Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 3 (*sqaure root sign*) t (20 − t), [0, 20]
Answers
9514 1404 393
Answer:
maximum: 15∛5 ≈ 25.6496392002minimum: 0Step-by-step explanation:
The minimum will be found at the ends of the interval, where f(t) = 0.
The maximum is found in the middle of the interval, where f'(t) = 0.
[tex]f(t)=\sqrt[3]{t}(20-t)\\\\f'(t)=\dfrac{20-t}{3\sqrt[3]{t^2}}-\sqrt[3]{t}=\sqrt[3]{t}\left(\dfrac{4(5-t)}{3t}\right)[/tex]
This derivative is zero when the numerator is zero, at t=5. The function is a maximum at that point. The value there is ...
f(5) = (∛5)(20-5) = 15∛5
The absolute maximum on the interval is 15∛5 at t=5.
Related Questions
the perimeter of a rectangle is 15x+17y. if the length is 7/2x+7y, then find the width of the rectangle
A.) 4x+3/2y
B.) 8x+3y
C.) 8x+10y
D.) 4x+3y
Answers
Answer:
A
Step-by-step explanation:
Length : [tex]\frac{7x}{2} + 7y[/tex]
Perimeter: [tex]15x + 17y[/tex]
Perimeter = 2(Length + Width)
15x + 17y = 2( [tex]\frac{7x}{2} + 7y[/tex] + Width)
15x + 17y = 7x + 14y + 2(Width)
15x + 17y -7x -14y = 2(Width)
8x + 3y = 2(Width)
Width = [tex]\frac{8x + 3y}{2}[/tex]
Width = 4x + 3y/2
The age of a first-grader on September 1 at Garden Elementary School has the following distribution: f (x )space equals space 1 comma space space 5.8 less or equal than x less or equal than 6.8 We randomly select one first-grader from the class. Find the probability that she is over 6.5 years old. Round to one decimal place.
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Answer:
lol
Step-by-step explanation:
lol
help me pls. answer correct
Answers
Answer:
1st answer is
[tex](x.y) = ( \frac{38}{5} . \frac{2}{5} ) \\ [/tex]
2nd answer is (x, y) =(36, 45)
What is the equation of this trend line?
Enter your answers by filling in the boxes.
K= J+
Answers
Answer:
K = -2 J = 28
Step-by-step explanation:
I took the k12 test
Answer:
The answer is K=-2 J+24.
Step-by-step explanation:
(02.01)Polygon ABCD slides 4 units left and 3 units up on the coordinate plane. If the original measure of angle A was 75 degrees, what is the measure of angle A'?
A-75 degrees
B-100 degrees
C-105 degrees
D-180 degrees
Answers
Item 16
Find the perimeter of the figure to the nearest hundredth. due today
Answers
Answer:
42.84 cm
Step-by-step explanation:
1) Find the perimeter of the top trapezoid. (In cm) 6 + 8 + 12 + 10 = 36 cm
2) Find the circumference of the semicircle with the formula 0.5(pie times D) where D is the diameter. Another formula is 0.5(pie times 2r) where r is the radius. Approximate pie to 3.14 so we should get 0.5 * 3.14 * 12 = 18.84 cm
3) We do not need the length of the base of the trapezoid so we take 36 + 18.84 - 12 = 42.84 cm
Mrs.Ziegler will use 1/5 of the 4gallons of milk she has to make chocolate pudding. How much milk will Mrs.Zirkle use to make chocolate pudding?
Answers
4 gallons. 100%
x gallons. 20%
x=4•20/100
x=80/100
x=8/10
x=4/5
Mrs. Zirkle will use 4/5 gallons of milk.
