Determine if the Mean Value Theorem for Integrals applies to the function f(x) = 3 - x2 on the interval the closed interval from 0 to the square root of 3 . If so, find the x-coordinates of the point(s) guaranteed by the theorem
Answers
Answer: Yes, Mean Value Theorem for Integrals applies for the function [tex]f(x)=3-x^{2}[/tex] and values of x are 1 and -1
Step-by-step explanation: Mean Value Theorem for Integrals states that if a function is continuous on a closed interval, there is a value c on the interval such that
[tex]f(c)=\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx[/tex]
where a and b are the closed interval given
As the graph of [tex]f(x)=3-x^{2}[/tex] shown below, the function is continuous on the interval [0,[tex]\sqrt{3}[/tex]], so the theorem applies.
To find the x-coordinates, first determine value of f(c) at [0,[tex]\sqrt{3}[/tex]]:
[tex]f(c)=\frac{1}{\sqrt{3} -0} \int\limits {3-\sqrt{x^{2}} } \, dx[/tex]
[tex]f(c)=\frac{1}{\sqrt{3}}[3x-\frac{x^{3}}{3} ][/tex]
[tex]f(c)=\frac{1}{\sqrt{3}}[ 3\sqrt{3}-\frac{(\sqrt{3})^{3}}{3} ][/tex]
[tex]f(c)=\frac{1}{\sqrt{3} } [2\sqrt{3} ][/tex]
f(c) = 2
The x-coordinates will be:
[tex]f(x)=3-x^{2}[/tex]
[tex]2=3-x^{2}[/tex]
[tex]x^{2}=1[/tex]
[tex]x=\sqrt{1}[/tex]
x = ±1
The values for x guaranteed by the Mean Value Theorem are +1 and -1.
Related Questions
one type of insect is 0.0052 meters long. what is this length in scientific notation?
Answers
5.2*10^(-3)
hope this helps!
happy thanksgiving
Answer:
Because scientific notation has to be in between 1 and 10, you would need this to be 5.2. Count the spaces and since its getting smaller your exponent is negative.
Your answer should be 5.2*10^(-3)
Step-by-step explanation:
They want me to put something here and the question is the picture
Answers
Answer:
D. (1, -2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define systems
5x - 2y = 9
3x + 4y = -5
Step 2: Rewrite systems
10x - 4y = 18
3x + 4y = -5
Step 3: Solve for x
Add to equations together: 13x = 13Divide 13 on both sides: x = 1Step 4: Solve for y
Define: 3x + 4y = -5Substitute in x: 3(1) + 4y = -5Multiply: 3 + 4y = -5Isolate y term: 4y = -8Isolate y: y = -2And we have our final answer!
Answer please
Fast
Fast
Answers
Answer:
A. 228.5
B. 10
Step-by-step explanation:
A. Since x represents the number of months, replace x with 6 in the equation. Then multiply 29x6, which equals 174. Then add 174+54.5, which equals 228.5.
B. You need to solve for x by switching the signs in the equation. Set the original equation (29x+54.5) equal to 344.50. To solve for x, first subtract 344.50-54.5, which equals 290 (you subtract because it's the opposite of adding). Then divide 290÷29, which equals 10. You can check your work by replacing x in the original equation with 10, and if you get 344.5, your answer is correct.
Good luck :)
What is the correct answer for both?
Answers
Answer:
11. C.
12. B.
Step-by-step explanation:
Factor them
inverse of the function f(x) = 2x + 5?
