The graph of f ′ (x), the derivative of f(x), is continuous for all x and consists of five line segments as shown below. Given f (0) = 6, find the absolute maximum value of f (x) over the interval [0, 5].
2
8
11
13
Answers
The maxima of f(x) occur at its critical points, where f '(x) is zero or undefined. We're given f '(x) is continuous, so we only care about the first case. Looking at the plot, we see that f '(x) = 0 when x = -4, x = 0, and x = 5.
Notice that f '(x) ≥ 0 for all x in the interval [0, 5]. This means f(x) is strictly increasing, and so the absolute maximum of f(x) over [0, 5] occurs at x = 5.
By the fundamental theorem of calculus,
[tex]\displaystyle f(5) = f(0) + \int_0^5 f'(x) \, dx[/tex]
The definite integral corresponds to the area of a trapezoid with height 2 and "bases" of length 5 and 2, so
[tex]\displaystyle \int_0^5 f'(x) \, dx = \frac{5+2}2 \times 2 = 7[/tex]
[tex]\implies \max\{f(x) \mid 0\le x \le5\} = f(5) = f(0) + 7 = \boxed{13}[/tex]
Related Questions
Bobby is reading a new book about dragons and wizards. He reads 1/5 of a chapter every night
before bed. There are 15 chapters in the book. How many days will it take Bobby to finish the
book?
Answers
Answer:
75 nights
Step-by-step explanation:
= 15 ÷ 1/5
= 15 × 5/1
=15×5/1 = 75
The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep the cable cars moving at a linear velocity of 16 miles per hour, how fast would the pulley need to turn (in revolutions per minute)? (1 mi = 5,280 ft. Round your answer to the nearest tenth.)
Answers
Answer:
32.0 rpm
Step-by-step explanation:
16 mi/h = (16 mi)(5280 ft/mi)/(60 min) = 1408 ft/min
One revolution is a distance of ...
C = πd
C = π(14 ft) ≈ 43.98 ft
So the number of revolutions per minute is ...
(1408 ft/min)/(43.98 ft/rev) = 32.01 rev/min
The pulley needed to turn at 32.0 rpm.
Three parrots A,B and Cwere parroting "hello" once every 3 minutes, 4 minutes and 5 minutes respectively. If three of the starts parroting at 7.00 a.m.,when will they parrots together again
Answers
Help me out. Struggling
Answers
Answer:
YES
Step-by-step explanation:
In Tanzania, Helen invested TZS X300,000 in the shares of company X and TZS X550,000 in the shares of company Y. After a year, she sold all the shares of both companies for TZS X400,000 and TZS X700,000 respectively. What is her profit from company X?
Answers
The profit from selling the shares in company X given the selling price and the purchase price is TZS X100,000.
What is the profit from the purchase?Profit is the total selling price less the purchase price. A profit is earned when the selling price is greater than the cost price. If this is not the case, a loss is earned.
Profit = TZS X400,000 - TZS X300,000 = TZS X100,000
To learn more about profit, please check: https://brainly.com/question/26181966
Find the measure of ∠ABC.
Answers
Answer:
I think it's just 100
Step-by-step explanation:
Its 100 because it's a litteraly on 100
ANSWER PLEASEEEEEEEEEEEEEEE
Answers
Answer:
2.75
Step-by-step explanation:because you subtracted 3 1/2 and6/8 and that’s your answer. If this is a big grade do not listen to me,if it’s not then go ahead and see if you got it write.
QUICKEST ANSWER GETS BRAINLIEST If you work more than 40 hours a week, then you are paid time and a half (1.5) for all hours over 40. If you work 46 hours this week, how much
did you earn if you are paid 9.25 an hour.
a
370
b
453.25
435.25
425.50
Answers
Answer:
I think its D 425.50
Step-by-step explanation:
If you do 46 times 9.25 it should be the answer
Which equation is equivalent to the given equation?
HELP
Answers
STEP-BY-STEP-EXPLANATION
X^2-6x=8
X^2-6x+9-9=8
X^2-6x+9=17
(X-3)^2=17
A chef trimmed fat off a steak and was left with a steak a weighing 8.80 ounces. If the weight of the fat was equal to 12 percent of the original weight, what was
the original weight, in ounces, of the steak?
