please helpFind the area between the graph of f(x) = ____ and the x-axis on the interval [4, 9]. Write the exact answer. Do not round.
![Please HelpFind The Area Between The Graph Of F(x) = ____ And The X-axis On The Interval [4, 9]. Write](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/XqgY1CrZ0iCPNtD2m2GSlVAGfU6rOpLN.jpeg)
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Recall that the area between the graphs of two functions on the interval [a,b] is:
[tex]\int ^b_a|f(x)-h(x)|dx\text{.}[/tex]Therefore, the area between f(x)=4√x and the x-axis with equation y=0, on the interval [4,9] is:
[tex]\int ^9_4|4\sqrt[]{x}-0|dx=\int ^9_4|4\sqrt[]{x}|dx\text{.}[/tex]Notice that
[tex]4\sqrt[]{x}>0,[/tex]for all x in the given interval, therefore:
[tex]\int ^9_4|4\sqrt[]{x}|dx=\int ^9_44\sqrt[]{x}dx=4\int ^9_4x^{\frac{1}{2}}dx=4(\frac{2x^{\frac{3}{2}}}{3})|^9_4=\frac{8}{3}(9^{\frac{3}{2}}-4^{\frac{3}{2}})=\frac{8}{3}(19)=\frac{152}{3}.[/tex]Answer: 152/3.
Related Questions
MATH HELP WILL MARK BRAINLEST
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The vertex form of the equation is y = (x - 3)² - 4 , the correct option is (b).
In the question ,
it is given that ,
the equation is y = x² - 6x + 5
we need to write the equation in the vertex form ,
we know that the vertex form of the equation is
y = m(x − a)² + b , where (a,b) is the vertex .
On using the completing the square method for the equation,
y = x² - 6x + 5
Adding and subtracting 9 , in the equation
y = x² - 6x + 9 + 5 - 9
y = x² - 6x + 3² + 5 - 3²
y = (x - 3)² - 4 ....because (x - 3)² = x² - 6x + 3²
Therefore , The vertex form of the equation is y = (x - 3)² - 4 , the correct option is (b).
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the Browns build at a restaurant is $60 how much money should mr. Brown leave as a tip if he plans to tip 50%
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We need to calculated first the 50% of $60
60*0.5=30
then we calculated the final bill
original bill + tip = money leave by mr Brown
60+30=90
he leave $90
Look at the system of equations shown.y = 3x + 7y = 2x + 8What is the x-coordinate of the solution to the system?Select one:10- 10O- 1o
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We have a system of 2 equation (Eq):
y = 3x + 7 (Eq 1)
y = 2x + 8 (Eq 2)
To solve the system, we can match both equations.
3x + 7 = 2x + 8
3x - 2x = 8 - 7
x = 1
(n-1)9. Expand11-11 + 2 + 3 + 4 + 5 + 60 + 1 + 2 + 3 + 4 + 5 + 60 + 1 + 2 + 3 +4 + 5AB(-1) + (-2) + (-3) + (-4) + (-5) + (-6)
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To expand the given summation, we proceed as follows:
[tex]\begin{gathered} \text{Given:} \\ \sum ^6_{n\mathop=1}(n-1) \\ \Rightarrow\text{ }\sum ^6_{n\mathop{=}1}(n)-\text{ }\sum ^6_{n\mathop{=}1}(1) \\ \text{Now:} \\ \sum ^6_{n\mathop{=}1}(n)\text{ is the sum of the first six natural numbers (1,2,3,4,5,6)} \\ \text{And:} \\ \sum ^6_{n\mathop{=}1}(1)\text{ is simply (6}\times1)--That\text{ is, the number 1 added to itself six times } \\ \text{Therefore, we have:} \\ \Rightarrow\text{ }\sum ^6_{n\mathop{=}1}(n)-\text{ }\sum ^6_{n\mathop{=}1}(1) \\ \Rightarrow(1+2+3+4+5+6)-(1+1+1+1+1+1) \\ \Rightarrow(1+2+3+4+5+6)-(6) \\ \Rightarrow(1+2+3+4+5) \\ \end{gathered}[/tex]Therefore:
[tex]\sum ^6_{n\mathop{=}1}(n-1)\text{ = 1+2+3+4+5}[/tex]So, the correct option is option C
This is because the sum: 0+1+2+3+4+5 gives the same value as the sum: 1+2+3+4+5
Determine the inverse of the function by interchanging the variables and solving for y in terms of X