Answers
Answer:
[tex]y^{-1} =\frac{1}{2} x-\frac{5}{2}[/tex]
Step-by-step explanation:
Answer:
x - 5
y = --------------
2
Step-by-step explanation:
1. Replace "f(x)" with "y:" y = 2x + 5
2. Interchange x and y: x = 2y + 5
3. Solve this result for y:
2y = x - 5, or
x - 5
y = --------------
2
An item has a listed price of $40. If the sales tax rate is 8% how much is the sales tax (in dollars)
Answers
Answer:
The sales tax will be $3.20
Step-by-step explanation:
Please help I need your help please please
Answers
Answer:
The one in the bottom left
Step-by-step explanation:
Solve 0=2y−8x+10 for y
Answers
Answer:y
y=4x−5
Step-by-step explanation:
1) h(x) = -3x + 5; Find h(-1-2)
Answers
Answer:
h(-1) = 8
h(-2) = 11
h(-12) = 41
Step-by-step explanation:
h(x) = -3x + 5
h(-1) = -3(-1) + 5 = 3 + 5 = 8
h(-2) = -3(-2) + 5 = 6 + 5 = 11
h(-12) = -3(-12) + 5 = 36 + 5 = 41
Geometry hw 2.6 big ideas math
Answers
what???
Explanation:
The angle bisectors of triangle ABC meet at point P. If PQ = 8 and PA = 17, what is the length of AR?
A. 8
B. 15
C. 17
D. Cannot be determined
Answers
Answer:
I'm not sure but I think it's B
HELP PLSSSS WILL MARK BRAINLIEST
Answers
‘ as a exponent it would be 486 -1 .
C personalities are organized and controlled. They take their time completing tasks accurately, like to research things thoroughly, and are always prepared. Because they put so much time and effort into everything they do, they hate to be criticized. They are perfectionists at heart and take even the smallest complaint personally. This makes them extremely difficult to confront. The best way to approach it is to focus on parts of the problem largely out of the C personality’s control or aspects of the problem they might not have considered. Make it clear that you appreciate all of their efforts and that you’re bringing something to their attention because it’s a variable that they need to have in the equation in the future. No matter what, don’t frame the conflict as a personal attack. If you do, the C personality will likely become resentful and go out of their way to avoid future interactions with you.%%%%%%%%%%%%%%%
Find the slope of the line that passes through (5,8) and (2,3).
Answers
Answer:
(-5,-3)
Step-by-step explanation:
y values minus y values over x values minus x values
f(x) = 2x - 4; g(x) = { f(x)
Answers
Answer:
Step-by-step explanation:
subtract the divied
How do you find a unit rate for $2.50 for 5 ounces
Answers
Answer:
You divide 2.50 by 5.
So 2.50/5 makes it $0.50 per ounce.
Answer: $0.50 for 1 ounce
Step-by-step explanation:
To find a unit rate, you have to find the cost for one. When we say it's $2.50 for 5 ounces, it's for 5, not 1. So we have to divide by 5.
2.50/5= 0.5 and 5/5=1
How many terms are there in the following expression: 3a + 3ab + 7b – 2c – 4d?
5
9
7
1
Answers
Answer: 5
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geometry, is this right if not whats the answer ?
Answers
==============================================
Explanation:
Because S and T are midpoints of segments PQ and QR, we know that ST is a midsegment of triangle PQR. Consequently, this means ST is parallel to PR.
From the same side interior angle theorem, the angles (11x-3) and (5x-9) are supplementary angles. This is only true because of the parallel lines.
So we can say the following:
(angle P) + (angle S) = 180
(5x-9) + (11x-3) = 180
(5x+11x) + (-9-3) = 180
16x - 12 = 180
16x = 180+12
16x = 192
x = 192/16
x = 12
--------------------------
Use this to find angle PST
angle PST = 11x-3
angle PST = 11*12-3
angle PST = 132-3
angle PST = 129 degrees
--------------------------
Optionally we can find angle QPR
angle QPR = 5x-9
angle QPR = 5*12-9
angle QPR = 60-9
angle QPR = 51 degrees
As a check, adding the two angles we found should get us 180
(angle PST)+(angle QPR) = 129+51 = 180
The answer checks out.
definicion de hipotenusa
Answers
Answer:
La hipotenusa es el lado opuesto al ángulo recto en un triángulo rectángulo, resultando ser su lado de mayor longitud.