Answers
Answer:
10.00
Hope it helps!!!brainliest pls!!!which problom can we solve with 60 devided by 6
Answers
Answer:
10
explanation:
60 divided by 6 equals 10, you could just use the division symbol, which is a slash, as we did above. The easiest way we found to answer the question "what 60 divided by 6 means", is to answer the question with a question: How many times does 6 go into 60?
Answer:
10
Step-by-step explanation:
A. 44
B. 112
C. 32
D. 35
Answers
Answer:
A. 44
Step-by-step explanation:
The area of a trapezoid is [tex]\frac{b_1+b_2}{2} * h[/tex], where b_1 and b_2 are the top and bottom bases, and h = height. We are given the bases as 8 and 14, and the height as 4.
[tex]\frac{8+14}{2} *4[/tex] [tex]\frac{22}{2} *4[/tex] [tex]11*4[/tex] [tex]44[/tex]Therefore, the answer is A. 44.
PLEASE HELP!!!!
For 13–17, use the table at right. The table gives the populations of Toledo, Ohio, and Lexington, Kentucky, during the last three U.S. Censuses.
Answers
Answer:
13)2000 per year
14)a_n = 350000 - 2000(n - 1)
15)3000 per year
16)a_n = 200000 + 3000(n - 1)
17)when when the number of years is more than 31 years, Lexington's population will be greater than toledo.
Step-by-step explanation:
13) From the table, the population of toledo is 350,000 in 1980 and 330000 in 1990.
Thus,population change from 1980 to 1990 is; 350000 - 330000 = 20000
Similarly, from 1990 to 2000, population went from 330000 to 310000. Change in population is; 330000 - 310000 = 20000
In both cases we see that in 10 years interval, the change is 20000 each.. Thus, for 1 year, change in population = 20000/10 = 2000 per year
14) The population of toledo after 1980 can be expressed using arithmetic progression. Formula is;
a_n = a + (n - 1)d
Where;
a is population in 1980
n is number of years after 1980
d is change in population per year.
Since the population decreases each year, then d will be negative. Thus;
Thus;. a_n = 350000 - 2000(n - 1)
15)From the table, the population of lexington is 200,000 in 1980 and 230000 in 1990.
Thus,population change from 1980 to 1990 is; 230000 - 200000 = 30000
Similarly, from 1990 to 2000, population went from 230000 to 260000. Change in population is; 260000 - 230000 = 30000
In both cases we see that in 10 years interval, the change is 30000 each.. Thus, for 1 year, change in population = 30000/10 = 3000 per year
16) like earlier stated The population of Lexington after 1980 can be expressed using arithmetic progression. Formula is;
a_n = a + (n - 1)d
Where;
a is population in 1980
n is number of years after 1980
d is change in population per year.
a_n = 200000 + 3000(n - 1)
17) we want to find the years in which the population of Lexington will be more than that of toledo.
This simply means the inequality is;
200000 + 3000(n - 1) > 350000 - 2000(n - 1)
Deduct 200000 from both sides;
200000 - 200000 + 3000(n - 1) > 350000 - 200000 - 2000(n - 1)
3000(n - 1) > 150000 - 2000(n - 1)
Add 2000(n - 1) to both sides to get;
3000(n - 1) + 2000(n - 1) > 150000
3000n - 3000 + 2000n - 2000 > 150000
5000n - 5000 > 150000
5000n > 150000 + 5000
5000n > 155000
n > 155000/5000
n > 31
Thus,when when the number of years is more than 31 years, Lexington's population will be greater than toledo.
Use synthetic division to solve (3x^4+6x^3+2x^2+9x+10)/(x+2) What is the quotient?
Answers
Answer: = ( x + 1) (3x^2 - 3x + 5)
Step-by-step explanation:
U juss cancel the comon facor x + 2
( x + 1) (x + 2) (3x^2 - 3x + 5)/ x + 2
and get ( x + 1) (3x^2 - 3x + 5)
Answer:
B --> 3x^3+2x+5
Step-by-step explanation:
For edge
12 is 60, percent of what number?
Answers
x = 20
Step-by-step explanation:Hi there !
12 .........60%
x............100%
x = 12×100/60
= 1200/60
= 20
Good luck !