I am not 100% sure.
ill mark brainlist plss help
Answers
Step-by-step explanation:
Perimeter of rectangle = 2(l+b)
= 2(97+17)
= 2(114)
= 228cm
Answer:
P = 228 inches
Step-by-step explanation:
P = 2(l + w)
l = 97 inches
w = 17 inches
P = 2 (97 + 17)
P = 2 x 114
P = 228
Cart 1 (500 g) moves to the right at 0.40 m/s. Cart 2 (250g) moves to the left at 0.50 m/s. a. If the carts stick after the collision, what will be their velocity?
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Answer:
after the collision cart 1 will stop and cart 2 will keep moving will 0.1.m/s after stop.
What is 0.11 / 22.77
Answers
Answer:
is your answer
0.00483091
Step-by-step explanation:
how do i solve this?
Answers
Answer:
m∠R = 60°
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA [Right Triangles Only] sinθ = opposite over hypotenuseStep-by-step explanation:
Step 1: Identify
Angle θ = ∠R
Opposite Leg of ∠R = 10√3
Hypotenuse = 20
Step 2: Solve
Substitute in variables [sine]: [tex]\displaystyle sin(R^\circ) = \frac{10\sqrt{3}}{20}[/tex][Equality Property] Trig inverse: [tex]\displaystyle R^\circ = sin^{-1}(\frac{10\sqrt{3}}{20})[/tex]Evaluate trig: [tex]\displaystyle R = 60^\circ[/tex]The following data represent the number of housing starts predicted for the 2nd quarter (April through June) of 2014 for a random sample of 40 economists.
984 1260 1009 992 975 993 1025 1164 1060
992 1100 942 1050 1047 1000 938 1035 1030
964 970 1061 1067 1100 1095 976 1012 1038
929 920 996 990 1095 1178 1017 980 1125
964 888 946 1004
Required:
a. Draw a histogram of the data.
b. Construct a 95 % confidence interval for the population mean forecast of the number of housing starts in the second quarter of 2014.
c. Construct a 90% confidence interval for the population mean forecast of the number of housing starts in the second quarter of 2014
Answers
Answer:
Kindly check attached picture ;
(999.494 ; 1046.056) ;
(1003.235 ; 1042.315)
Step-by-step explanation:
Given the data:
888, 920, 929, 938, 942, 946, 964, 964, 970, 975, 976, 980, 984, 990, 992, 992, 993, 996, 1000, 1004, 1009, 1012, 1017, 1025, 1030, 1035, 1038, 1047, 1050, 1060, 1061, 1067, 1095, 1095, 1100, 1100, 1125, 1164, 1178, 1260
Using calculator to obtain the mean and standard deviation :
Mean, x = 1022.775
Standard deviation, s = 75.124
Sample size, n = 40
Zcritical at 95% = 1.96
Zcritical at 90% = 1.645
Using the relation :
x ± E
E = error margin = Zcritical * s / sqrt(n)
At 95% ;
Error margin = 1.96 * 75.124/ sqrt(40) = 23.281
At 90% ;
Error margin = 1.645 * 75.124/ sqrt(40) = 19.540
Confidence interval at 95%:
(1022.775 - 23.281) ;(1022.775 + 23.281)
(999.494 ; 1046.056)
Confidence interval at 90%:
(1022.775 - 19.540) ;(1022.775 + 19.540)
(1003.235 ; 1042.315)
Write the equation of the line in fully simplified slope-intercept form.
Y
12
11
10
9
8
7
6
5
4
3
2
1
-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
2 3 4 5 6 7 8 9 10 11 12
-2
-3
-4
-5
-6
-8
-9
-10
-11
-12
Answers
Rise / run between any two points = slope (m)
Where the line crosses the y axis is (yint) (b)
Slope is -1/2
Yint = -8
So the equation is y=(-1/2)x - 8
The expression (x^3) (x12) is equivalent to x^n. What is the value of n?
3 and n are exponents
Answers
Answer:
Step-by-step explanation:
(x^3) (12x)
(x^4)(12)
12x^4
We can really find the exponent without knowing what x is equal to but I hope this helps
the mean age of swimers for all of these teams is 10. what does a large mad tell you.eade help
Answers
Step-by-step explanation:
We know that the mean absolute deviation (MAD) helps to know whether the mean of a data is a worthy indicator for the data values .
