Find the area between f(x) = 3x and f(x) = x2 on the interval (0,3]
Answers
Answer:
[tex]A=4.5[/tex]
Step-by-step explanation:
The area between two curves over the interval [tex][a,b][/tex] is [tex]A=\int\limits^b_a {f(x)-g(x)} \, dx[/tex] where [tex]f(x)[/tex] is the upper function and [tex]g(x)[/tex] is the lower function.
Therefore:
[tex]A=\int\limits^3_0 {3x-x^2} \, dx[/tex]
[tex]A=\frac{3}{2}x^2-\frac{x^3}{3}\Big|_0^3[/tex]
[tex]A=[\frac{3}{2}(3)^2-\frac{(3)^3}{3}]-[\frac{3}{2}(0)^2-\frac{(0)^3}{3}][/tex]
[tex]A=\frac{3}{2}(9)-\frac{27}{3}[/tex]
[tex]A=\frac{27}{2}-\frac{27}{3}[/tex]
[tex]A=\frac{9}{2}[/tex]
[tex]A=4.5[/tex]
So, the area between [tex]f(x)=3x[/tex] and [tex]g(x)=x^2[/tex] on the interval [tex](0,3][/tex] is [tex]4.5[/tex] square units.
![Find The Area Between F(x) = 3x And F(x) = X2 On The Interval (0,3]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/BOLTeAOt98HjWgmCBZlorxNmJGv5Fi1n.png)
Related Questions
Which is the graph of 2x + 3y > -3
Graph: C
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write the ratio as a fraction in simple form 14 boxes:8 boxes
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Haseena bought 1 pencil box, 4 pencils and 4 notebooks from a store. She paid Rs. 95 in all. Some ink fell on the bill that she got from the store. So the price of 1 notebook cannot be seen from the bill.What is the price of the one notebook?
Answers
The price of the one notebook will be Rs. 10.6
Let the price of one notebook be x.If Haseena bought 1 pencil box, 4 pencils and 4 notebooks from a store, with a total of Rs. 95 paid in all, then;
1x + 4x + 4x = 95
9x = 95
x = 95/9
x = 10. 6
Hence the price of the one notebook will be Rs. 10.6
Learn more on ratio here: https://brainly.com/question/20346769
Coffee then:45 calories Coffee now:270 calories what is the percent of increase
Answers
Answer:
611.111 repeating
Step-by-step explanation:
Take 270 and divide it by 45 and then move the decimal point 2 times over to the right to make it a percent.
Answer:
+600%
Step-by-step explanation:
[tex]\frac{270}{45} =\frac{x}{100} \\270x100=45x\\27,000=45x\\\frac{27,000}{45} =x\\x=+600%[/tex]
hope that helps!
Help me solve these
Answers
Answer:
hello you need to tell me the equation not the worksheet
Step-by-step explanation:
h(x) = x^2 - 5x +7
Find h(-5)
Answers
Answer:
57
Step-by-step explanation:
h(-5) = (-5)^2 - 5(-5) + 7
h(-5) = 25 + 25 +7
h(-5) = 57
Answer:
[tex]\bold{h(-5)=57}[/tex]
Step-by-step explanation:
Substitute [tex]-5[/tex] for everywhere there is [tex]x[/tex]
[tex]h(x) = x^2 - 5x +7\\=-5^2 - 5(-5) +7[/tex]
[tex]-5^2 - 5(-5) +7[/tex]
PEMDAS order of operations
Parenthesis
[tex]\bold{-5\times(-5)}\\=25[/tex]
[tex]-5^2+25 +7[/tex]
Exponents
[tex]\bold{-5^2}\\=-5\times-5\\=25[/tex]
[tex]25+25 +7[/tex]
Addition
[tex]25+25+7\\=50+7\\=57[/tex]
Therefore, [tex]\bold{h(-5)=57}[/tex].
Given: △ABC, m∠A=60°,
m∠C=45°, AB=9
Find: Perimeter of △ABC,
Area of △ABC
Answers
Answer:
Perimeter of ΔABC: [tex]\frac{27}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] units
Area of ΔABC: [tex]\frac{81}{8}*\sqrt3 + \frac{243}{8}[/tex] units
Skills required: HS Geo, Special Triangles
Step-by-step explanation:
1) The best option is to break down this triangle. Let's draw an altitude from Point B down to Segment AC. The point from the altitude that intersects AC is Point D. BD is the height of our triangle, AC is the base.
2) Angle A is 60 degrees, and since Angle BDA is 90 degrees, Angle ABD is 30 degrees. We can use the 30-60-90 degree right triangle property for the triangle BDA.
This states that if the side opposite the 30 degree angle is [tex]x[/tex], the side opposite the 60 degree angle is [tex]x*\sqrt3[/tex], and the side opposite the 90 degree angle is [tex]2x[/tex].AB is 9 units, and it is opposite the 90 degree angle. This means that [tex]2x=9, x = \frac{9}{2}[/tex] ==> This then means that AD, the segment opposite the 30 degree angle in this triangle is [tex]\frac{9}{2}[/tex] units. Segment BD (the height) is [tex]\frac{9}{2} * \sqrt3[/tex].
3) Angle C is 45 degrees, and Angle BDC is 90 degrees, which means that Angle CBD is 45 degrees. We can use the 45-45-90 degree right triangle property for the triangle BCD.
This states that if the side opposite the 45 degree angle is [tex]x[/tex], the other side opposite a 45 degree angle is also [tex]x[/tex], but the hypotenuse (side opposite the right (90 degree) angle) is [tex]\sqrt{2}*x[/tex].BD is [tex]\frac{9}{2} * \sqrt3[/tex], which means DC is the same. BC, which is the hypotenuse is BD multiplied by square-root-2, which is [tex]\frac{9}{2} * \sqrt6[/tex].
4) Area is [tex]\frac{1}{2}*b*h[/tex], the base (b) is AC (which is [tex]\frac{9}{2}+\frac{9}{2}*\sqrt3[/tex]), the height is BD ([tex]\frac{9}{2}*\sqrt3[/tex]). When multiple you will get [tex]\frac{81}{4}*\sqrt3 + \frac{243}{4}[/tex], then this multiplied by 1/2 is
[tex]\frac{81}{8}*\sqrt3 + \frac{243}{8}[/tex] <--> this is the area!
5) Perimeter is just the sum of all side: 9 + [tex]\frac{9}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] = [tex]\frac{27}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] unit
Could someone help. Please show work
Answers
Answer:
x=-2 and y=5
x=-1 and y=4
Step-by-step explanation:
hope tha work
Please help me , correct answer will get brainiest!
Answers
answer is probably just 4
4/1 rise over run
What is the length of EF in the right triangle below?
Answers
Answer:
A.24
Step-by-step explanation:
EF=√(25)²-(7)²
EF=√625-49
EF=√576=24
Kim performed a transformation on rectangle ABCD to create rectangle A'B'C'D', as shown in the figure below: Rectangles ABCD and A prime B prime C prime and D prime are shown. A is at negative 1, 2. B is at negative 1, 5. C is at negative 3, 5. D is at negative 3, 2. A prime is at 2, 1. B prime is at 5, 1. C prime is at 5, 3. D prime is at 2, 3. What transformation did Kim perform to create rectangle A'B'C'D'? Rotation of 270 degrees counterclockwise about the origin Reflection across the line of symmetry of the figure Reflection across the yâ€axis Rotation of 90 degrees counterclockwise about the origin.
Answers
The transformation rule for Rotations of 270 degrees counter clockwise is (x, y) —> (y, -x).
Kim performs to create rectangle A'B'C'D' Transformation, ''Rotation of 270 degrees counterclockwise about the origin'' and it can be determined by using the rules of transformation.
Given that,Kim performed a transformation on rectangle ABCD to create rectangle A'B'C'D', as shown in the figure below:
Rectangles ABCD and A prime B prime C prime and D prime are shown.
We have to determine,What transformation did Kim perform to create rectangle A'B'C'D'?
According to the question,Kim performed a transformation on rectangle ABCD to create rectangle A'B'C'D', as shown in the figure below:
Rectangles ABCD and A prime B prime C prime and D prime are shown.
Transformation involves changing the position of the given shape.
The transformation on rectangle ABCD to A'B'C'D' is (a) rotation of 270 degrees counterclockwise.The coordinates of ABCD are given as:A (1, -2),
B (-1, 5)
C (-3, 5)
D (-3, 2)
The coordinates of A'B'C'D' are given as:A (2, 1),
B (5, 1)
C (5, 3)
D (2, 3)
The transformation from ABCD to A'B'C'D is 270 degrees counterclockwise about the origin.
And the proof is as follows.
The rule of 270 degrees counterclockwise about the origin is:
The given coordinates;
A (2, 1) - (-1, 2)
B (5, 1) - (-1, 5)
C (5, 3) - (-3, 5)
D (2, 3) - (-3, 2)
Hence, Kim performs to create rectangle A'B'C'D' Transformation, ''Rotation of 270 degrees counterclockwise about the origin''.
For more details about Rotation refer to the link given below.
https://brainly.com/question/10624834
Giải phương trình: 2x + x + 12 =0
Answers
Answer:
x = - 4
Step-by-step explanation:
Or 3x +12=0
The cost of 2.25
pounds of grapes is
$6.75. The cost of 5
pounds of grapes is
$15. Find the slope in
dollars per pound.
Answers
Answer:
Hope this helps! <3
Step-by-step explanation:
The slope or increase in cost per pound is 3. (1 pound of grapes costs $3)
(5a^3-2)(5a^3+2) expand and combine like terms
Answers
Step-by-step explanation:
(5a³-2)(5a³+2)
5a³×5a³+ 5a³×2 - 2× 5a³+ 5a³×2 5a³+10a³- 10a³ + 10a³5a³+10a³ + 10a³-10a³15a³ AnswerWhat is the equation of the line that passes through the point (8,-4) and has a slope of 3?
Answers
Answer: The equation of a line that passes through the point (8,-4) and has a slope of 3 is y = 3x - 28.
Explanation:
y = -4, x = 8
By putting above values in equation (i)
-4 = 3 (8) + b
-4 = 24 + b
-28 = b
b = -28
y = 3x - 28
An item is regularly priced at $35. It is now priced at a discount of 55% off the regular price. What is the new price?
Answers
Emily is eating her colored candies in the following pattern: one green, one blue, one red , one orange, one brown, one green, one blue, and so on. If this pattern continues, the 27 candy she eats will be what color?
Answers
Answer:
blue
Step-by-step explanation:
a b c d e
1 2 3 4 5
27-25=2
so b, or blue
1 6. ) b) The weight of an object on moon is 1/6 of its weight on Earth. If weight of an object on Earth is 18/5 kg, what would be its weight on moon? Plzz help me
Answers
Answer:
Solution given:
weight of moon=1/6 th of Earth
If weight of Earth is 18/5 kg
weight of moon=?
we have
weight of moon: 1/6 of weight of Earth
=1/6*18/5
=3/5kg
Its weight on moon is 3/5 kg
I need help with this
Answers
Answer:
a and b
Step-by-step explanation:
please help I give you 30 points
Answers
Answer:
The last one, 14 3/4
Step-by-step explanation:
I hope this helped :)
the graph of the function f is shown above. what is limx→2f(x)
Answers
The value of y as x tends to 2 is infinity since the curve progresses to infinity at this point that is [tex]\lim_{x \to 2} f(x) = \infty[/tex]
Find the graph attached. From the graph, we can see that the range of the function is the values along the y-axis and is from the minimum point on the curve (y = -2) to infinity
The range of the given graph in interval notation will be expressed as R = 2≤y<∞ or y ≥ 2. Note that 2 is included since the circle on the value of 2 is shaded.From the graph, we can deduce that the value of y as x tends to 2 is infinity since the curve progresses to infinity at this point.