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We are required to find the inverse of the function
The first step is to interchange the variable x for y
[tex]x=\frac{y}{2}-\frac{3}{2}[/tex]The next step is to make y the subject of the formula
[tex]\begin{gathered} x=\frac{y}{2}-\frac{3}{2} \\ \frac{y}{2}=x+\frac{3}{2} \\ \text{ Multiply the equation throughout by 2} \\ y\text{ = 2x + 3} \end{gathered}[/tex]The answer is y = 2x + 3
Melissa won a week-long cruise in a contest and is working out the details of the trip. She can choose from 4 destinations and 5 departure dates. Since each cruise lets passengers pick one of 5 different day trips, Melissa also needs to choose one of those. How many different cruises can Melissa plan?
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To solve this problem, it is necessary to use the fundamental counting principle, which is the multiplication counting rule.
It says that if we have two events, a and b. The total number of possible outcomes will be a times b (a*b).
In this case, a are the destinations she can choose and b are the departure dates. To find how many cruises can she plan, multiply the number of options of a and b, this is 4*5:
[tex]4\cdot5=20[/tex]In this case, she can plan 20 different cruises.
Alan needs to manufacture a circular metal plate with a perimeter of `10pi` centimeters. If the allowed error tolerance in the perimeter is `+-1` centimeter, how close to the ideal radius must he control the radius of the plate?
A. `1/(5pi)`
B. `1/(10pi)`
C. `2/pi`
D. `1/(2pi)`
Answer: D. `1/(2pi)`
Your Welcome :)
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The ideal radius Alan must control is [tex]\frac{1}{2\pi }[/tex] cm.
Define perimeter of circle.The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The area of a circle determines the space it takes up. A circle's diameter is equal to the length of a straight line traced through its center. Usually, it is stated in terms of units like cm or m.
Given data -
Perimeter of circular plate = 10[tex]\pi[/tex] cm
We know that perimeter of a circle is 2[tex]\pi[/tex]r
Therefore 10[tex]\pi[/tex] = 2[tex]\pi[/tex]r
r = 5 cm
The given error Alan can make is +-1 cm.
Minimum radius is given by
2[tex]\pi[/tex]r = 10[tex]\pi[/tex] - 1
r = [tex]\frac{10\pi - 1 }{2\pi }[/tex]
r = 5 - [tex]\frac{1}{2\pi }[/tex]
Maximum radius is given by
2[tex]\pi[/tex]r = 10[tex]\pi[/tex] + 1
r = [tex]\frac{10\pi + 1 }{2\pi }[/tex]
r = 5 + [tex]\frac{1}{2\pi }[/tex]
The ideal radius Alan must control is [tex]\frac{1}{2\pi }[/tex] cm.
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There were 24 dinner tables with 8 chairs at each table.Each dinner ticket cost $12.50. If 3/4 of thr dinner tables were full,how much money was raised from the dinner ticket sales?
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we have the next information
24 dinner tables
each has 8 chairs
First we need to calculate 3/4 of the tables
24 mesas ----- 4/4=1
x ----- 3/4
x = the number of tabl
Logarithmic help is needed. Be sure to note the differences between logarithmic and exponential forms in each equation.
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The pattern in converting logarithmic form to exponential form and vice versa is this:
[tex]y=b^x\leftrightarrow\log _by=x[/tex]For the first exponential equation that is 16 = 8^4/3, our y = 16, b = 8, and x = 4/3. Let's plug this in the logarithmic pattern.