The larger the MAD tells us the values are spread out far from the mean .
Also, larger the MAD makes the mean less worthy as an indicator of the data elements within the data set.
Is this a rational number
Answers
Answer:
Note that it is not a perfectly elastic result so it is irrational
A seller has a house that is 1800 square feet. The neighborhood comps show
the line of best fit to be y = 0.074x +50 48. What is a fair price for this house?
A. $150,000
B. $183.68
C. $150.00
D. $184,000
SUBMIT
Answers
A fair price for this house is $183.68. Therefore, option B is the correct answer.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, a seller has a house that is 1800 square feet.
The neighborhood comps show the line of best fit to be y = 0.074x+50.48.
Substitute x=1800 in the given equation, we get
y=0.074×1800+50.48
y=$183.68
Therefore, option B is the correct answer.
To learn more about the equation of a line visit:
https://brainly.com/question/2564656.
#SPJ1
What is the product?
One-third times 33.99
Answers
Answer:
11.33
Step-by-step explanation:
um I'm not that good at explaining but...
33/3=11
99/3=33
put it together
11.33
Identify the vertex and the y-intercept of the graph translated 1 unit right from the parent function f(x)=x2
Vertex ( ?,?)
y-intercept: ?
Answers
Answer:
Step-by-step explanation:
y = (x-1)²
vertex (1,0)
y-intercept = (0-1)² = 1
POSSIBLE POINTS: 15
A can of soda contains 0.355 liters of soda. How many milliliters of soda are in one can?
Answers
6/15=3/x
HELPP PLEASE
Answers
Answer:
15/2 or 7.5 :)
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]\frac{6}{15} = \frac{3}{x}[/tex]
simply cross multiply
[tex]6x = 45[/tex]
divide both sides by 6
[tex]\frac{6x}{6} = \frac{45}{6}[/tex]
hence x will be equal to [tex]7.5[/tex]
Is it required to for it to be in decimals?
Easy Points! whats 2+2?
Answers
Answer:
4
Step-by-step explanation:
Anastasia went shopping for birthday gifts and bought three of the same board game. She also spent $9.75 on birthday cards. Anastasia spent a total of $69.60. What was the price of each board game?
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What’s the slope of the line I forgot how to do it when it comes to negative ones :((!!
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PLEASE HELP ME ITS URGENT ❗❗❗❗❗❗❗❗❗❗❗
Answers
Answer: W is your answer :)
Step-by-step explanation:
PLEASE HELP!!! DUE IN 10 MIN!!!
Answers
Answer:
[tex]64[/tex]cm³
Step-by-step explanation:
[tex]8 \times 2 \times 4 \\ = 64[/tex]
Answer:
64
Step-by-step explanation:
Hello There!
The formula for volume of a rectangular prism is
[tex]V=lwh[/tex]
where w = width
l = length
h = height
They give us the following dimensions
height = 4
width = 2
length = 8
all we have to do is plug in the values
[tex]V=2(4)8\\2*4=8\\8*8=64\\V=64[/tex]
Thus the answer is 64
Geometry!! Will give brainliest
Answers
it's the second one.
You are building a frame for a window. The window will be installed in the opening shown in the diagram. Determine whether the opening is a rectangle. Then give the length of the diagonals.
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Answer:
dfffffdf
Step-by-step explanation:
choose all answers that apply
Answers
Answer:
none of the above
Step-by-step explanation:
An isosceles trapezoid cannot be rotated to create the same image therefore it has no angle of rotational symmetry.
WILL GIVE BRAINLIEST
Answers
Answer:
C
Step-by-step explanation:
It's not A and B because an exponent to the negative number leads to the fraction.
e.g. 10^-a = 1/(10^a)
It's not D because 5,030,000 rounds to 5,000,000 and not 6,000,000.
