The derivative of the function f is given by f′(x)=x^2−2−3xcosx. On which of the following intervals in [−4,3] is f decreasing?
Answers
The function f'(x) = x² - 2 - 3xcosx is decreasing on (- 4, - 3) and (- 1, 1).
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f'(x) = x² - 2 - 3xcosx.
We know a function f(x) is decreasing if f'(x) is < 0.
Therefore,
x² - 2 - 3xcosx < 0.
x² - 3xcosx < 2.
x(x - 3cosx) < 2.
Now, 3cosx can be [- 3, 3].
x(x - 3) < 2 and x(x + 3) < 2.
x < 2 Or x - 3 < 2 and x < 2 or x + 3 < 2.
x < 2 Or x < 5 and x < 2 or x < - 1.
But x should be in [- 4, 1], Therefore it is decreasing at (- 4, - 3) and (- 1, 1).
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Related Questions
The function f(x)= square root of x is translated using the rule (x,y) (x-7,y+2) to create f(x)what is the domain of f(x)?
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The value inside the square root should be greater than or equal to zero. Then the domain of the function will be [7, ∞).
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
f(x) = √x
The function after the transformation, then we have
f(x) = √(x - 7) + 2
The value inside the square root should be greater than or equal to zero. Then the domain of the function will be given as,
x - 7 ≥ 0
x ≥ 7
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HELP! aaa 5,6,7,8 bonus
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find the volume of a cake with radius of 8 and height of 5
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how to work out the area of a parallelogram
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the base timed by the height
Popcorn at the Movies - Exit Slip
You and a friend go to the movies and decide to share a large bucket of popcorn. Write a story to describe the graph.
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How can you divide polynomials? What are the different methods you can use?Which method do you prefer and why?
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Solve: -7(3x - 7) + 21x > 50
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Answer: Option 2
Step-by-step explanation:
[tex]-7(3x-7)+21x \geq 50\\\\-21x+49+21x \geq 50 \\\\49\geq 50[/tex]
This is false, so there are no solutions.
Help please look at picture!!^^
Answers
9514 1404 393
Answer:
8167.14 m²
Step-by-step explanation:
The radius of the circle is half the diameter, so is 51 m. The area of the circle is given by the formula ...
A = πr²
Filling in the given numbers, we find the area to be ...
A = 3.14(51 m)² ≈ 8167.14 m²
Find the area. The figure is not to scale
Answers
Answer:
5.4 cm^2
Step-by-step explanation:
Given,
Height ( h ) = 2 cm
Base ( b ) = 5.4 cm
To find : Area ( triangle ) = ?
Formula : -
Area ( triangle ) = bh / 2
Area ( triangle )
= 5.4 x 2 / 2
= 5.4 cm^2
6p – 9 = 9; then p=?
Answers
Answer:
p = 3
Step-by-step explanation:
I need help solving this problem :) please help
Answers
Answer:
25
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
Which question is a statistical question?
A. How tall is the oak tree?
B. How much did the oak tree grow in one year?
C. What are the heights of the oak trees in the schoolyard?
D. What is the difference in height between the oak tree and the pine tree?
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Explain: you have to create a chart to demonstrate the grow of the three in one year. A chart is part of statistical
Math homework please help look at picture!!
Answers
Answer:
a = 327 m²
Step-by-step explanation:
Area of bed
r = 22/2 = 11
a = 3.14(11²)
a = 379.94
Area of bed and sidewalk
r = 11 + 4 = 15
a = 3.14(15²)
a = 706.5
Area of sidewalk
a = 706.5 - 379.94
a = 327 m² (rounded to whole number
a circular picture whose diameter is 4 decimeter is framed in a rectangle board with dimension of 6 decimeter by 4 decimeter what is the area of the board that can be seen
Answers
Answer is [tex] \bf \dfrac{80}{7} [/tex] dm².
In order to calculate the area of the board that can be seen, we need to calculate the area of the the rectangular board and the circular frame. The difference of both's area is the required answer.
Refer to the attachment for step by step solution. :)
The area of the board that can be seen is 11.44 decimeter square.
What is the area of the board that can be seen?The area of the board that can be seen is equivalent to the difference between the area of the circular picture and the area of the rectangular board.