[tex]\begin{gathered} \log _by=x \\ \log _816=\frac{4}{3} \end{gathered}[/tex]The logarithmic form of the first equation is log₈ 16 = 4/3.
Now, let's move to the second one.
[tex]\log _5(15,625)=6[/tex]b = 5, y = 15, 625, and x = 6. Let's plug these in to the exponential pattern.
[tex]\begin{gathered} y=b^x \\ 15,625=5^6 \end{gathered}[/tex]Hence, the exponential form of the second equation is 15, 625 = 5⁶.
i need to provide a two column proof. don’t except if you cannot do this. please
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Statement Reason
angle P = angle S Given
angle P + angle Q = 180 Given
angle R + angle S = 180 Given
If we substitute angle P = angle S into angle R + angle S = 180, then
angle R + angle P = 180
Find the slope, if it exists, of the line containg the pairs of pointsplease answer them all :(1. ( -4, -1 ) and ( 4, 4 )2. ( 0, 3 ) and ( 4, 0 )3. ( 0, 1 ) and ( 3, 0 )4. ( 7, 8 ) and ( -7, 8 )5. ( 1, 5 ) and ( -8, 5 )
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The formula for determine the slope is given by
m = ( y2-y1)/(x2-x1) where ( x1,y1) and (x2,y2) are points on the line
m = ( 4 - -1)/(4 - -4)
Rewriting
m = ( 4+1)/( 4+4)
= 5/8
The slope is 5/8
Which of the following words best completes this sentence? "The real roots of a quadratic equation correspond to the of the graph of the related function."
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This is an example of a quadratic function
The real roots are where it crosses the x axis
Where it crosses the x axis are also called the zeros of the function or the x intercepts. They can also be called the roots of the quadratic.
Without the choices, I am unsure of the words to fill in the blank.
The length of a 12 foot by 8 foot rectangle is increasing at a rate of 3 feet per second and the width is decreasing at 2 feet per second (a) How fast is the perimeter changing? (b) How fast is the area changing?
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The rate of change of the perimeter of this rectangle is equal to 2 feet per second.
The rate of change of the area of this rectangle is equal to 20 feet per second.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2L + 2W
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.The rate of change for the perimeter of this rectangle is given by:
P = 2L + 2W
Differentiating with respect to t, we have:
dP/dt = 2dl/dt + 2dw/dt
Substituting the given parameters into the formula, we have;
dP/dt = 2(3) + 2(-2)
dP/dt = 6 - 4
dP/dt = 2 feet per second.
For the rate of change of the area of this rectangle, we have:
dA/dt = ldw/dt + wdl/dt
dA/dt = 8(-2) + 12(3)
dA/dt = -16 + 36
dA/dt = 20 feet per second.
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What about takes four hours to travel 128 km going upstream and return it takes two hours going down stream what is the rate of the boat in Stillwater and what is the rate of a Current
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Since the rate = distance/time
Since the distance is 128 km
Since the time of upstream is 4 hours
Then the rate of the boat in the still water is
[tex]\begin{gathered} R_s=\frac{128}{4} \\ R_s=32km\text{ per hour} \end{gathered}[/tex]Since the boat took 2 hours downstream, then
The rate of the current is
[tex]\begin{gathered} R_c=\frac{128}{2} \\ R_c=64km\text{ per hour} \end{gathered}[/tex]a school day is 8 hours how many minutes are in a school day
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In order to solve this exercise you need to remember the following:
[tex]1\text{ }hour=60\text{ }minutes[/tex]In this case, based on the information given in the exercise, a school day is 8 hours. Then, you need to make the conversion from hours to minutes.
