A = \int\limits^4_3 {2x} \, dx + \int\limits^4_3 {3} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle A = 2 \int\limits^4_3 {x} \, dx + 3 \int\limits^4_3 {} \, dx[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = 2 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^4_3 + 3(x) \bigg| \limits^4_3[/tex][Integrals] Integrate [Integration Rule - FTC 1]: [tex]\displaystyle A = 2 \bigg( \frac{7}{2} \bigg) + 3(1)[/tex]Simplify: [tex]\displaystyle A = 10[/tex]∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
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.......................................
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What is the expression in radical form ?
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Step-by-step explanation:
Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.
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Step-by-step explanation:
GIVING BRAINLIEST!!!!
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Answer:
Zack is correct with the -4.5
Step-by-step explanation:
When multiplying by .5 just cut the number in half so 4.6 becomes 2.3 and since the .5 was negative the 2.3 becomes a negative so -2.3 -2.2=-4.5
Hope this helped.
A brainliest is always appreciated.
Average movie prices in the United States are, in general, lower than in other countries. It would cost
$79.45 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two
tickets in Japan would cost $76.10. How much does an average movie ticket cost in each of these
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Answers
30points! need help asap
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Answer:
b
Step-by-step explanation:
The following question has 2 parts. First, answer part A. Then, answer part B.
Use the image below to answer the questions.
A grid with 10 equal columns is shown with 5 shaded in. A second grid is shown, identical in size, containing 100 squares with 3 shaded in.
Part A
Write a problem that represents the addition model shown above. Don't solve the problem.
Part B
Emma incorrectly gave the sum as
8
100
. Explain what Emma did incorrectly and use the model to correct her work. Solve the problem in your answer.
Answers
The fraction that represents the addition model shown above will be 53/100.
How to solve the fraction?From the information given, a grid with 10 equal columns is shown with 5 shaded in. This will be expressed as 5/10.
Also, a second grid is shown, identical in size, containing 100 squares with 3 shaded in. This will be expressed as 3/100.
Therefore, the problem that represents the addition model shown above will be:
= 5/10 + 3/100
= 50/100 + 3/100
= 53/100
In this case, the answer given by Emma is incorrect as he added 5 to 3 and got 8/100.
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Answer:
Q1/6.5
Q2/ 12.5
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.
Step-by-step explanation:
per minute means ÷ mins (on the denominator)
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The triangle ABC is a right triangle
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Represent the length AC with b.
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[tex]\cos(A) = \frac{b}{AB}[/tex]
Substitute known values
[tex]\cos(22.6) = \frac{b}{13}[/tex]
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Evaluate the product
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Answer:
56.57
Step-by-step explanation:
18 x 3.14 = 56.52
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Look at the image below
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Answer:
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Step-by-step explanation:
We first need to round to the nearest dollar for both prices. Lets examine both numbers.
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Now we must find the tax for each number. We can do that by multiplying each number by 0.13 since that is 13% in decimal form. Lets do that now
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Now we can find the final price for each number by adding the tax to the rounded price.
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Answers
Answer:
$1,800
Step-by-step explanation:
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Answers
Answer:
x -4y = -24
Step-by-step explanation:
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An equation for the desired line is ...
x -4y = -24
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Additional comment
The standard form equation has a positive leading coefficient, so the choice of which coefficient to negate will take that into account.
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Step-by-step explanation:
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PLEASE ASAP ROCKY PLEASE
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Answer:
96 cubic inches
Step-by-step explanation:
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Answer:
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8:9
Step-by-step explanation:
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Solution:
Note that:
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Answer:
No, Susan is not right.
Step-by-step explanation:
Susan's time = 5:55
Jamal's time = 11:42
Half of Jamals time = 5:51
5:55<5:51
Susan is not right
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42 seconds.
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Answer:
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Step-by-step explanation:
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I have to type this to post it
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Answer:
256
Step-by-step explanation:
(a^n)^m = a^nm
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=2³×⅔×⁴ (8 = 2³)
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Please mark my answer the brainliestAnswer:
Step-by-step explanation:
8 = 2*2*2 = 2³
[tex]\left[8^\left(\dfrac{2}{3}\right) \right]^{{4}}=\left[2^{3}^\left(\dfrac{2}{3}\right) \right]^{{4}}\\\\\\=2^{3*\dfrac{2}{3}*4}\\\\\\=2^{2*4}\\\\\\=2^{8}[/tex]
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Answers
Answer:
Step-by-step explanation:
Evaluate. f(x )=17−5x at x =a −3,
Answers
Answer:
x=17/5
i hope this helps
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Answer:
125 and 0.292
Step-by-step explanation:
Think about it as a system of equations:
1)
[tex]a+b=125 +1/3\\a=125.33-b\\\\2) ab=36+1/2\\[/tex]
at this point you can insert the equation you got from 1.
[tex](125.33-b)b=36.5\\125.33b-b^2=36.5\\b^2-125.33b+36.5=0[/tex]
with this form, you can use the quadratic equation to find your two possible answers.
following the quadratic equation we find that our answers are 125 and 0.292
James is making a presentation about how to pick the right kind of pet. Which image would BEST Support
A) a picture of common house pets
B) a picture of common pet supplies
a chart displaying the amount of care pets require
D) a chart displaying which pets are the most popular
Answers
Answer:
C. A chart displaying the amount of care pets require.
Step-by-step explanation:
(A). A picture of common house pets.
This wouldn't be effective since everyone knows what most common house pets look like.
(B). A picture of common pet supplies.
This wouldn't be effective since pet supplies vary with every animal.
(C). A chart displaying the amount of care pets require.
This would be the best choice since the image would show the required necessities for each different pet.
(D). A chart displaying which pets are the most popular.
This wouldn't be effective since popularity is mostly based on preference.