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
217.8 as mixed number
Answers
Answer:
27 1/8
Step-by-step explanation:
217/8= 27.125 = 27
217 - (8 x 27) = 1
We've now simplified 217/8 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:
27 1/8
Simplifying our fraction
In this case, our fraction (1/8) can be simplified down further. In order to do that, we need to calculate the GCF (greatest common factor) of those two numbers. You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 1 and 8 is 1.
1/1 = 1
8/1 = 8
When we put that together, we can see that our complete answer is:
27 1/8
Answer:
217 4/5
Step-by-step explanation:
PLEASE HELP!!!!!! This is very important to me PLEASE HELP ASAP and if you help me god bless you
Answers
Answer:
try the 3rd one
Step-by-step explanation:
if it's not right then i'm sorry
Answer:
Below!
Step-by-step explanation:
The slope is un-defined because the x axis on both points are the same. Therefore, the slope is un-defined.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Help Plz
Rewrite in simplest terms: 4(3d+7f)-5f-3(9f+3d)4(3d+7f)−5f−3(9f+3d)
Answers
Answer:
its easy
Look at the pictures.
Please mark brainlest
If you cant see the result is 24f+24d
Ayo runs a fairground game.In each turn, a player rolls a fair dice numbered 1 - 6 and spins a fair spinner numbered 1 - 12.It costs a player £1.40 for a turn.A player can win £6 or £3 as in the diagrams:If 216 people are to play, how much profit can Ayo expect to make?
Answers
Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.
The expected value is given by the sum of each outcome multiplied by it's respective probability.
In this problem:
The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is [tex]\frac{1}{6} \times \frac{1}{12} = \frac{1}{72}[/tex].The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is [tex]\frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}[/tex]In the other cases, Ayo wins £1.40, with [tex]1 - \frac{18}{72} = \frac{54}{72}[/tex] probability.Hence, his expected profit for a single game is:
[tex]E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583[/tex]
For 216 games, the expected value is:
[tex]E = 216(0.2583) = 55.8[/tex]
Ayo can be expected to make a profit of £55.8.
To learn more about expected value, you can take a look at https://brainly.com/question/24855677
expand and simplify 2(8x + 4y - 10)
[tex]2(8x + \\4y - 10)[/tex]
Answers
Answer two questions
25 points
Answers
Answer:
1) -2x - 3
2) -2a - 2
Step-by-step explanation:
Problem 1
To solve this problem, we only have to combine like terms. What are the like terms in this problem? Well, we have two x-terms (-10x and 8x) and two integers, or constants (1 and -4). So, let's rearrange the expression and then combine those terms.
-10x + 8x + 1 - 4
-2x - 3
Problem 2
This expression is a little more complicated since we have to distribute a 2 onto the two terms in the parentheses.
2(1 - a) - 4
2(1) - 2(a) - 4
2 - 2a - 4
Next, we can combine like terms.
-2a + 2 - 4
-2a - 2
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\huge\text{Number 1}[/tex]
[tex]\large\textsf{-10x + 1 + 8x - 4}\\\large\text{COMBINE the LIKE TERMS}\\\large\textsf{= (-10x + 8x) + (1 - 4)}\\\large\textsf{= -2x - 3}\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{-2x - 3}}}\huge\checkmark[/tex]
[tex]\huge\text{Number 2}[/tex]
[tex]\large\textsf{2(1 - a) - 4}\\\large\text{DISTRIBUTE 2 WITHIN the PARENTHESES}\\\large\textsf{= 2(1) + 2(-a) - 4}\\\large\textsf{= 2 - 2a - 4}\\\large\text{COMBINE the LIKE TERMS}\\\large\textsf{= (-2a) + (2 - 4)}\\\large\textsf{= -2a - 2}\\\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{-2a - 2}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \&}\\\huge\textbf{enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]A baseball team won about 62% of 162 games in a season.
About how many games did they win?
Answers
Answer:
the one about 100 games
Step-by-step explanation:
62 percent *162 =
(62:100)*162 =
(62*162):100 =
10044:100 = 100.44
this rounds to 100
Answer:
About 100 games
Step-by-step explanation:
162 * 0.62 = 100.4
100.4 rounded is 100
A ball is thrown upward from a height of 15 feet with an initial upward velocity of 5 feet per second. Use the formula b(t)= -16t^2 + 5t + 15 to find the time it takes for the ball to reach the maximum height of the ball. Round to the nearest tenth
A. 0.2 seconds
B. 0.1 seconds
C. 0.3 seconds
D. 0.9 seconds
Answers
Answer:
0.2 seconds
Step-by-step explanation:
The graph of b(t) = -16t^2 + 5t + 15 is a parabola opening downward. The maximum value of b(t) occurs at the vertex. The t-coordinate of the vertex is t = -5 / (2(-16)) = 5/32 = 0.15625 sec ≈ 0.2 sec.
Answer:
A) 0.2 seconds
Step-by-step explanation:
[tex]b(t)=-16t^2+5t+15[/tex]
[tex]v(t)=-32t+5[/tex] <-- Take the derivative
[tex]0=-32t+5[/tex] <-- Set equal to 0
[tex]-5=-32t[/tex]
[tex]\frac{5}{32}=t[/tex]
[tex]t=\frac{5}{32}[/tex]
[tex]t\approx0.2[/tex]
Therefore, it will take the ball about 0.2 seconds to reach its maximum height (which happens to be about 15.4 feet BTW).
Alternatively, another non-calculus approach is the fact that the parabola opens downward, and as such, the maximum of [tex]b(t)[/tex] occurs at the vertex where [tex]t=-\frac{b}{2a}[/tex], therefore [tex]t=-\frac{5}{2(-16)}=\frac{-5}{-32}=\frac{5}{32}\approx0.2[/tex]
Solve for x.
3x - 3
4x - 6
X =
= [?]
Answers
Answer:
x=27
Step-by-step explanation:
Same side exterior angles are supplementary when the lines are parallel
3x-3 + 4x-6 = 180
7x -9 =180
Add 9 to each side
7x-9+9 = 180+9
7x = 189
Divide each side by 7
7x/7 = 189/7
x =27
what is the value of 5/6 divded by 1/2 helpi am bad at math
Answers
Answer:
5/3 or 1 2/3
Step-by-step explanation:
when you multiply fractions, you must 'multiply by the reciprocal'
you keep the first fraction the same, then you change the operation to multiplication, and finally you flip the second fraction so the denominator becomes the numerator and vice versa
5/6 ÷ 1/2 is the same as 5/6 × 2/1 = 10/6
always reduced to lowest terms when you can . . .
10/6 equals 5/3
Answer:
1.6667 as a decimal
Step-by-step explanation:
Hope this helps! Have a great rest of your day!
In a lab experiment, 5300 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 23 hours. How long would it be, to
the nearest tenth of an hour, until there are 10500 bacteria present?
Answers
Answer: x = 22.7
Step-by-step explanation:Based on the given conditions, formulate: 5300x2(x divided by 23) = 10500
Divide both sides of the equation by the coefficient of variable: 2 x/23 = 10500/5300
Reduce the fraction:2 x/23 = 105/53
Convert exponential to logarithm form: x/23 = long^2 105/53
Divide both sides of the equation by the coefficient of variable:x = log^2 105/53 x 23
Rewrite the expression: x = 23 long^2 105/53
Round the number: x = 22.7
Answer: x = 22.7
HELPPP ASAPPPPPPPPPPP
Answers
I can't see it can you retake the picture please so I can try to help if I know it?
Harriet and tom run and walk, respectively, a 12 mile course
they both want to finish the course together at the same time
tom sets off at 8:15
am and walks at a constant speed of 4 mph
Given that Harriet runs at a constant speed of 8 mph, at what time should she set off
Answers
Answer:
t = S / v time = distance / speed
For Tom t = 12 m / 4 mph = 3 hours to cover course
Tom will finish at 8:13 + 3 = 11:15
th = 12 m / 8mph = 1.5 hours to cover course
11:15 - 1.5 = 9:45 time Harriet should start to finish in 1.5 hours
help me please brainlist if right
Answers
Step-by-step explanation:
1B.) Zero power rule
C.) 1
2B.) Product of powers rule
C.) y^(7+11) = y^18
3B.) Quotient of powers rule
C.) b^(18-5) =b^13
4B.) Power of a power rule
C.) 3^(2×2) =3^4= 81
5B.) None
C.) 729
two more and that it 30 + 30 × 30 + 20 ÷ 20
Answers
Let's see
30+30×30+20/2030+30^2+131+900931Done!
GUYS PLEASE HELP!!!
Answers
Answer:
C (5,4)
Step-by-step explanation:
(x,y)
fist number in the ordered pair is the X value
Second number in the ordered pair is the Y value
A (-3,0) means you go 3 spaces to the left in the negative direction and zero spaces in the Y axis
B(-2,1) means you go 2 spaces to the left on the x axis (negative) and 1 space up (positive) in the Y axis
C (5,4) means you go 5 spaces to the right on the x axis (positive) and 4 spaces up on the Y axis (positive)
After doing all of these we see that C does not end up on the line
Can someone pls help me
Answers
Answer:
A = Π R^2 = 3.14 * 6^2 m = 113 m^2 area of entire circle
102/360 = a = area of sector
a = 102/360 * 113 m^2 = 32 .0 m^2
triangle abc has an area of 6 and a perimeter of 12. if the triangle is dilated by a scale factor of 3 centered at the origin, what is the area and perimeter of its image, triangle a'b'c'?
Answers
Answer:
perimeter: 36 unitsarea: 54 square unitsStep-by-step explanation:
The perimeter is multiplied by the scale factor:
image perimeter = 3 × original perimeter = 3×12 = 36 units
The area is multiplied by the square of the scale factor:
image area = 3² × original area = 9×6 = 54 square units
Martin spent six dollars on four avocados how much money does he spend for two avocados
Answers
Answer:
$3
Step-by-step explanation:
cut the price in half because the amount of items was reduced by half
Answer:
three dollars
Step-by-step explanation:
$6 for 4
$x for 2
6=4
x=2
cross multiply
2×6=4×x
12=4x
Divide through by 4
x= 3
If y varies inversely with x and y = 5 when x = 4, which equation that relates x and y?
Select one:
Answers
solve the equation. 2(3x-4)=3x+1
Answers
Answer:
x=3
Step-by-step explanation:
What’s the slope intercept form?
At first I thought it was y=-4/3x+7 but it’s not. Pls help!
Answers
Answer:
y = - [tex]\frac{5}{4}[/tex] x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (4, 2) ← 2 points on the line
m = [tex]\frac{2-7}{4-0}[/tex] = [tex]\frac{-5}{4}[/tex] = - [tex]\frac{5}{4}[/tex]
The line crosses the y- axis at (0, 7 ) ⇒ c = 7
y = - [tex]\frac{5}{4}[/tex] x + 7 ← equation of line
Look at the question !
Answers
The Appalachian Trail is about 2,175 miles long.
If Katia averages 18 miles each day, how long will it take her to hike the length of the trail?
Answers
Answer:
121 days to hike the length of the trail.
Step-by-step explanation:
Divide 2175 miles by 18 miles/day. The unit 'miles' will cancel out, leaving with us the unit 'days.'
2175 miles
------------------- = 121 days
18 mi/day
where dp you see yourself in the future?
Answers
Answer:
Happy
Step-by-step explanation:
© There is a bag with only milk and dark chocolates.
5
The probability of randomly choosing a dark chocolate is
5/12
There are 25 dark chocolates in the bag and each is equally likely to be chosen.
Work out how many milk chocolates there must be.
Answers
Answer:
I think it's 35, because if there's 25 dark and you divide 25 by 5 you get 5, so 1/12 is equal to 5
additive inverse of −9x+3
Answers
Answer:
(3x−4) −(x−5)
Step-by-step explanation:
Answer:
The additive inverse of −9x + 3 is 9x - 3Step-by-step explanation:
All we need to do is multiply −9x + 3 by -1.=> -1(−9x + 3)=> 9x - 3Therefore, the additive inverse of −9x+3 is 9x - 3.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
313 people were surveyed in total. 183 of the people surveyed are from East Harlem and 130 people are from the Upper East Side. What percent of people surveyed are from each neighborhood?
Answers
1. The percentage of people surveyed in East Harlem is 58.5%
2. The percentage of people surveyed in Upper East Side is 41.5%
From the question given above, the following data were obtained:
People surveyed in East Harlem = 183People surveyed in Upper East Side = 130Total people surveyed = 3131. Determination of the percentage of people surveyed in East Harlem.
People surveyed in East Harlem = 183Total people surveyed = 313Percentage of East Harlem =?Percentage of East Harlem = (people surveyed in East Harlem / Total) × 100
Percentage of East Harlem = (183/313) × 100
Percentage of East Harlem = 58.5%
2. Determination of the percentage of people surveyed in Upper East Side.
Percentage of East Harlem = 58.5%Total percentage = 100%Percentage of Upper East Side =?Percentage of Upper East Side = (Total percentage) – (Percentage of East Harlem)
Percentage of Upper East Side = 100 – 58.5
Percentage of Upper East Side = 41.5%
Learn more about percentage:
https://brainly.com/question/14899205
By which angle measures can the regular pentagon be rotated so it maps onto itself?
Select each correct answer.
72°
90°
135°
144°
216°
300°
Answers
Answer:
hi there the answer is 72
Step-by-step explanation:
sorry but my work is on a piece of paper in front of me
To map the regular pentagon onto itself, rotate it at angles of 72, 144, 216, and 288 degrees.
What is a regular polygon?A polygon is a geometric form with a limited number of sides that exists in two dimensions. On the sides or edges of polygons, single-direction segments are joined end to end to form a closed shape. Vertices or corners are the points at which two line segments converge to form an angle.
It is given that:
There are five sides to the pentagon.
We are known that the typical pentagon has five vertices and interior angles of 72 degrees each. Rotational symmetry is also present in a regular pentagon.
Angles are 72°,144°,216°, and 288°
Thus, to map the regular pentagon onto itself, rotate it at angles of 72, 144, 216, and 288 degrees.
Learn more about the regular polygon here:
brainly.com/question/11810316
#SPJ2
Given h(x)=-3x-4h(x)=−3x−4, find h(0)
Answers
Answer:
h(0) = -4
Step-by-step explanation:
Put the value where the variable is and do the arithmetic.
h(x) = -3x -4
h(0) = -3·0 -4 = 0 -4
h(0) = -4
_____
Additional comment
In general, a polynomial function evaluated when the variable is zero will have the value of any added constant. All of the variable terms will be zero. Since the constant in this function is -4, we know immediately that h(0) = -4.