You can set up the following:
[tex](8\text{ }hours)(\frac{60\text{ }minutes}{1\text{ }hour})[/tex]Therefore, evaluating you get:
[tex]=\frac{(60\text{ }minutes)(8\text{ }hours)}{1\text{ }hour}=480\text{ }minutes[/tex]Hence, the answer is:
[tex]480\text{ }minutes[/tex]in circle R, mCB=73° and mAD=57° what is M
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The measure of the angle ∠CEB is 65°.
We are given a circle. The center of the circle is denoted by R. There are two chords, AB and CD. The point of intersection of the chords is E. The angles subtended by the arcs CB and AD are 73° and 57°, respectively. We have to find the measure of the angle ∠CEB. We can see that there is no direct relationship between the angles, but it is certain that the angle ∠CEB lies between the measures of angles subtended by the two arcs. So, we can write it in the form of an inequality. The measure of the angle ∠CEB is more than 57° but less than 73°. We can take the average value of these angles as an approximation. The average is (57° + 73°)/2 = 65°.
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list the following information about the function: y = 2 (x-3)^2-1 (parent graph y = x^2)
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Given
The function is defined as:
[tex]y\text{ = 2\lparen x -3\rparen}^2\text{ - 1}[/tex]x-intercepts
The x-intercepts of the function y are the values of x when y = 0
Substituting 0 for y and solving for x
[tex]\begin{gathered} 2(x-3)^2\text{ -1 = 0} \\ 2(x-3)^2\text{ = 1} \\ Divide\text{ both sides by 2} \\ (x-3)^2\text{ = }\frac{1}{2} \\ Square\text{ root both sides} \\ x-3\text{ = }\pm\sqrt{\frac{1}{2}} \\ x\text{ = 3 }\pm\text{ }\sqrt{\frac{1}{2}} \end{gathered}[/tex]Hence, the x-intercepts are:
[tex](\sqrt{\frac{1}{2}}\text{ + 3, 0\rparen, \lparen-}\sqrt{\frac{1}{2}}\text{ + 3,0\rparen}[/tex]y-intercepts
The y-intercepts are the values of y when x = 0
[tex]\begin{gathered} y\text{ = 2\lparen0-3\rparen}^2-\text{ 1} \\ =\text{ 2}\times9-1 \\ =\text{ 17} \end{gathered}[/tex]Hence, the y-intercept is (0, 17)
Maximum or minimum of the function
The given equation is in vertex form.
[tex]\begin{gathered} y\text{ = a\lparen x-h\rparen}^2\text{ + k} \\ Where\text{ \lparen h,k\rparen is the vertex} \end{gathered}[/tex]Hence, the minimum value of the function is (3,-1)
A teacher wants to track the number of books students have read each week,encouraging them to increase their reading throughout the school year. Which ofthe following graphs might be most effective to inspire the student?
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We have to find which of the graph options is best to track the number of books that the students read each week and encourage them to increase them.
Option 1 (scatter plot): in this case, it is not useful in the sense that we can not compare the evolution in time of each student. We can only see the number of books per student for specific weeks.
Option 2 (time series): in this case, the attendance is not a variable of interest, so it is not suitable.
Option 3: A pie chart is only useful to compare proportions and percentages, and not track an evolution of a variable in time.
Option 4: This aggregation of the data in a Pareto only allows to compare the total number of books per week, but the evolution is not clear, as we sort the columns by the number of books instead of time.
Option 5: A time series with weeks in the x-axis and number of books in the y-axis let the teacher clearly see the evolution of books read in time. So this option is the most suitable.
Answer: Option 5 (time series)
2. Damian is buying movie tickets to a movie. The tickets cost $4.35 per ticket. Damian has $40.00. What is the greatest amount of tickets he can buy?
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Given:
Cost of one ticket is, c = $4.35.
Total amount with Damian is, T = $40.00.
The objective is to find the number of tickets Damian can buy with this total amount.
Consider the number of tickets as x.
The equation for this situation can be represented as,
[tex]\begin{gathered} \text{Total amount=cost per ticket}\times\text{number of tickets } \\ T=c\times x \end{gathered}[/tex]Now, substitute the given values in the above equation.
[tex]\begin{gathered} 40=4.35x \\ x=\frac{40}{4.35} \\ x=9.19 \\ x\approx9 \end{gathered}[/tex]Hence, Damian can buy maximum 9 tickets with total cost of $40.00.
what can you prove congruent from your given
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Answer:
a. line OL bisects angle MLN
b. triangle MLO is congruent to triangle OLN
c. line OL proves that they are congruent through reflexive property.
Step-by-step explanation:
hope this helps!
Simplify (3.8 x 10^-2)(5.14 x 10^-10). Write the final answer in scientific notation.
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Answer:
1.9532×10⁻¹¹
Step-by-step explanation:
You want the product (3.8 × 10^-2)(5.14 × 10^-10) in scientific notation.
ProductThe product is computed in the usual way, making use of the rules of exponents.
(3.8 × 10^-2)(5.14 × 10^-10) = (3.8×5.14) × (10^-2)(10^-10)
= 19.532 × 10^(-2-10) = 19.532 × 10^-12
Moving a factor of 10 from the coefficient to the exponent gives ...
= 1.9532×10^-11 . . . . . . final answer in scientific notation
__
Additional comment
Scientific notation has 1 digit to the left of the decimal point in the coefficient.
Here, we had to divide by 10 to put the coefficient decimal point in the right place. To keep the number at the same value, we had to increase the exponent of 10 by 1 from -12 to -11.
Your calculator can display the product in scientific notation for you, as can any spreadsheet.
Sometimes it is convenient to adjust the exponents before the multiplication. Here, you can see the product of the coefficients will be greater than 10, so will ultimately need to be divided by 10. One way to get there is rewriting the problem as (0.38×10^-1)(5.14×10^-10). This will give a product coefficient between 1 and 10 with an exponent of -11.
<95141404393>
please help me find ALL of the questions this thing is asking :). Non helping (just to obtain points) questions will be reported.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answers
Answer:
B
Step-by-step explanation:
x + y = 180
co-interior
co-interior starts with C and x + y make a C shape (easier to remember)
Elizabeth wraps a gift box in the shape of a square pyramid. The figure below shows a net for the gift box. 6 in 6.8 in
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The wrapping paper used by Elizabeth is equal to the area of the square pyramid which is 127.84 in.².
Dimension of the square base:
Side = 6.8 in.
Area of the base = 6.8 in. × 6.8 in.
A = 46.24 in.²
Dimension of the triangle:
Base = 6.8 in.
Height = 6 in.
Area of 1 triangle = 1/2 × 6.8 in. × 6 in.
A (triangle) = 20.4 in.²
Area of 4 triangles = 4 × 20.4 in.²
A' = 81.6 in.²
Total area of the square pyramid = A + A'
T = 46.24 in.² + 81.6 in.²
T = 127.84 in.²
Therefore, the wrapping paper used by Elizabeth is equal to the area of the square pyramid which is 127.84 in.².
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Your question is incomplete. Please refer the content below:
Elizabeth wraps a gift box in the shape of a square pyramid.
The figure below shows a net for the gift box.
How much wrapping paper did she use?
The equation that models Earth's elliptical orbit around the sun is (x+2.5)^2/22,350.25+y^2/22,344=1 in millions of kilometers. If the sun is located at one focus and it’s coordinates are (0,0), find Earth's farthest distance from the sun in millions of kilometers.
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Given the equation of the elliptical orbit is (x+2.5)^2/22,350.25+y^2/22,344=1.