Area of a circle = πr²
Where :
π = pi = 3.14R = radius = diameter = 4/2 = 23.14 x 2² = 12.56 d²
Area of the rectangle = length x width
6 x 4 = 24
Area of the board that can be seen = 24 - 12.56 = 11.44 decimeter square
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two equivalent ratios for 17:5?
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Answer:
34/10 is equivalent to 17/5 because 17 x 2 = 34 and 5 x 2 = 1051/15 is equivalent to 17/5 because 17 x 3 = 51 and 5 x 3 = 1568/20 is equivalent to 17/5 because 17 x 3 = 68 and 5 x 3 = 20
Step-by-step explanation:
hii, how are you
A family buys a studio apartment for $140,000 They pay a down payment of $35,000
a. Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $7,000 down payment be?
Answers
Answer:
a. Their down payment is 25% of the purchase price.
Calculation:
Down payment ÷ Purchase price = Percentage
$35,000 ÷ $140,000 = 0.25 = 25%
b. A $7,000 down payment would be 5% of the purchase price.
Calculation:
Down payment ÷ Purchase price = Percentage
$7,000 ÷ $140,000 = 0.05 = 5%
Nika rolls an 8-sided cube with faces numbered 1 through 8. Which of the following statements is true?
P(even number) = ⅛
P(odd number) = ½
P(number less than 8) = 1
P(the number 9) = 1
Answers
Answer: Statement 2 (P(odd number) = 1/2) is true
Step-by-step explanation:
Statement 1: there are 4 even numbers (2, 4, 6, 8) so therefore a 1/2 chance, not a 1/8. [FALSE]
Statement 2: there are 4 odd numbers (1, 3, 5, 7) so therefore a 1/2 chance, so this is true. [TRUE]
Statement 3: 8 is the biggest number, so there are 7, not 1, numbers less than it. [FALSE]
Statement 4: there is no 9 on an 8 sided cube. [FALSE]
While taking a hike 80% or 20 of the participants wore hiking boots. How many participants were on the hike?
Answers
20 beacuse you need hiking boots to hike
Answer:
25
Step-by-step explanation:
let x = # of participants on the hike
(.80)x = 20
x = 20/0.80 = 25
CAN SOMEONE HELP PLEASE???
When a car's tire pressure is 30 pounds per square inch (psi), it averages mpg of gasoline. If the tire pressure is increased to 35 psi, the car averages mpg of gasoline. Answer parts a) through c).
If someone drives an average of 21,000 mi per year, how many gallons of gasoline will he save in a year by increasing his tire pressure from 30 to 35 psi?
If gasoline costs $2.00 per gallon, how much will he save in a year?
Assume that there are about 130 million cars in a country and that these changes are typical of each car, how many gallons of gasoline would be saved if all drivers increased their cars' tire pressure?
Answers
Answer:he will save 100 $
Step-by-step explanation:
Answer: $142
Step-by-step explanation: assume 20miles per gallon.
Then 0.05 gallon per mile.
35psi gives 30/35= 0.85 times the surface on the ground, gives square 0.85^2= 0.73 times more deflection so heatproduction a cycle or at same speed. This gives more fuelconsumption.
I once determined that when driving 50mph/80kmph constant, tires use 25% of the total fuel-consumption.
Higher speed same fuelconsumption by the tires, but more bij the higher speed. But to keep it simple only 50mph.
The fuelconsumption at 30 psi 0.05 gpm, 25% by the rolling resistance is 0.0125mpg. 35psi ,0.73 x0.0125=0.0091gpm.
The windforce stays the same 75% of total is 0.0375mpg+ 0.0091= 0.0466mpg,0.0466gpm/0.05= 93% used of fuel with 35psi then at 30 psi.
So 21000mpj x 0.05gpm= 1050 gallon
21000mpjx 0.466gpm= 979gallon.
Saving 1050-979= 71 gallonx $2= $142
Rounded here and there, and other speeds give other divisions, but to show the idea how to calculate it.
Also if 25% used is right is discussable.
PLEASE HELP IMMEDIATELY!!
Answers
Answer:
B
Step-by-step explanation:
45-45-90
find hypotenuse: leg × root 2
[tex]8 \times \sqrt{2} [/tex]
Sharon is painting her house. she needs 5 gallons of brown paint for every 7 gallons of white paint. How many gallons of white paint does she need if she already bought 14 gallons of brown paint?
