Answer:
The conclusion of the Mean Value Theorem says that there is a number
c
in the interval
(
1
,
3
)
such that:
f
'
(
c
)
=
f
(
3
)
−
f
(
1
)
3
−
1
To find (or try to find)
c
, set up this equation and solve for
c
.
If there's more than one
c
make sure you get the one (or more) in the interval
(
1
,
3
)
.
For
f
(
x
)
−
−
2
x
2
−
x
+
2
, we have
f
(
1
)
=
−
1
, and
f
(
3
)
=
−
18
−
3
+
2
=
−
19
Also,
f
'
(
x
)
=
−
4
x
−
1
.
So the
c
we're looking for satisfies:
f
'
(
c
)
=
−
4
c
−
1
=
f
(
3
)
−
f
(
1
)
3
−
1
=
−
19
−
−
1
3
−
1
=
−
18
2
=
−
9
So we need
−
4
c
−
1
=
−
9
. And
c
=
2
.
Note:
I hope you've been told that actually finding the value of
c
is not a part of the Mean Value Theorem.
The additional question"find the value of
c
" is intended as a review of your ability to solve equations. For most functions, you will not be able to find the
c
that the MVT guarantees us is there..
Answer:
x = -1
Step-by-step explanation:
Simplify by starting in the innermost parentheses and moving outwards:
[tex]1 + 3(1 + 3(1 + 3(1+x)))=13\\1 + 3(1+3(1+3 + 3x)) = 13\\1 + 3(1 +3(3x + 4)) = 13\\1 + 3(1 + 9x + 12)) = 13\\1 + 3(9x + 13) = 13\\1 + 27x + 39 = 13\\27x + 40 = 13\\27x = -27\\x = -1[/tex]
Write the following equation in standard form and show your work : x^2+y^2-22y+96=0
Answer:
[tex]x^2 + (y-11)^2 = 5[/tex]
Step-by-step explanation:
Completing the square gives us that
[tex]x^2+y^2-22y+96=0\\x^2 + (y-11)^2 - 11^2 + 96 = 0\\x^2 + (y-11)^2 = 121 - 96\\x^2 + (y-11)^2 = 25\\x^2 + (y-11)^2 = 5[/tex]
Which is the standard form of a circle.
Yo someone help i'm lost
Answer:
convert the task into ratios
(1) if $24 = 4 walks
how many $ for a walk
= (24/4) $/walk
= $6 per walk
•the first one is correct
•the second is wrong, cause it interprete $12/3 walks, which is rationalized to $3 per walk
•the third one is correct, cause it can also be rationalized ($30/5walks) to $6 per walk.
also, rationalizing this would equate to 3 miles per hour (6miles/2hrs)
• one is wrong cause it's 4 miles per hour
•two is correct, it's saying 3 miles per hour (12/4)
• third, likewise is correct 3 miles per hour (9/3) miles/hrs
Andy works at a grocery store. The manager of the store would like Andy to set up a display of apples. Part of the display will include bags of apples. If there are 39 pounds of apples in the back of the store, how many bags of apples can Andy make for the display?
Given that ABCD is a rhombus, what is the value of x?
B
с
(Ax-25)
O A. 29
O B. 23
O C. 46
OD. 38
O E. 45
F. Cannot be determined
Answer:
D
Step-by-step explanation:
i did the test
Answer:
I think it is B. 23
Step-by-step explanation:
i need help on this im strugling
Answer:
D. (2, 3, 4)
Step-by-step explanation:
Substitute the answers into the equation to see if its true. If it is true, then it works.
D is the only answer where it is true.
9 subtracted from the product of 2 and b is less than or equal to -21*
b = 3
b = -6
b<=5
Answer:
I'm not 100% sure what you asking but if I read it it is more then -21 because it equals 8
What are the domain and the range of this function? f(x) = log(x + 3) - 2
A. domain: (-3, ∞); range: (∞, 2)
B. domain: (3, ∞); range: (∞, 2)
C. domain: (3, ∞); range: (∞, ∞)
D. domain: (-3, ∞); range: (∞, ∞)
Domain: (3,∞) {x∣x>3} and Range: (−∞,∞) {y∣y∈R}
What are domain and the range of a function?The domain of a function includes all possible x values of a function, and the range includes all possible y values of a function.
The domain and the range of function f(x) = log(x + 3) - 2
Domain: (3,∞) {x∣x>3} since log is undefined for 0 or negative values
Range: (−∞,∞) {y∣y∈R}
Learn more about domain and the range of function here:
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Evaluate the following if a=-3, b=8, and c=-4. 202 + 5b
Answer:
242
Step-by-step explanation:
202+ 40= 242
if my answer helps please mark as brainliest.
Lauren has a purse full of dimes and quarters. She has 25 less dimes than quarters. If she has a total of $10.45, which system of equations would she write to find the number of dimes, d and quarters, q?
Answer:
D(0.10) + Q(0.25) = 10.45
Q = D + 25 (or Q - D = 25)
Step-by-step explanation:
D = number of dimes
Q = number of quarters
D(0.10) + Q(0.25) = 10.45
Q = D - 25 (or D - Q = 25)
We multiply the number of dimes she has by $0.10, because that is the worth of each dime, and we multiply the number of quarters she has by $0.25 because that is the worth of each quarter. We then set that equal to $10.45, the overall value of her coins.
Because she has 25 less dimes than quarters, the number of dimes she has should be 25 less than the number of quarters she has. So the number of quarters she has should be equal to the number of dimes she has plus 25.
what is |8|
-16
–8
8
16
Answer:
8
Step-by-step explanation:
Anything in an absolute value is positive.
This graph shows the value of Jessica's vehicle at different years after she purchased it.
Which answer is the best estimate for the average rate of change between year 0 and year 3
A. -$6300/year
B. -16000/year
C. -$5300/years
D. -$4000/year
Answer:
B
it goes down by $16,000 in that time frame
B2. Write any four alchemies of nature mentioned in the passage:
(iv)
PLEASE HELP I WILL GIVE BRAINLEST!!!
Answer:
option B, 13 to the 3rd power
Step-by-step explanation:
Use the figure 25m circle find the circumference. Round your answer to the nearest hundredth use 3.14 for *pi sign*
Please help me with this question!!
Scott is getting balloons for his uncle's birthday party. He wants each balloon string to be 6 feet long. At the party store, string is sold by the yard. If Scott wants to get 59 balloons, how many yards of string will he need?
1 foot =
1
3
yard
help if you can please :)
12 people fit comfortably in a 5 feet by 5 feet area. Use this value to estimate the size of a crowd that is 25 feet deep on both sides of the street along a 3-mile section of a parade route. (Hint: 1 mile = 5,280 ft)
Answer:
380,160 people
Step-by-step explanation:
what is 4(1 + 9x) simplified?
Answer:
4 + 36x is your expression
Step-by-step explanation:
4 x 1 = 4
4 x 9x = 36x
so 4 + 36x is your expression because you can't add numbers with different variables or if they don't even have one.
Answer:
4 + 36x
Step-by-step explanation:
distribute
4 x 1 = 4
4 x 9x = 36x
put answer together to make new equation
4 + 36x
2+2
3x5
44+5
pels help meeeeeeee
Answer:
4 15 51
Step-by-step explanation:
if you now what I mean
What is the value of s?
units
Use the diagram below to find angle KNM.
Answer:
145 degree
Step-by-step explanation:
pls answer, show work A jacket at a clothing store is being discounted by 10%. If the jacket was originally priced at x dollars, which of the following expressions does NOT represent the final price of the jacket before sales tax is added?
A.
x – 0.10x
B.
x(1 – 0.10)
C.
x – 1.10x
D.
0.90x
Answer:
C
Step-by-step explanation:
This is the only possible correct answer because the other three all show the final price as 0.90x, which is correct since the price is the normal one minus 10 percent. C is incorrect because it suggests the normal price has a 10% tax, or extra value on it.
One number is 8 times
a first number.
A third number is 100 more than the
first. If the sum of the three numbers
IS 630 find the numbers.
Answer:
Step-by-step explanation:
one number = 46.24
first number = 5.78
third number = 578
Hi can you help me pls I would very much appreciate it!!!
Answer:87
Step-by-step explanation:
What is the value of x in the figure? Enter your answer in the box. 145 degrees and (2x + 15) degrees
Answer:
65°
Step-by-step explanation:
2x + 15° = 145° ( being vertically opposite angles)
2x = 145° - 15°
2x = 130°
x = 65°
Hope it will help :)✔
The value of x is 65 degrees.
What is Vertically opposite angle?When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.
Given:
angles are: 145 and (2x +15)
As, the pair of angle are in relation of vertically opposite angle
145 = 2x +15
2x= 130
x= 130/2
x= 65 degree.
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PLEASE HELP ME ASAP I WILL GIVE YOU BRAINLEST. PLEASE PLEASE I BEG OF YOU
Answer:
Hiii, I really did try my best, hopefully this helps :)
Step-by-step explanation:
1st: 37.5 units
2nd: 34.5 units
3rd: 24 + 9.125 π units
4th: 42 units
5th: 49.5 units
14 apartments on 2 floors =
apartments on 1 fioor
Answer:
7
Step-by-step explanation: You would divide 14 by 2 which then equals(=) 7.
7 Apartments for each floor.
Is 18.4 rational or irrational ?
Answer:
It is Rational.
Step-by-step explanation:
Answer:
It 18.4 is rational
Step-by-step explanation:
........
A force of 192 lb is required to hold a spring stretched 3 ft beyond its natural length. How much work W is done in stretching it from its natural length to 6 inches beyond its natural length
Answer:
The work done in stretching the spring is 8 lb.ft
Step-by-step explanation:
Given;
Applied force, F = 192 lb
extension of the spring, x = 3 ft
Determine the spring constant from the applied force and extension;
[tex]k = \frac{F}{x} \\\\k = \frac{192 \ lb}{3 \ ft} \\\\k = 64 \ lb/ft[/tex]
When the spring is stretched 6 inches beyond its natural length, the work done is calculated as follows;
x = 6 inches = 0.5 ft
[tex]W = \frac{1}{2} kx^2\\\\W = \frac{1}{2} (64 \ lb/ft)(0.5 \ ft)^2\\\\W = 8 \ lb.ft[/tex]
Therefore, the work done in stretching the spring is 8 lb.ft