This equation can be written as
[tex]\begin{gathered} \frac{(x+2.5)^2}{22350.25}+\frac{y^2}{22344}=1 \\ \frac{(x+2.5)}{(149.5)^2}+\frac{y^2}{(149.479)^2}=1 \end{gathered}[/tex]Now, if we shift this path by 2.5 units to left then we get
[tex]\frac{x^2}{(149.5)^2}+\frac{y^2}{(149.479)^2}=1[/tex]The farthest distance of the earth from the sun will be 149.5 - 2.5 = 147 million of kilometers
Thus, option C is correct.
(a)The perimeter of a rectangular garden is 306m.If the width of the garden is 69m, what is its length?Length of the garden: m (b)The area of a rectangular window is 6364cm2.If the length of the window is 86cm, what is its width?Width of the window: cm
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Answer
The length of the garden = 84 m
Explanation
Part (a)
The given parameters are:
Perimeter of the rectangular garden = 306 m
The width of the garden = 69 m
The length of the garden = ?
Solution:
Using the formula for the perimeter of a rectangle:
[tex]\begin{gathered} Perimeter=2(Length+Width \\ \\ 306m=2(L+69m) \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }2 \\ \\ \frac{306m}{2}=\frac{2(L+69m)}{2} \\ \\ 153m=L+69m \\ \\ L=153m-69m \\ \\ L=84\text{ }m \end{gathered}[/tex]The length of the garden = 84 m
Part (b):
The given parameters are:
The area of the rectangular window = 6364 cm²
The length of the window = 86 cm
The width of the window = ?
Solution:
The width of the rectangular window can be calculated using the formula for the area of a rectangle.
[tex]\begin{gathered} Area=Length\times Width \\ \\ 6364cm^2=86cm\times W \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }86cm \\ \\ \frac{6364cm^2}{86cm}=\frac{86cm\times W}{86cm} \\ \\ W=74\text{ }cm \end{gathered}[/tex]The width of the window = 74 cm
When the price of petrol increases by 20%,
a motorist decreases his volume of petrol
consumption by 10%. Find the percentage
increase in his petrol bill.
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Answer:
The percentage increase in his petrol bill is 16 2/3%
The percentage increase in his petrol bill would be equal to 16 2/3%
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
Given that When the price of petrol increases by 20%, a motorist decreases his volume of petrol consumption by 10%.
Let the inital price be 100 and consumption be 100t.
Now increased price
= 120 % of 100
= 120
New consumption
= 100 x 100 / 120
= 83.33
Hence, percentage reduction in the consumption will be;
(100 - 83.33)/ 100 x 100
16 and 2/3 %
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David and Victoria are playing ths integer card game. David drew three cards, -6, 12, and -4. What is the sum of the cards in his hands? Model your answer on the number line below. PLEASE HELP. Brainliest, will give.
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The sum of -6 ,12 and -4 is,
[tex]\begin{gathered} S=-6+12-4 \\ S=2 \end{gathered}[/tex]Express it on number line implies,
What is the positive solution for x^3 + 3x - 9 = x -1 + 2x?
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Given:
[tex]\begin{gathered} x^3+3x-9=x-1+2x \\ x^3+3x-9=3x-1 \\ x^3+3x-3x=-1+9 \\ x^3=8 \\ x^3=2^3 \\ \text{Therefore, x=2} \end{gathered}[/tex]Hence, the postive solution for the gven equation is x=2
Below is a sample space for a family with 3 children. BGG stands for the oldest child being a boy, the middle child a girl, and the youngest a girl. Use the sample space to answer the question: What is the probability (in simplest form) that the oldest child is a a girl? _____Sample Space BBB BBG BGB BGG GBB GBG GGB GGG
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The probability that the oldest child is a girl is given by the quotient between two numbers:
- The number of combinations where a girl is the oldest child i.e. the number of elements in the sample space that start with a G.
- The total number of elements in the sample space.
The first number is 4 since we have 4 elements starting with G: GBB, GBG, GGB, GGG. The second number is 8. Therefore the probability that we are looking for is given by:
[tex]P=\frac{4}{8}=\frac{1}{2}[/tex]AnswerThen the answer is 1/2.