Answers
The values of c on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].
According to the Mean Value Theorem for Integrals, if f(x) is continuous on the interval [a, b], then there exists a value c in [a, b] such that:
f(c) = 1/(b-a) . ∫(a to b) f(x) dx
For f(x) = x⁴ on the interval [-5, 5], we have:
∫(-5 to 5) x⁴ dx = (1/5) . (5⁵ - (-5)⁵)/5
= (1/5) . (3125 + 3125)
= 1250
So we need to find c such that f(c) = 1250/10 = 125.
f'(x) = 4x³, so we can use the Mean Value Theorem for Derivatives to find a value of c that satisfies the condition.
f'(c) = (1/(5-(-5))) . ∫(-5 to 5) f'(x) dx
= (1/10) . [f(5) - f(-5)]
= (1/10) . [(5⁴) - ((-5)⁴)]
= 100
Therefore, by the Mean Value Theorem for Derivatives, there exists a value c in [-5, 5] such that f'(c) = 100.
Now, we need to check if there exists a value c in [-5, 5] such that f(c) = 125.
f(c) = c⁴, so we need to solve the equation c⁴ = 125.
c = ±[tex]5^{1/4[/tex]
Both of these values are in the interval [-5, 5], so they satisfy the Mean Value Theorem for Integrals.
Therefore, the values of c that satisfy the Mean Value Theorem for integrals for f(x) = x⁴ on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].
Learn more about Mean value theorem here:
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Related Questions
Two ships leave port at the same time. One travels north at 70 knots (that is, 70 nautical miles per hour), and the other west at 70 knots. The distance between the ships increases at a constant rate. At what rate is the distance between the two ships increasing
Answers
Answer:
99miles is more likely correct
or 114miles as knots is usually higher mileage
Step-by-step explanation:
70^2 + 70^2 = c^2
sqrt 4900 + sqrt 4900 = c^2
sq rt 9800 = c^2 = 98.9949494
99 x 1.1507794480225 = 113.927165 = 114miles if converted to 80.6m/ph
70 Knots is equivalent to 80.554561361578 Miles/Hour. How to convert from Knots to Miles/Hour The conversion factor from Knots to Miles/Hour is 1.1507794480225. To find out how many Knots in Miles/Hour, multiply by the conversion factor or use the Velocity converter.
After 4 tests,Alex average score was 65.After the 5th test his average score increased by 5 .How much did he score in his 5th test?
Answers
Answer:
329 вот правильный ответ
△XYZ is similar to △XVW. Enter the congruence statements that must be true.
The congruence statements that must be true are
Answers
Answer:
angle X is congruent to angle X
angle Y is congruent to angle V
angle Z is congruent to angle W
Step-by-step explanation:
A restaurant has 23 tables. Some of the tables seat 4 persons and the rest seat two persons. In all, 76 persons can be seated at once. How many tables of each kind are there?
Answers
Answer:
15 tables with 4 seats and 8 tables with 2 seats.
Step-by-step explanation:
x = 4 seated tables
y = 2 seated tables
x + y = 23
4x + 2y = 76
Multiply first equation by -2 to cancel y's:
-2x - 2y = -46
4x + 2y = 76
2x = 30
x = 30 / 2
x = 15
And we said 23 tables so:
23 - 15 = 8
x = 15
y = 8
−3x−8y=−8
y=2−x
yes or no
Answers
Answer:
No
Step-by-step explanation:
-3x-8y=-8
3x+8y=8 (multiply all terms by -1)
8y=8-3x (take 3x from both sides)
y=1-(3/8)x (divide each term by 8)
1-(3/8)x ≠ 2-x
Please help a brotha out
Answers
Answer: a=1,b=1
Step-by-step explanation:
b
A piece of fabric is 2 yards long. The fabric is cut into 24 pieces of equal length.
How long is each piece?
2 inches
3 inches
4 inches
6 inches
Answers
Answer:
3 inches
Step-by-step explanation:
Answer:
3 in
Step-by-step explanation:
Determine whether the following statements are true and give an explanation or counterexample. If f is not one-to-one on the interval [a, b], then the are of the surface generated when the graph of f on [a, b] is revolved about the x-axis is not defined.
Answers
Answer:
Step-by-step explanation:
The missing equation is:
[tex]S = \int ^b_a 2 \pi f(y) \sqrt{1 + f' (y)^2 } \ dy[/tex]
Suppose f = nonnegative function whose first derivative is within (a,b) and it is continuous, Then the area of the surface generated is revolved about the x-axis:
The area of the surface revolution is:
[tex]S = \int ^b_a 2 \pi f(x) \sqrt{1 + f' (x)^2 } \ dx[/tex]
So; if [tex]x = g(y)[/tex] for [tex]y \ \varepsilon \ [c,d][/tex]
Then; substituting a with c and b with d; f(x) also with g(y) and dx with dy;
Then;
[tex]S = \int ^d_c 2 \pi g(y) \sqrt{1 + g' (y)^2 } \ dy[/tex]
SInce;
[tex]g(y) \ne f(y)[/tex]; Then the statement is false.
Provided that the semicircle [tex]y = \sqrt{1-x^2}[/tex] isn't on [tex][-1,1][/tex] interval.
Then, the solid generated by the revolution about the x-axis is a sphere.
However, the surface is well defined and the statement is false.
The flux hotel recently installed a triangular pool as shown below. If the hotel manager needs to order a cover for the pool and the cost is $35 per square foot, how much can he expect to spend?
Answers
Answer:
[tex]Total = \$6545[/tex]
Step-by-step explanation:
Given
[tex]Base = 17ft[/tex]
[tex]Height = 22ft[/tex]
[tex]Slant\ Height = 32ft[/tex]
[tex]Cost = \$35[/tex] per square ft
Required
Determine the expected spending
First, calculate the area of the pool.
[tex]Area = \frac{1}{2} * Base * Height[/tex]
[tex]Area = \frac{1}{2} * 17ft * 22ft[/tex]
[tex]Area = 17ft * 11ft[/tex]
[tex]Area = 187ft^s[/tex]
The total cost is:
[tex]Total = Cost * Area[/tex]
[tex]Total = 35 * 187[/tex]
[tex]Total = \$6545[/tex]
What is 643 divided by 8.4?
Answers
Or if you round it to one decimal place 77 is the answer
Hi there!
643*8.4=76.5476190476
Which expression represents the distance between the points (11, 4) and (5,8)?
Answers
Answer:
[tex]\displaystyle d = 2\sqrt{13}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (11, 4) → x₁ = 11, y₁ = 4
Point (5, 8) → x₂ = 5, y₂ = 8
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(5-11)^2+(8-4)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{(-6)^2+(4)^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{36+16}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{52}[/tex][√Radical] Simplify: [tex]\displaystyle d = 2\sqrt{13}[/tex]In a carnival game, there are six identical boxes, one of which contains a prize. A contestant wins the prize by selecting the box containing it. Before each game, the old prize is removed and another prize is placed at random in one of the six boxes. Is it appropriate to use the binomial probability distribution to find the probability that a contestant who plays the game five times wins exactly twice
Answers
Answer:
The probability that a contestant who plays the game five times wins exactly twice is [tex]16.08[/tex] %
Step-by-step explanation:
We will use binomial theorem here
[tex]C_{n,k}p^k(p')^{n-k}[/tex]
Substituting the available values in above equation, we get
[tex]C_{5,2} * \frac{1}{6}^2*\frac{5}{6}^3[/tex]
[tex]0.1608[/tex]
OR
The probability that a contestant who plays the game five times wins exactly twice is [tex]16.08[/tex] %
A hot dog bun (volume 240cm3) with a density of 0.15g/cm3 is crushed in a picnic cooler into a volume of 195cm3. What is the density of the bun?
Answers
Answer:
weight of hot dog bun = 240 cm^3 x 0.15 g/cm^3 = 36 gram
36 gm / 195 cm^3 = 0.185 g/cm^3
Step-by-step explanation:
Density is mass/volume. The mass of the bun never changes, only its volume. Solve for the original mass.
Now think about it logically. Should the bun be more sense now that it has been crushed? Of course! The math proves it.
Therefore the answer is: 0.185 g/cm^3
Use substitution to solve the linear system of equations.
2y = X - 6
x=9
(9, 24)
(9, 3/2)
(3/2, 9)
(9,9)
Answers
Answer:
2y=X-6
×=9
(9, 3/2)
Step-by-step explanation:
Hope this help!
Answer: 65
Step-by-step explanation: 65
2(-4y-7)+3=11 solve for y
Answers
Answer:
y = -11/4
Step-by-step explanation:
2 ( -4y - 7) + 3 = 11
-8y - 14 + 3 = 11
-8y - 11 = 11
-8y = 22
y = -11/4
Answer:
12
Step-by-step explanation:
-4 + 12 =7
Sapna and Robbie have some biscuits.
Altogether they have 14 biscuits.
Sapna has 2 more biscuits than Robbie.
How many biscuits do Sapna and Robbie each have?