The bar graph shows your cell phone data usage for five months. A vertical bar graph, titled Cell Phone Data Uses. The vertical axis is labeled Gigabytes. The horizontal axis is labeled Month. For May, the bar height is 0.9. For June, the bar height is 1.85. For July, the bar height is 3.82. For August, the bar height is 2.19. For September, the bar height is 1.24. Describe how the outlier affects the mean. 4 / 10000 Word Limit it makes it higher. Question 2 Use the data to answer the statistical question, "How much cell phone data do you use in a month?" gigabytes
Answers
The outlier of the cell phone data usage has its value to be relatively higher or lower than other values
The outlier would make the mean higherYou use 1.85 gigabytes of data monthlyHow to determine the outlier
From the bar graph, we have the following entries:
May = 0.9
June = 1.85
July = 3.82
August = 2.19
September = 1.24
The outlier of the dataset is 3.82.
This is so because it is relatively higher and far from other data elements
So, the outlier would make the mean higher
How much cellphone data you used monthlyThe outlier affects the mean, but it does not affect the median.
So, we calculate the median.
When the dataset is arranged, we have:
0.9, 1.24, 1.85, 2.19, 3.82
The middle value is 1.85.
This represents the median.
Hence, you use 1.85 gigabytes of data monthly
Read more about outliers at:
https://brainly.com/question/3631910
Answer: How funny, I was answering this to.
Step-by-step explanation: I do not know this yet but somone is answering RN
What do you already know about stem-and-leaf plot?
Answers
Answer:
A stem and leaf plot, or stem plot, is a technique used to classify either discrete or continuous variables.
Step-by-step explanation:
If the m 4 = 12x - 10 and m5 is 10x + 10. Find the value of x.
Answers
12x - 10 = 10x + 10
2x = 20
x = 10
can you look at this please
what is the value of a? What is the value of b?
Answers
Answer:
[tex]\huge\boxed{a=36;\ b=-9}[/tex]
Step-by-step explanation:
[tex](6x-3)(6x+3)=ax^2+b\qquad|\text{use}\ (a-b)(a+b)=a^2-b^2\\\\(6x)^2-3^2=ax^2+b\\\\6^2x^2-9=ax^2+b\\\\36x^2-9=ax^2+b\Rightarrow a=36;\ b=-9[/tex]
What is the factored form of x2 - 6x – 16?
O (x – 4)(x - 2)
O (x + 4)(x - 2)
O (x-2)(x + 8)
O (x-8)(x + 2)
Answers
(x - 8)(x + 2)
x^2 + 2x - 8x - 16
x^2 - 6x - 16
The factored form of equation x² - 6x - 16 is,
⇒ (x - 8) (x + 2)
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The equation is,
⇒ x² - 6x - 16
Now, We can simplify as;
⇒ x² - 6x - 16
⇒ x² - 8x + 2x - 16
⇒ x (x - 8) + 2(x - 8)
⇒ (x - 8) (x + 2)
⇒ (x - 8) (x + 2)
Thus, The factored form of equation x² - 6x - 16 is,
⇒ (x - 8) (x + 2)
Learn more about the multiplication visit:
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Please answer quick and show work !
The price of a bicycle that ms. motyka wants to buy is $282. How much will she pay for the bicycle if there is a 4% sales tax.
Answers
Answer: $293.28
Step-by-step explanation:
We know that 282 is the 100% price tag on the bicycle. And there is a 4% tax applied to the 282. So we need to find out how much is 4% of 282.
282/100% = x/4% (we don’t know how much is 4% so its represented by X.
do a cross over where you end up with this:
282 (4) = x (100) we want to have X on its own as it represents the 4% to which we are looking for the amount in dollars. So you end up with this:
282 (4) /100 = x
solve the multiplication first and then divide.
1128/100 = x
11.28 = x
so now we know 4% of 282 is $11.28 so we add it to know how much does this person pay.
$282 + $11.28 = $293.28
What is the percent of a hot dog? To show the price went down, use a negative number. 2000: $250 and 2015: $2.00
Answers
Answer:
The percentage of the hot dog decreased by 20%
Step-by-step explanation:
20% of 2.50 is 50 cents, meaning that the price went down by 50 cents.
Hope this helps!
Write and equation for each line
Answers
To find the equation of all the lines, we must:
1. Find the slope
Choose any two pointsSubstitute the coordinates into the slope formulaSolve for the slope.2. Find the y-intercept by looking at the graph
Finding the equation of the green line:
Step-1: Choose any two points on the line
Chosen points: (0, 4) and (-4, 0)Step-2: Review the slope formula
[tex]\rightarrow \text{Slope = m} = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]Where:
x₁ = x coordinate of the first pointx₂ = x coordinate of the second pointy₁ = y coordinate of the first pointy₂ = y coordinate of the second pointStep-3: Substitute the coordinates into the slope formula.
[tex]\rightarrow \frac{y_{2} - y_{1} }{x_{2} - x_{1} } = \text{Slope of green line}[/tex][tex]\rightarrow \frac{0 - 4 }{-4 - 0 } = \text{Slope of green line}[/tex][tex]\rightarrow \frac{-4 }{-4} = \text{Slope of green line}[/tex][tex]\rightarrow 1 = \text{Slope of green line}[/tex]Step-4: Find the y-intercept of the green line
The y-intercept is the intersection of the line on the y-axis. Looking at the graph, we can tell that the intersection of the y-axis made by the green line is 4.
[tex]\text{y-intercept} = 4[/tex]Step-5: Create the equation
Slope intercept form: y = (m)x + (b) [m = slope; b = y-intercept]Equation of green line: y = (1)x + (4) [m = 1; b = 4]Equation of green line: y = x + 4Finding the equation of the yellow line
The yellow line is a vertical line intersecting (1,0). Since the y-coordinate is 0, the equation will be:
x = x coordinate of (1,0)The x coordinate of (1,0) is 1.
x = 1Finding the equation of the blue line
Step-1: Choose any two points on the line
Chosen points: (0, 4) and (2, 0)Step-2: Substitute the coordinates into the slope formula.
[tex]\rightarrow \frac{y_{2} - y_{1} }{x_{2} - x_{1} } = \text{Slope of green line}[/tex][tex]\rightarrow \frac{0 - 4 }{2 - 0 } = \text{Slope of green line}[/tex][tex]\rightarrow \frac{-4}{2} = \text{Slope of green line}[/tex][tex]\rightarrow -2 = \text{Slope of green line}[/tex]Step-3: Find the y-intercept of the green line
Looking at the graph, we can tell that the intersection of the y-axis made by the blue line is 4.
[tex]\text{y-intercept} = 4[/tex]Step-4: Create the equation
Slope intercept form: y = (m)x + (b) [m = slope; b = y-intercept]Equation of green line: y = (-2)x + (4) [m = -2; b = 4]Equation of green line: y = -2x + 4The owner of a soybean farm raises guinea hens for food and insect control. Guinea hens will eat grasshoppers and other insect pests and ticks. They also act as a "watchdog" by making a lot of noise when intruders approach their territory. The farmer allows the hens free range in his fields during the day and provides roosts for them at night. You may make these assumptions: ∙
1. The farmer lives on 1 hen/day for a year.
2. 1 hen eats 25 grasshoppers/day.
3. 1,000 grasshoppers have a mass of 1 kg.
4. 1 grasshopper requires about 30 g of soy/yr.
6. 1 human requires about 600 grasshoppers/day.
7. dry soybeans have about 3.3 cal/g.
Required:
a. Calculate the number of grasshoppers a hen needs per year.
b. How many grasshoppers are needed for a year's supply of hens for the farmer each year?
c. What is the total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year?
d. How many kilograms of soybeans are needed to feed all the grasshoppers for one year?
Answers
Answer:
a. A hen needs 9,125 grasshoppers per year
b. 3,330,625 grasshoppers are needed for a year's supply of hens for the farmer each year
c. The total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year 3330.625 kg
d. 99918.750 kg of soybeans are needed to feed all the grasshoppers for one year.
Step-by-step explanation:
a. To calculate the number of grasshoppers a hen needs per year.
There are 365 days days in a year.
From the question, 1 hen eats 25 grasshoppers/day
If 1 hen eats 25 grasshoppers per day, then
1 hen will eat 25 × 365 grasshoppers per year
25 × 365 = 9125
Hence, a hen needs 9,125 grasshoppers per year.
b. To determine how many grasshoppers are needed for a year's supply of hens for the farmer each year
From the question, The farmer lives on 1 hen/day for a year.
That is, for a year, the farmer lives on 365 × 1 hen = 365 hens
Now, we will determine how many grasshoppers 365 hens will need for a year.
Since, a hen needs 9,125 grasshoppers per year
Then, 365 hens will need 365 × 9125 grasshoppers per year
365 × 9125 = 3330625 grasshoppers
Hence, 3,330,625 grasshoppers are needed for a year's supply of hens for the farmer each year.
c. To determine the total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year
From the question, 1,000 grasshoppers have a mass of 1 kg.
That is, 1,000 grasshoppers have a mass of 1000 g
(NOTE: 1000g = 1kg)
If 1,000 grasshoppers have a mass of 1000 g
Then, 1 grasshopper will have a mass of (1 × 1000) /1000 = 1 g
From b., the total number of grasshoppers needed to feed all the hens for one year is 3,330,625 grasshoppers.
Now, we will determine the mass of 3,330,625 grasshoppers
1 grasshopper have a mass of 1 g
∴ 3,330,625 grasshoppers will have a mass of (3,330,625 × 1) / 1 = 3,330,625 g
Now, we will convert this to kilograms (kg)
If 1000 g = 1 kg
Then, 3,330,625 g = (3,330,625 × 1) / 1000 = 3330.625 kg
Hence, the total mass, in kilograms, of the grasshoppers needed to feed all the hens for one year 3330.625 kg.
d. To determine how many kilograms of soybeans are needed to feed all the grasshoppers for one year
From the question, 1 grasshopper requires about 30 g of soy/yr
From b., 3,330,625 grasshoppers are needed for a year's supply of hens for the farmer each year
If 1 grasshopper requires about 30 g
Then, 3,330,625 grasshoppers will require (3,330,625 × 30) / 1 = 99918750 g of soy/yr
Now, we will convert this to kilograms
If 1000 g = 1 kg
Then, 99918750g = (99918750 × 1) / 1000 = 99918.750 kg
Hence, 99918.750 kg of soybeans are needed to feed all the grasshoppers for one year.
What is the product of (4^-2)(4^-1)
Answers
can anyone help me find the surface area of the problem and give an explanation, too. it would be very appreciated!
I'm assuming the formula is SA= hp+ 2(B)
hp= height * perimeter
2(B)= 2 * base
Answers
Answer:
731 square feet
Step-by-step explanation:
The surface area can be found using the given formula, along with the formula for the area of a trapezoid. (The bases have the shape of a trapezoid.)
We are given "h", so we need to find "p" and "B" for the formula.
__
Lateral Area dimensionsThe perimeter is the sum of the side lengths:
p = 13 ft + 7 ft + 10 ft + 8 ft = 38 ft . . . perimeter
The height is shown as 15 ft.
__
Base AreaThe base area is the area of a trapezoid with base lengths 13 ft and 10 ft and height 7 ft. (The height is the perpendicular distance between the parallel bases. The two right angle corners show you the bases are parallel, and that 7 ft is the distance between them.)
A = 1/2(b1 +b2)h
A = 1/2(13 ft +10 ft)(7 ft) = 80.5 ft²
__
Total Surface AreaUsing your formula for the surface area, we find ...
SA = hp +2(B)
SA = (15 ft)(38 ft) +2(80.5 ft²) = 570 ft² +161 ft²
SA = 731 ft²
The area of the trapezoidal prism is 731 square feet.
What is the equation of the given line in standard form?
–6x + 7y = –17
–6x + 11y = –13
–11x + 6y = –13
–6x +11y = 13
Answers
Answer:
-6x + 11y = 13
Step-by-step explanation:
the equation in slope-intercept form is:
from the two points we can find the slope, 2-(-1) / 1.5-4)
slope = 6/11
y-intercept can be found by using a point and the slope:
-1 = 6/11(-4) + b
-1 = -24/11 + b
b = 1 2/11 or 13/11
so we have:
y = 6/11x + 13/11
if we multiply everything by 11 we get:
11y = 6x + 13
subtract 6x from each side to get:
-6x + 11y = 13
115 km 10 hm what is that answer
Answers
Answer:
115 km. 10= 1 hm
115 km= 1150 hm
Step-by-step explanation:
mark me brainliest!!
list two numbers that have the same value as 34 divided 3
Answers
Answer:
89/8
99/9
Step-by-step explanation:
34/3 =11.33
Which is the graph of the linear inequalityx-2y> -6?
Answers
Answer:
4th graph (in bottom right corner)
Step-by-step explanation:
First, convert the given equation into slope-intercept form.
Given :-
1/2x - 2y > -6
-2y > -1/2x - 6
2y < 1/2x + 6
y < 1/4x + 3
As the < sign indicates, the line will be dotted and the solution set will be towards the origin in this case.
The correct option is the 4th graph (in bottom right corner)