Therefore we can conclude that [tex]\lim_{x \to 2} f(x) = \infty[/tex]
Learn more on the limits of a function here: https://brainly.com/question/23935467
an arrow is shot vertically upward from a platform 18ft high at a rate of 184ft/sec. When will the arrow hit the ground? Use the formula: h=−16t2+v0t+h0. (Round your answer to the nearest tenth.)
Answers
Answer:
h(t) = -16t2 + 184t + 18
at the ground h = 0
hence; -16t2 + 184t + 18 = 0
solving this quadratic equation using the quadratic formula ; a = -16, b = 184, c = 18 ; x = (-b +-(b2 - 4ac)1/2)/2a
gives t = 11.597 seconds and rounded to the nearest tenth, t = 11.6 (note that the negative root has no practical significance)
Step-by-step explanation:
A box has 30 pencils in it.the probability of picking a red pencil is 1/6.How many red pencils are in the box
Answers
Answer:
[tex]\huge\boxed{\sf 5\ red\ pencils}[/tex]
Step-by-step explanation:
Total pencils = 30
Probability of picking a red = 1/6
Red pencils in the box = probability × total pencils
= 1/6 × 30
= 5 red pencils
So, there are 5 red pencils in the box.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807What do I need to know?
I need help on this question please
Answers
Answer:
i cant see the Q
Step-by-step explanation:
Find the height of the building below by using your knowledge of trigonometry.
Answers
Answer:
50[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The figure represents a 30-60-90 special triangle
in this special right triangle the measure of sides lengths is represented by
a, a[tex]\sqrt{3}[/tex], and 2a
The side length that sees angle measure 30 is represented by a and here we see a = 50m
The height of the building, which sees angle measure 60, is equal to
50[tex]\sqrt{3}[/tex]
A restaurant customer left $2.60 as a tip. The tax 6% was and the tip was 20% of the cost including tax.
a. Which information is not needed to compute the bill after tax and tip?
b. What was the total bill?
Answers
Based on the tip left and its proportion of the total bill, the following answers are true:
a. The tax rate is not needed to compute the after tax and tip bill b. The total bill is $13.00A tip of $2.60 was left and this is said to be 20% of the bill including the tax.
The total bill is therefore:
Tip = Total bill x 20%
2.60 = Total bill x 20%
Total bill = 2.60 / 20%
= $13.00
We can see that the tax rate was not needed to compute the total bill.
In conclusion, the tax rate was irrelevant and the total bill was $13.00.
Find out more about taxes and tips in bills at https://brainly.com/question/24976122.
Given the graph below, write an equation in slope-intercept form.
Answers
The slope is how much it goes up, it goes up 3, over 1 which makes a fraction 3/1 which is 3
The y-intercept is 2 because that’s the y value when x is 0
Hope this helps!!
Simplify the expression:
10v + -5 + 7
Answers
Answer:
10v + 2
Step-by-step explanation:
Answer:
10v + 2
Step-by-step explanation:
Ok, so when were adding varibles, whenever theres the same varible, we add them. In this case we have v and numbers. -5+7 is 2 because -5 and positive 5 cancel eachother out so were left with 2 from the 7. now the equation is 10v+2!
Identify the slope and y-intercept of the function y = –8x + 1. A. The slope is 8. The y-intercept is (0, 1). B. The slope is –8. The y-intercept is (0, 1). C.The slope is 1. The y-intercept is (0, 8). D. The slope is 1. The y-intercept is (0, –8).
Answers
Answer:
b
Step-by-step explanation:
-8 Is the slope and yintecept is 0,1
STUDY
1. Simplify the expression below
5p + 14p
4(x - 2) + 6x
2. Evaluate
Answers
Answer:
(11)(B) Simplify numeric and algebraic expressions using the laws of exponents, including integral ... Evaluate the expression for d = -2, d = 0, and d = 1.
Step-by-step explanation:
Answer:
5p + 14p= 19p
4 (x-2)+6x
4x-8+6x
10x-8