Step-by-step explanation:
Answer:
Lado opuesto al ángulo recto en un triángulo rectángulo.
If F, G, and H are the midpoints of the sides of triangle JKL , FG = 37, KL = 48, and GH = 30 find each measure
Answers
Answer:
The measure of JK is 60
Step-by-step explanation:
It is given that the points F, G, and H are the midpoints of the sides of triangle JKL , FG = 37, KL = 48, and GH = 30.
The point F is midpoint of JK, point G is midpoint of KL and the point H is midpoint of LJ as shown in figure .
According to the midpoint theorem, the line connecting the midpoints of two sides is parallel to the third and its length is half of the third si
Answer:
60
Step-by-step explanation:
In a right triangle, measure of one of the acute angles is 10 degrees more than 3 times the measure of the other angle. What are the measures of the three
angles?
Answers
Answer:
How do you find the angle of a right triangle with 3 sides?
Step-by-step explanation:
Step 1 The two sides we know are Adjacent (6,750) and Hypotenuse (8,100).
Step 2 SOHCAHTOA tells us we must use Cosine.
Step 3 Calculate Adjacent / Hypotenuse = 6,750/8,100 = 0.8333.
Step 4 Find the angle from your calculator using cos-1 of 0.8333:
There are over 2,700 species of snakes in the world. Over
600 species are venomous. Write the fraction of species that are not
venomous as a decimal.
Answers
Answer:
4.5
Step-by-step explanation:
2,700 ÷ 600 = 4.5
not a 100% sure just trying to help
Solve for x. Type only the number in the space below.
Answers
Answer:
-6
Step-by-step explanation:
x+56+x+136=180
2x+192=180
-192 -192
2x=-12
/2 /2
x=-6
x-intercept=4 y-intercept= -2 what is the slope of this line?
Answers
Answer:
gradient = change in y/change in x
--> -2/4 = -1/2
Therefore slope = -1/2
Step-by-step explanation:
Please give BRAINLIEST, it is appreciated, hope this helps!
Why is is that....we park on drive ways but drive on drive ways
Answers
Answer:
What kind of question is this??
Step-by-step explanation:
Please help i'm timed!!
In the equation 19.8 x 2.3 = n, what is the value of n?
Answers
Answer:
45.54
Step-by-step explanation:
hope this helps
Answer:
n=45.54
Step-by-step explanation:
simplifying both sides of equation
A spinner with 4 colors is spun for a total of 50 trials. Yellow was selected 10 times. What is the experimental probability of the spinner landing on yellow? StartFraction 2 over 25 EndFraction One-fifth One-fourth Two-fifths
Answers
Answer:
b
Step-by-step explanation:
i did it
Answer:
b. 1/5
Step-by-step explanation:
i took the unit test on edge
Could triangle ABC be congruent to ADC by SSS? Explain
Answers
Answer: it’s C
Step-by-step explanation:
Answer: A
Step-by-step explanation:
The cost of a babysitting service is $8 for the first hour and $10 for each
additional hour. If the total cost of babysitting Josue is $58, how many
hours TOTAL was Josue with the babysitter?
Answers
Answer:
6 hours
Step-by-step explanation:
8 dollar - 1st hour = 8
10 dollar times 5 hours= 50dollar
total - 58 dollars for 6hours
Answer:
she was with the babysitter for 6 hours.
Step-by-step explanation:
how many millimeters equal 40.7 cm?
Answers
Answer:
407
Step-by-step explanation:
Which of the number(s) below are potential roots of the function? q(x) = 6x3 + 19x2 – 15x – 28
Answers
Answer:
±2/3, ±7/2, ±14
Step-by-step explanation:
edge:) 2020
Answer: ±2/3, ±7/2, ±14
Step-by-step explanation: edge 2020