Answers
Each square in the grid is a 1 x 1 centimeter square.
What is the area of the shape?
Answers
8square centimeters
Step-by-step explanation:
1 square is 1cm2. theres 8 squares so 8cm2
What is the CIRCUMFERENCE of the given circle?
12.57 in
30.23 in
25.13 in
50.27 in
Answers
Use — 2pi * radius
So.
2pi*4. = 25.13
if ON=7x-5, LM= 6x+3, NM =x-4, and OL =2y+5, find the value of x and y given that LMNO is a parallelogram
Answers
Answer:
x=8, y=-1/2
Step-by-step explanation:
parallelogram's opposite sides are equal.
LM=ON, NM=OL
6x+3=7x-5, solve for x, x=8
x-4=2y+5
y=-1/2
7/8 percent equivalent to the nearest whole percent?
Answers
Answer:
88%
Step-by-step explanation:
7/8 = 87.5%
I need to know the probability of a yellow marble not being drawn at all.
Answers
Answer:
9/13
Step-by-step explanation:
8.15 = e + 6* the answer would be E=2.15 right if it’s not plz correct me if I’m wrong
Answers
Find the Area Please
Answers
Answer:
The area of this shape is super close/equal to 18.283 [tex]m^{2}[/tex]
Step-by-step explanation:
The area of this shape will be equal to the sum of the area of the trapezoid with the height being 4m and parallel lines being 2m and 4m long, and the area of the semi-circle with the radius of 2m. And so we get...
Let "A" be the total area of this shape, then...
[tex]A = \frac{(a + b)h}{2} +[/tex] π[tex]r^{2}[/tex]/2
[tex]A = \frac{(2 + 6)4}{2} +[/tex] π [tex]2^{2}[/tex]/2
[tex]A[/tex] ≈ 12 + 6.283
A ≈ 18.283 [tex]m^{2}[/tex]
Bill paid $45in tax on a laptop that cost $500. What percent sales tax did Bill pay?
Answers
Answer:
9%
Step-by-step explanation:
9% of 500 is 45
In the parallelogram below, solve for Y
Options
4
10
25
100
Answers
Answer:
x = 4
y = 4
Step-by-step explanation:
the front triangle has two 40° angles (sum of all ∡'s must be 180°)
the unlabeled lower-left angle then is 40°; this angle corresponds to the angle in the other triangle labeled as 10y°
therefore, 10y = 40 so y = 4
Since opposite angles in a parallelogram are congruent then we can write:
40° + 25x° = 100° + 10(4)°
25x° = 140 - 40°
25x = 100°
x = 4
Who ever gets this right gets branliest
Answers
Answer:
2 1/2
Step-by-step explanation:
Answer: 2 1/2
Step-by-step explanation: Its positive and lands between 2 and 3 halfway
After lunch, you see the bumper cars and want to ride them. Here’s what the sign says:
Bumper Cars:
6 minutes: 8 tickets
8 minutes:12 tickets
Which one gives you more time for your money?
Answers
Answer:
The option of 6 minutes with 8 tickets given more time for the money.
Step-by-step explanation:
Which one gives you more time for your money?
We have to find the time per ticket, which is the number of minutes divided by the number of tickets.
6 minutes: 8 tickets
6/8 = 0.(60/8) = 0.75 minutes per ticket.
8 minutes:12 tickets
8/12 = 2/3 = 0.(20/3) = 0.667 minutes per ticket.
So the option of 6 minutes with 8 tickets given more time for the money.
HELP
Sairam has two jobs. He earns $8 per hour babysitting
his neighbor's children and he earns $11 per hour
working at the coffee shop.
Write an inequality to represent the number of hours,
x, babysitting and the number of hours, y, working at
the coffee shop that Sairam will need to work to earn
a minimum of $200.
Answers
Answer:
sairam will have to work around 18.18 hours at coffee shop to get 200$
Step-by-step explanation:
WHOEVER HELPS AND GETS IT RIGHT I WILL GIVE BRAINLY!!!!!
Answers
Answer:
3
Step-by-step explanation:
4x-5y=18 determine the missing coordinate in the ordered pair (-2,?) so that it will satisfy the given equation
Answers
Because plug in numbers
(x,y)
4(-2) - 5y = 18
Pemdas
-8 -5y = 18
Add 8 to both sides
-5y = 26
Divide -5 both sides
y = -5.2
Check:
4(-2) -5(-5.2) = 18
Pemdas
-8 -5(-5.2) = 18
Pemdas, two negatives make a positive
-8 +26 = 18
18 = 18
Perhaps