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] ?
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)
Read more about instantaneous rate at:
https://brainly.com/question/24592593
What is the solution for the following equation 2(y+3) squared
Answer:
2y² + 12y + 18
Step-by-step explanation:
2(y + 3)²
First use formula (a + b)² = a² + 2ab + b² to expand (y + 3)²:
(a + b)²
(y + 3)²
y² + 2*y*3 + 3²
y² + 6y + 9
Dont forget the 2:
2(y² + 6y + 9) <== distribute and multiply
2y² + 12y + 18
Hope this helps!
Which angles are corresponding angles
Answer:
second option is correct onee
Step-by-step explanation:
mark me brainliest
The entire rectangle below has an area of 36 ft2. Find the area of the shaded triangle. Be sure to include the correct unit in your answer.
2.) Mila completed a half marathon race over the weekend. The full race was
13.1 miles and she jogged the first 4/5 of the race, then walked the remaining
distance.
How many miles did she jog?
Answer:
10.48 miles.
Step-by-step explanation:
That is 4/5 * 13.1
= 10.48 miles.
How do you find the surface area of a cube if one side measures 10cm? show your solution.
Answer:
600 cm squared :)
Step-by-step explanation:
Surface area of cube: 6 x s^2
Now lets solve!!
6 x 10^2
6 x 100
600
Have an amazing day!!
Please rate and mark brainliest!!
How many solutions can be found for the equation 5x + 3(x − 1) = 10x − 2x − 3? (4 points) None
One
Two
Infinitely many
Answer:
infinitely many
Step-by-step explanation:
5x+3(x-1)=10x-2x-3
5x+3x-3=10x-2x-3
8x-3=8x-3
2/3a-1/6=1/3 what is the solution
Here is your Answer:
3/4
Which set of side lengths forms a right triangle?
A. 6,8,10
B. 2,4,6
C.1,2,3
D. 2,3,4
Answer:
A. 6,8,10
Step-by-step explanation:
For a right triangle the the values for the three sides we pick must satisfy the Pythagorean theorem:
a(2 + b(2= c(2
A. 6,8,10
6(2 + 8(2 = 10(2
36 + 64 = 100
100 = 100
Bingo!
(For example lets solve the rest)
B. 2,4,6
2(2 + 4(2 = 6(2
4 + 16 = 36
20 ≠ 36
Nope.
C. 1,2,3
1(2 + 2(2 = 3(2
2 + 4 = 9
6 ≠ 9
No again!
D. 2,3,4
2(2 + 3(2 = 4(2
4 + 9 = 16
13 ≠ 16
Not this one.
Therefore our answer is A.
what is the mean of this data set
56,87,90,42,36,77
Answer:
64.7 when rounded up to one decimal place
Step-by-step explanation:
List three solutions for the inequality x≥5 and give one example of a number that is not a solutions.
Answer:
Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number. Swapping left and right hand.JUST FOLLOW THE TEXT TO GET THE ANSWER OF THE INEQUALITY ×>5
What is the domain of the function y = √√x+6-7?
x>_-7
x>_-6
x>_6
x>_7
the domain is
[tex]x \geqslant - 6[/tex]
When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller
squares is equal to the area of the largest square. Which three squares support this statement?
5 cm
3 cm
Answer:
Top right (one what has 16cm^2 and 9cm^2)
Step-by-step explanation:
The one in the top right and even though I cannot see what the area is of the biggest square, I can tell what it should be the two smaller squares combined
Hope this helps :)
Please help me and tysm!
Answer:
200
Step-by-step explanation:
156.7
since the number before the hundred is more than 4
it becomes 200
help me pls (2x+3) (x+5)
Answer: C
Step-by-step explanation:
[tex]\left(2x+3\right)\left(x+5\right)[/tex]
[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
[tex]=2xx+2x\cdot \:5+3x+3\cdot \:5[/tex]
[tex]$$Simplify[/tex]
[tex]=2x^2+13x+15[/tex]
what is 13 x 350?
My calculator does not work
Select Statistical or Not Statistical to classify each question.
1. How many feet are in 4 yards?
2. How many siblings do you have?
3. How many weeks are in a year?
Answer:
1. Not statistical
2. Statistical
3. Not statistical
Answer:
lol cant belive he could lie like that- anyways here is half the test since you can only post 5 pictures
Step-by-step explanation:
Harvey the wonder Hamster can run 3 1/6 km in 1/4 hour. Harvey runs at a constant rate find his average speed in kilometers per hour
let's firstly convert the mixed fractio to improper fraction.
[tex]\stackrel{mixed}{3\frac{1}{6}}\implies \cfrac{3\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{19}{6}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{ccll} Km s&Hour\\ \cline{1-2} \frac{19}{6}&\frac{1}{4}\\[1em] x&1 \end{array}\implies \cfrac{~~ \frac{19}{6}~~}{x}~~ = ~~\cfrac{~~ \frac{1}{4}~~}{1}\implies \cfrac{~~ \frac{19}{6}~~}{\frac{x}{1}}=\cfrac{1}{4}\implies \cfrac{19}{6}\cdot \cfrac{1}{x}=\cfrac{1}{4} \\\\\\ \cfrac{19}{6x}=\cfrac{1}{4}\implies 76=6x\implies \cfrac{76}{6}=x\implies \cfrac{38}{3}=x\implies 12\frac{2}{3}=x[/tex]
I dont understand this to save my life, Please help !
The graph below shows the cost, in
dollars, per notebook at the school store.
Which equation represents the total cost, T, per n notebooks?
Answer:
t = 2.4n
Step-by-step explanation:
y = mx + c
t = mn + c
c = y-intercept (where the graph line crosses the cost line)
c = 0
mx/mn= gradient ( rise/run, up/across)
mn= 12/5 ( you could have picked any point in the graph )
mn= 2.4
the m is unnecessary now so we discard it
t = 2.4n + 0
Write the equation of the line tangent to
y = x^3 – 2x + 3 at x = -1.
Answer: y = x + 5
Step-by-step explanation:
Determine the equation of the circle with center (-7,7)(−7,7) containing the point (-2,-5)(−2,−5)
Circular equations are often organized in the following form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](h,k)[/tex] is where the circle is centered[tex]r[/tex] is the radiusTo find the equation of a circle given its center and a point:
Plug the center into the general equation as (h,k)Plug the given point into the general equation as (x,y)Solve for r²Plug (h,k) and r back into the original equationSolving the QuestionWe're given:
Center: (-7,7)Point: (-2,-5)Plug the center into the general equation:
[tex](x-(-7))^2+(y-7)^2=r^2\\(x+7)^2+(y-7)^2=r^2[/tex]
Plug in the given point (-2,-5) and find r²:
[tex]((-2)+7)^2+((-5)-7)^2=r^2\\(5)^2+(-12)^2=r^2\\25+144=r^2\\r^2=169[/tex]
Plug the center and radius back into the original equation:
[tex](x-h)^2+(y-k)^2=169\\(x+7)^2+(y-7)^2=169[/tex]
Answer[tex](x+7)^2+(y-7)^2=169[/tex]
What do we do to both sides of this equation to solve?
x/3 =5
Question 4 options:
Add 3 to both sides
Subtract 3 from both sides
Multiply both sides by 3
Divide both sides by 3
Answer:
Multiply both sides by 3
Step-by-step explanation:
x/3 = 5
x/3 × 3 = 5×3
x = 15
Answer:
multipy both sides by 3
Step-by-step explanation:
Is the following shape a square?, How do you know?
Answer:
C. No, because the sides aren't congruent
Step-by-step explanation:
what is 8(4 - x) = 7x + 2
Answer: x = 2
Step-by-step explanation:
8(4 - x) = 7x + 2= 8(-x + 4) = 7x + 2= -8x + 32 = 7x + 2= -8x + 32 - 32 = 7x + 2 - 32= -8x = 7x + 2 - 32 = -8x = 7x = 30= -8x - 7x = 7x + 30 - 7x= -15x = 7x - 30 - 7x= -15x = 30 -15x/-15 = -30/-15 = x = -30/-15= x = 2And thats how you get the answer!
The measure of an angle is 88 degrees. FInd the measure of its complement and the measure of its supplement.
Answer:
Step-by-step explanation:
Complementary angles add to 90 degrees, so the measure of its complement is 90-88=2 degrees.
Supplementary angles add to 180 degrees, so the measure of its supplement is 180-88=92 degrees.
find p if t=6 years , r=12% and I=$240
Answer:
the future value would be 473.72 if p is referring to future value
if p is referring to present value it is 121.59
if p is referring to payment it is 58.37
Step-by-step explanation:
you can use spreadsheets to solve this equation using =pmt/=fv/=pv
Step-by-step explanation:
[tex]s .i = \frac{prt}{100} [/tex]
[tex]240 = p \times \frac{12}{100} \times 6[/tex]
[tex]240 = \frac{18}{25} p[/tex]
[tex]240 \div \frac{18}{25} = p[/tex]
[tex]p = 333.3333[/tex]
Which expressions are equivalent to 3(6+b)-(2b + 1)?
Select two answers.
Step 1 - Use the distributive property and pick your first answer
Step 2 - Combine like terms and pick your second answer.
Answer:
18+3b-2b-1
b+17
Step-by-step explanation:
[tex]\mathrm{Using\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b[/tex]
[tex]-\left(2b+1\right)=-2b-1[/tex]
[tex]=3\left(6+b\right)-2b-1[/tex]
[tex]=18+3b-2b-1[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=3b-2b+18-1[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:18-1=17[/tex]
[tex]=3b-2b+17[/tex]
[tex]\mathrm{Add\:similar\:terms:}\:3b-2b=b[/tex]
[tex]=b+17[/tex]
[RevyBreeze]
Need some help with a math problem. The problem is: The figure is made by attaching semicircles to each side of an 11 ft-by-11-ft square. Find the area, in square feet, enclosed by the figure. Use 3.14 for pi. Round to the nearest whole number.
Three $1 bills are equal to _____ cents.
Answer: 300 cents and/or pennies
Step-by-step explanation:
