Let f be the function defined by 1 2 1 1 4 3 2 f x( ) = x − x + x − x 4 3 2 2 . For how many values of x in the open interval (0, 1.565) is the instantaneous rate of change of f equal to the average rate of change of f on the closed interval [0, 1.565] ?
Answers
There are three values of x where the instantaneous rate of change of f(x) are equal in the open and closed intervals
How to determine the number of x values?The function is given as:
[tex]f(x) = \frac 14x^4 - \frac 23x^3 + \frac 12x^2 - \frac 12x[/tex]
Calculate f(0)
[tex]f(0) = \frac 14 * 0^4 - \frac 23 * 0^3 + \frac 12 *0^2 - \frac 12 * 0[/tex]
[tex]f(0) = 0[/tex]
Calculate f(1.565)
[tex]f(1.565) = \frac 14 * 1.565^4 - \frac 23 * 1.565^3 + \frac 12 *1.565^2 - \frac 12 * 1.565[/tex]
[tex]f(1.565) = -0.613[/tex]
The average rate of change is then calculated using:
[tex]m = \frac{f(1.565) - f(0)}{1.565 - 0}[/tex]
This gives
[tex]m = \frac{-0.613 - 0}{1.565 - 0}[/tex]
[tex]m = -0.392[/tex]
Differentiate the function f(x)
[tex]f'(x) = x^3 - 2x^2 + x - \frac 12[/tex]
Set f'(x) to [tex]m = -0.392[/tex]
[tex]x^3 - 2x^2 + x - \frac 12 = -0.392[/tex]
From the graph of the above equation (see attachment), we have three values of x at:
x = 0.1492, x = 0.5614 and x = 1.2894
Hence, there are three values of x in the open interval (0,1.565)
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Related Questions
based on the diagram given, find the value of x and y
Answers
Answer:
x = 6 , y = 2
Step-by-step explanation:
81x + 10 = 5y + 486 ............ (1)
9x + 40 = 20y + 54 ............ (2)
(1) × 4 - (2)
315x = 1890
x = 6 -------> (2)
9(6) + 40 = 20y + 54
20y = 94 - 54
y = 2
Identify the solution to the system of equations
{x=-2y-6 -3x-7y=18
Answers
Answer:
(- 6, 0 )
Step-by-step explanation:
x = -2y - 6 → (1)
- 3x - 7y = 18 → (2)
substitute x = - 2y - 6 into (2)
- 3(- 2y - 6) - 7y = 18 ← distribute parenthesis and simplify left side
6y + 18 - 7y = 18
- y + 18 = 18 ( subtract 18 from both sides )
- y = 0 , then
y = 0
substitute y = 0 into (1)
x = - 2(0) - 6 = 0 - 6 = - 6
solution is (- 6, 0 )
Answer:
(x, y) = (-6, 0)
Step-by-step explanation:
A system of equations is easily solved using a graphing calculator. The attached shows the solution to be ...
(x, y) = (-6, 0)
__
The first equation gives a convenient expression for substituting for x in the second equation:
-3(-2y -6) -7y = 18
18 -y = 18 . . . . . . . . simplify
y = 0 . . . . . . . . add y-18
x = -2(0) -6 = -6
The solution by substitution is (x, y) = (-6, 0).
1.5 = 0.25 + g
solve the equation and find the value of the variable
Answers
Answer:
its easy it should be 1.25 or well that the answer I got
The graph of this system of equations is which of the following?
2x + y = 6
6x + 3y = 18
Overlapping lines
Parallel lines
Intersecting lines
A curve intersecting with a line
Answers
Answer:
They are the same line. It means that they are overlapping line.
Answer:
Overlapping
Step-by-step explanation:
Divide every term of the second equation, it would be 2x + y = 6, which is the same as the first equation.
Find c.
Write your answer in simplest radical form.
Answers
Answer:
c = 3.46
Step-by-step explanation:
use tangent to find c
2 tan 60 = c
firstly label the sides
let me know if you need further explanation on how I got my answer
Find the perimeter of the composite figure using pi
Answers
Answer:
(3 +1.5π) ft ≈ 7.71 ft
Step-by-step explanation:
We see a semicircle, not a "composite figure." The perimeter of the semicircle is the sum of the length of the arc and the length of the straight edge:
P = (1/2)πd +d . . . where d is the diameter and πd is the full circumference
P = d(1 +π/2)
P ≈ (3 ft)(1 +1.57) = 7.71 ft . . . . . using 3.14 for π
The perimeter of the figure is about 7.71 feet.
__
In terms of pi, the perimeter is ...
P = (3 +1.5π) ft
PLS HELP ME ILL GIVE YOU BRAINIEST
Answers
given data 4,x,9,5,2,7 find x if the mode is 4
Answers
Answer:
x = 4
Step-by-step explanation:
This is because the definition of mode is the number that appears the most or is the popular of the numbers in the data set.
This could be any number since each number is listed once, but the requirements/directions say the mode is 4 so you need another 4 in order to have a mode of 4.
Peter is saving to buy a new skateboard. He deposits the same amount each week into his savings account. How much money does he save each week?
Week Money in Savings Account
0 $12.00
1 $17.75
2 $23.50
3 $29.25
Answers
PLEASE SOMEONE HELP!!
Answers
Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
Answers
3^2+b^2=5^2
9+b^2=25
b^2=16
b=Sqrt[16]
b=4
Length of the third side = 4
PLEASE HELP ME????
THank you ! :)
Answers
you can replace the m with 14 to get an equation of: 52+14=66
How do u solve this equation? I’m struggling with it.
2a+3c=61
3a+5c=96
Answers
Answer:
a=17
c=9
Step-by-step explanation:
balls
Answer:
c=9 and a=17
Step-by-step explanation:
1. 2a+3c=61
2. 3a+5c=96
the LCM between 2 and 3 is 6 so
equation 1 *3
3.6a+9c+183
equation 2*2
4. 6a+10c=192
equation 3 - equation 4
5. -c=-9
c=9
substitute c into equation 1 or 2 to find a
3a+5(9)=96
3a+45=96
3a=51
a=17
what would you do to solve the system: y=x+3 and y=x^2+x-6
Answers
Is 336 − –5,083 positive or negative?
Answers
Answer:
positive
Step-by-step explanation:
if you subtract a negative number, it’s the same as adding a positive number. If you add 2 positive numbers, you get a positive number, so the expression is positive.
(1+sint)/(cost)-(cost)/(1-sint)
Answers
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)}{1-\sin(t)}[/tex]
Multiply through the second term by [tex]1+\sin(t)[/tex] :
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)}{1-\sin(t)}\cdot\dfrac{1+\sin(t)}{1+\sin(t)}[/tex]
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)(1+\sin(t))}{1-\sin^2(t)}[/tex]
Recall that [tex]\cos^2(x)+\sin^2(x)=1[/tex] for all x :
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{\cos(t)(1+\sin(t))}{\cos^2(t)}[/tex]
If [tex]\cos(t)\neq0[/tex], we can cancel a factor of it in the second fraction.
[tex]\dfrac{1+\sin(t)}{\cos(t)} - \dfrac{1+\sin(t)}{\cos(t)}[/tex]
and this simplifies to
[tex]\dfrac{(1+\sin(t))-(1+\sin(t))}{\cos(t)} = \boxed{0}[/tex]
Consider the number 9,953.
Is this number divisible by 2, 3, 4, 5, 9, or 10? Provide justification for
each number without using a calculator.
Hint: If a number is not divisible by 2, then what other numbers is it
also not divisible by?
Write your answer in complete sentences.
Answers
Answer:
No for all of them
Step-by-step explanation:
2 --> not even
3 --> of the sum of the numbers are not divisible by three
4 --> the last two digits are not equal to a multiple of four
5 --> the last digit is not ending with 0 or 5
9 --> the sum of the digits is not equal to a multiple of nine
10 --> the last number is not zero
You want to save for retirement. assuming you are now 25 years old and you want to retire at age 50, you have 25 years to watch your investment grow. you decide to invest in the stock market, which has earned about 13% per year over the past 80 years and is expected to continue at this rate. you decide to invest $1,000 today. required: how much do you expect to have in 25 years?
Answers
Answer:
4250
Step-by-step explanation:
0.13 = 13%
1000×0.13=130
130×25= 3250 + 1000 = 4250
What I did:
You have to turn the percent to a decimal first
Then multiply the decimal by the first investment amount (1000)
then multiply that by the years that you have before retirement
You add that amount plus the 1000 you have started with
Determine the equation of the line shown in the graph:
10
-8 -6 -4 -2.
-
I
y = -1
y = 0
Ox=-1
X=0
Answers
Answer:
X=-1
Step-by-step explanation:
As you can see the line is not intercepting at y also
Please help me on this equation
3 3/4 ÷ 5/7 =
Answers
Answer:
5 1/4
Step-by-step explanation:
3 3/4 / ( 5/7) =
15/4 / ( 5/7) =
15/4 * 7/5 =
(15*7) / (4*5 )
105 / 20 = 5 1/4
Answer:
5.25
Step-by-step explanation:
Turn mixed number into a improper fraction.
Divide fraction by 20.
It doesn’t matter if 5 1/4, or 21/4 or 5.25., they all equal the same.
The point B is at the centre of the circle. The points P and Q are on the circumference of the circle. Calculate the area of the shaded sector. Take it to be 3.142 in your working. Give your final answer to 1 decimal place.
Answers
Answer: 24.7 square cm
Step-by-step explanation:
דיי יוטורסם
$9000 is invested at 8% compounded quarterly. In how many years will the account have grown to $14,500?
Round your answer to the nearest tenth of a year
Answers
Can someone help???????
Answers
Answer:
8x-3y-24
Step-by-step explanation:
[tex] \frac{3}{4} y = 2x - 6 \\ \\ \\ 3y = 4(2x - 6) \\ \\ 3y = 8x - 24 \\ \\ 8x - 3y - 24 = 0 \\ \\ \\ is \: the \: required \: equation[/tex]
The length of the escalator is 36 ft and the
vertical height it rises is 9 ft. what is the angle
of elevation?
a. 90
b. 75. 52
c. 14. 48
d. 14. 04
Answers
Answer:
sin θ = 9 / 36 = 1/4
θ = 14.48 deg (ans C)
Find the volume of the prism or compound shape.
Answers
The volume of the compound shape, that is the object formed by two hemispheres and a right cylinder is 66π in³.
How to determine the volume of the compound shape
The volume is the space occupied by an object. The volume of the compound shape equals the sum of the individual volumes, that is, of each part, which are represented by two hemispheres and a right cylinder.
Now we proceed to determine the volume of the compound shape (V), in cubic inches, by apply the following calculation:
V = (4/3) · π · (3 in)³ + π · (3 in)² · (10 in)
V = 66π in³
The volume of the compound shape, that is the object formed by two hemispheres and a right cylinder is 66π in³. [tex]\blacksquare[/tex]
To learn more on volumes, we kindly invite to check this verified question: https://brainly.com/question/13338592
Which temperature during the week is farther from 0? Explain how you decided this using absolute value
Answers
Answer:
The farthest temperature from zero during the week is 5 °F because it's absolute value, 5, is the highest out of all the other numbers.
Step-by-step explanation:
If f(x)=3x^6+4x^3-4, then what is the remainder when f(x) is divided by x+1?
Answers
Answer:
-5
f(-1) would be the remainder
18
p.7 Central Angles and Inscribed Angles
#4 What is the measure, in degrees, of arc JKI ?
4) MJKI
80°
K
mJKI =
degrees
Answers
Answer:
280°
Step-by-step explanation:
There are 360° in a circle. you are given an arc that is 80°.
To find the arc JKI, subtract 80 from 360.
360 - 80 = 280°
Bella is typing a 400 word essay. She types 50 words in 2 minutes.
Enter an equation in the form of y=mx+b, that represents the number of words (y) remaining to type after x minutes.
Answers
Answer:
[tex]y=25x[/tex]
Step-by-step explanation:
If Bella types 50 words in 2 minutes, we can divide 50 by 2 to see how many words she types in 1 minute.
[tex]50/2=25[/tex]
So, Bella types 25 words per minute. When she first began writing her essay, she did not have words to start with, so there is no y-intercept ([tex]b[/tex]).
Therefore, the equation that represents this relation is [tex]y=25x[/tex].
Solving the equation
We can divide 400 by 25 to determine how many minutes it would take her to finish her essay.
[tex]\frac{400}{25} =16[/tex]
Therefore, it will take her 16 minutes to complete her essay.
#LearnWithBrainly
Roger has a rope that is 3 feet long.He needs to cut it into 12 equal length pieces.How many feet loń should each piece of the rope be?
Answers
Answer:
0.25
Step-by-step explanation:
3/12 is 0.25
3 divided by 12 when simplified or reduced
The fraction 3/12 is equal to the exact decimal number.