A. 10 gallons. B. 19.6 gallons
C. 16 gallons. D. 25 gallons
Answers
Answer:
19.6
Step-by-step explanation:
The ratio of brown paint to white paint is, 5:7 or [tex]\frac{5}{7}[/tex] so if he bought 14 gallons of white paint we need to figure out:
[tex]\frac{5}{7} =\frac{14}{x}[/tex]
which we can as it only has one unknown:
5x=14×7
5x=98
x=19.6
So the answer is 19.6
Answer:
B. 19.6 gallons
Step-by-step explanation:
5 Gallons of Brown ⇒ 7 Gallons of White
14 Gallons of Brown ⇒ x
x = 7 into 14 / 5
x = 98 / 5
x = 19.6
HOPE IT HELPS :)
Which set of angle measures can be used to construct an acute scalene triangle?
Answers
Answer:
C = 36°, 57°, 87°
Step-by-step explanation:
scalene = all angles are different.
acute = all angles are under 90°.
triangle = all angles add up to 180°.
The only option that works for this is C) 36°, 57°, 87°
5.7935 rounded to the nearest thousand
Answers
Answer:
5.794
Step-by-step explanation:
The seven after the decimal point is the tenth digit, the nine is the hundredth, and the 3 is the thousandth place. Therefore, we look at our neighbor (the number next to the thousandth place) and if its 5 or more we round up, but if its 4 or less we keep it the same.
A six pack of soda costs $3.00. What is the price per can?
PLEASEEE HELPPPPPPPPPPPPPPPP
MI PAN ZUZUZUZUZUUZU
Answers
Answer:
price per can is 0.5
Step-by-step explanation:
please help fast for my math project and its due today !!!!!!! fasttttb pleaseeee
Answers
1) Note that in the problem above, the complete table is given as:
Team Number: 1 2 3 4 5
Best Jump (ft) 20.6 21.5 20.9 19.4 20.2
2) If Best Jump is denoted as y and Team number as x then, Best Jump is the Range while Team Number is the Domain.
3) For each element of the domain, there is a corresponding element of the range. So this relation is a function.
Why are the Domain and Range Important?Domain and range are crucial characteristics that aid in the definition of a relationship. The domain is a collection of input values.
The independent variable represents these values, which are graphed on the axis of a coordinate graph. A function's range is its collection of output values.
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A rectangular playground area is 3,162 meters. The width is 51 meters. Find the length?
Answers
Work Shown:
area = length*width
length = area/width
length = 3162/51
length = 62 meters
PLS HELP WILL GIVE BRAINLIEST
If a sprinkler waters 1 over 15 of a lawn in 1 over 3 hour, how much time will it take to water the entire lawn?
5 hours
15 hours
18 hours
45 hours
Answers
Answer:
5 hours
Step-by-step explanation:1 over 5 of an hour is 20 minutes. 20 minutes = 1 over 15 of lawn.
20 x 15 = 300
300 divided by 60 = 5 (hours)
Determine whether the scenario involves independent or dependent events.
A bag contains six red marbles and five blue marbles. You randomly pick a marble and then pick a second marble without returning the marbles to the bag. The first marble is red and the second marble is blue
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I believe this is correct, sorry if it’s not
find the surface area of the prism
Answers
Answer:
62ft²
Step-by-step explanation:
Hi there!
Surface area is calculated by this formula:
2(length*width)+2(width*height)+2(length*height)
*note: we multiply each area by 2, as the prisim has 6 faces, or 2 of each face
we're given a length of 5 ft, a width of 2 ft, and a height of 3ft
now let's calculate the surface area
to find the area of the first two faces:
2(length*width)
2(5*2)
2(10)
20 ft²
now to find the area of the second two faces:
2(width*height)
2(2*3)
2(6)
12 ft²
finally, find the area of the last two faces:
2(length*height)
2(3*5)
2(15)
30 ft²
now add up all the values
SA=20+12+30=62 ft²
your answer is 62ft²
Hope this helps!
is the pie sign a integer, rational number or irrational number?
Answers
Answer:
pi is considered to be irrational because it is a non-terminating, non-repeating decimal
Step-by-step explanation: