Answers
the mean value theorem states, that the function for such value to exist, must be continuous and differentiable, graph wise, that means the graph of the function between those bounds, must be "a smooth line", without any abrupt jumps or changes like a spike or a sharp sink.
so, rewording the material some, the piece-wise function has 3 subfunctions, and within the interval of [0, 2], those 3 must meet seamlessly at the junction points, namely 0 and 1, so the "4" part must seamlessly blend in with the ax + b part at 0, and the ax + b part must meet seamlessly with the x²+5x+c.
that said, we could simply freely pick a "c" value for the third subfunction, and from there, make the second subfunction to meet it at that point, so let's do so.
let's say, we pick c = 3, so the 3rd subfunction is x² + 5x + 3.
now, what's f(x) for that parabola at x = 1?, well, is 1²+5(1)+3, or 9, so it lands on the ( 1, 9 ) point then.
now, the "4" subfunction is just a horizontal line, well, at x = 0, is really just a dot, so, ax + b must meet that dot and also must meet the parabola at (1, 9), given that c = 3.
so, now, what's the equation of a line that passes through (0, 4) and (1, 9)?
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ 4}})\quad % (c,d) &({{ 1}}\quad ,&{{ 9}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{9-4}{1-0}\implies 5 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=5(x-0)\implies \boxed{y=5x+4}[/tex]
so, that'd be the 2nd subfunction, meeting "4" and x² + 5x + 3, and surely you can see what "a" and "b" are.
check the picture below.
and since they meet seamlessly, they meet the mean value theorem at [0, 2].
Related Questions
which function has no horizontal asymptote?
A) f(x)=2x-1/3x^2,
B) f(x)=x-1/3x,
C) f(x)=2x^2/3x-1
D)f(x)=3x^2/x^2-1
Answers
In other words, where the numerator has a higher exponent than the denominator.
Answer:
C) exponent on top is 2, exponent on bottom is 1
Function has no horizontal asymptote is C) f(x)=2x^2/3x-1
Further explanationThe rational functions graphs can be recognised by the fact that they often break into two or more parts. These parts go out of the coordinate system along an imaginary straight line called an asymptote.
Vertical asymptotes can be found by solve the equation n(x) = 0, where n(x) is the function denominator. This only applies if the numerator t(x) is not zero for the same x value. The graph has a vertical asymptote with the equation x = 1.
The three rules that horizontal asymptotes are based on the degree of the numerator, n, and the degree of the denominator, m.
If n < m, the horizontal asymptote is y = 0. If n = m, the horizontal asymptote is y = a/b. If n > m, there is no horizontal asymptote.A rational function has no horizontal asymptote when the degree of the numerator is greater than the denominator.
A) f(x)=2x-1/3x^2, the degree of the numerator is lower than the denominator.B) f(x)=x-1/3x, the degree of the numerator is lower than the denominator.C) f(x)=2x^2/3x-1 , the degree of the numerator is greater than the denominator.D)f(x)=3x^2/x^2-1 , the degree of the numerator is lower than the denominator.Learn moreLearn more about asymptote https://brainly.com/question/2914025Learn more about function https://brainly.com/question/12397187Learn more about horizontal asymptote https://brainly.com/question/4221615Answer details
Grade: 9
Subject: mathematics
Chapter: Graphs of rational functions
Keywords: asymptote, function, horizontal asymptote, horizontal, mathematics
Use the graph to find the x-intercept for the equation y + 2 = 2(x + 3). The x-intercept is
Answers
Answer:
(-2,0)
Step-by-step explanation:
I just did the assignment
Who should fill out the W-2 form?
a.
the taxpayer’s employer
b.
the taxpayer
c.
a qualified tax professional
d.
the IRS
Answers
The correct answer is A. The taxpayer's employer
Explanation:
In the U.S. the W-2 form is a special format that should be filled by employers to report payments to employees and the taxes derived from these. This form is part of the IRS or the Internal Revenue System and therefore it is mandatory for taxpayer's employers to fill the form every year. Additionally, employers need to fill the form by each worker and then send it to them. According to this, the person that should fill out the W-2 form is the taxpayer's employer.
The rectangular box shown in the figure has dimensions 8" × 7" × 4" (a = 8, b = 7, c = 4). Approximate the angle θ formed by a diagonal of the base and a diagonal of the 7" × 4" side. (Round your answer to two decimal places.)
Answers
Answer:
Rectangle
four
Length and width
Step-by-step explanation:
Write a real-life situation that can be modeled by the expression 1 1/3 x 2.
1 1/3 is a mixed number
Answers
I came up with this...good luck
You have 2 2/3 cakes. You tend to share 2 of them. How many will your friend get?
Hope this helps!
which of the following three dimensional objects has a rotational symmetry about a line
Answers
Answer choices:
A. a car
B. a set of rectangular stairs
C. a rolling pin
D. a stapler
The answer is C. a rolling pin
Maude sees 3 more foxes than Henry. Henry see 4 foxes. How many foxes did Maude see?
Answers
Maude sees 3 more foxes than Henry and Henry sees 4 foxes then Maude
sees 7 foxes.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Henry sees 4 foxes and Maude sees 3 more foxes than Henry.
∴ Maude sees (4 + 3) = 7 foxes.
Some more insights:
Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
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Mark bought a double oven electric range for 1350 he made a 15% down payment and finance the balance paying 150 a month for 10 months how much did mark pay for all the range
Answers
I believe it's 1702.5, but I'm not the best at math.
15% of 1350 is 202.5.
Then 150 dollars is paid every 10 months, so 150*10 is 1500. Then you just add the two together!
Good luck!
Down payment+total payments
Down payment
1,350×0.15=202.5
Total payments
150×10 months=1,500
So Amount paid is
202.5+1,500=1,702.5...answer
Hope it helps!
Find the state that has the largest number for the execution variable in 1993. (the variable exec is total executions in 1991, 1992, and 1993.) how much bigger is this value than the next highest value?
Answers
5×143=use distributive property
Answers
+
5x40 = 200
+
5x3 = 15
———————
715
=5*(100+40+3)
=5(100)+5(40)+5(3)
=500+200+15
=715
Hope this helps!
Your fortune is "Be careful of who you choose to be with."
Gregg subtracted some number x from 47, then multiplied the result by two, subtracted 15 and got 45. What was Gregg's number?
(PLEASE ANSWER WITH WORK, THANKS)
Answers
45 + 15= 60. 60/2= 30. 30 + x = 47.
So, x= 47-30.
x= 17.
A person standing close to the edge on top of a 56-foot building throws a ball vertically upward. The quadratic function h ( t ) = − 16 t 2 + 104 t + 56 h(t)=-16t2+104t+56 models the ball's height about the ground, h ( t ) h(t), in feet, t t seconds after it was thrown. a) What is the maximum height of the ball?
Answers
The maximum height of the ball at a time of 3.25 seconds will be 275 feet.
What are the maxima and minima of a function?For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.
The maximum and minimum value of the function is at f'(x) = 0.
An individual standing near the edge on top of a 56-foot building tosses a ball upward vertically.
The quadratic function is given below.
h(t) = - 16t² + 104t + 56
The value of 't' at which the ball is at its maximum height. Then we have
h'(t) = 0
-32t + 104 = 0
32t = 104
t = 3.25 seconds
Then the maximum height of the ball is given as,
h(t) = - 16(3.25)² + 104(3.25) + 56
h(t) = -16 x 10.5625 + 338 + 56
h(t) = - 169 + 444
h(t) = 275 feet
The maximum height of the ball at a time of 3.25 seconds will be 275 feet.
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Hypatia has read 13 chapters of a 22 chapter book what percent has she read
Answers
Answer:
59.09%
Step-by-step explanation:
We can calculate it with a direct rule of 3. If 22 chapters are the 100% of the book, what percent is 13 chapters?
[tex]\text{22 chapters} -\!\!\!-\!\!\!- 100\%\\ \\\text{13 chapters} -\!\!\!-\!\!\!- x\%[/tex]
We use the formula of the direct rule of 3:
[tex]x = \frac {13* 100}{22} \\ \\ x = \frac {1300}{22}[/tex]
x = 59.09
She has read the 59.09% of the book.
Find the value of the following expression:
(3^8 ⋅ 2^-5 ⋅ 9^0)^-2 ⋅ (2^ -2 / 3^3) ^4 ⋅ 3^28
Write your answer in simplified form. Show all of the steps.
Answers
(3^8 ⋅ 2^-5 ⋅ 9^0)^-2 ⋅ (2^ -2 / 3^3) ^4 ⋅ 3^28 =
(6561 * 0.03125 * 1)^2 * (0.00925)^4 * 22876792454961 =
42037.81348 * 0.00000000732094 * 22876792454961 =
7040477235.56798349
round answer as needed
the ratio of number of miles walked by fernando in a week to the number walked by julia in a week is 4 to 3. julia waled 15 miles. how many miles did fernando walked in a week?
Answers
15*(4/3) = F
20 = F
list the partial products of 42 x 28
Answers
= 800 + 320 + 40 + 16
Answer:
The partial product of [tex]42\times 28[/tex] are 800,320,40,16 and their sum is 1176.
Step-by-step explanation:
The given expression is,
[tex]42\times 28[/tex]
In number 42 the place value of 4 is 40 and the place value of 2 is 2. In number 28 the place value of 2 is 20 and the place value of 8 is 8.
To find the partial product, we have multiply the place values of first number with the place values of second number.
Place values of 42 are 40 and 2. Place values of 28 are 20 and 8.
[tex]40\times 20=800[/tex]
[tex]40\times 8=320[/tex]
[tex]2\times 20=40[/tex]
[tex]2\times 8=16[/tex]
Therefore the partial product of [tex]42\times 28[/tex] are 800,320,40 and 16.
To find the total product, we have add all partial products.
[tex]T=800+320+40+16=1176[/tex]
The value of given expression is 1176.
Related Rates Problem: The radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week. The thickness of the rind is always one tenth of the radius. The volume of the rind is growing at the rate __?__ cubic centimeters per week at the end of the fifth week. Assume that the radius is initially zero. ...?
Answers
so, if we grab the whole volume of the watermelon, and then subtract the volume of the inner sphere of 9/10, what we're left with is 1/10 of the volume, which is the volume of the rind, recall the rind has a radius of 1/10 of the radius, so we're simply taking off 1/10 from the radius and using the 9/10 and subtracting the volume with that radius.
now, after the 5th week, the radius of the watermelon has then grown to 2*5, or 10 cm, and the rind is 1/10 of that or just 1 cm.
[tex]\bf \cfrac{4\pi \left( \frac{9r}{10} \right)^3}{3}\implies \cfrac{4\pi \cdot \frac{729r^3}{1000}}{3}\implies \cfrac{\frac{2916\pi r^3}{1000}}{3}\implies \cfrac{2916\pi r^3}{3\cdot 1000}\implies \cfrac{243\pi r^3}{250}\\\\ -------------------------------\\\\ V_{rind}=\cfrac{4\pi r^3}{3}~~-~~\cfrac{243\pi r^3}{250}\implies V_{rind}=\pi r^3\left(\cfrac{4}{3}-\cfrac{243}{250} \right)[/tex]
[tex]\bf V_{rind}=\pi r^3\left( \cfrac{271}{250}\right)\implies \boxed{V_{rind}=\cfrac{271\pi }{250}r^3} \\\\\\ \cfrac{dV_{rind}}{dt}=\cfrac{271\pi }{250}\cdot \stackrel{chain~rule}{3r^2\cdot \cfrac{dr}{dt}}\implies \cfrac{dV_{rind}}{dt}=\cfrac{813\pi r^2\cdot \frac{dr}{dt}}{250} \\\\\\ \begin{cases} \frac{dr}{dt}=2\\\\ r=10 \end{cases}\implies \cfrac{dV_{rind}}{dt}=\cfrac{813\pi 10^2\cdot 2}{250}\implies \cfrac{dV_{rind}}{dt}\approx 3043.29[/tex]
A restaurant uses 4 pounds of potatoes for a party of 12 people. If they are cooking potatoes for a party of 60 people, what should they do?
Answers
5·4=20
They should use 20 pounds of potatoes
Hope this helps
Two-fifths of the fish in Gary's fish tank are guppies.One-fourth of the guppies are red.What fraction of the fish in Gary's tank are red guppies?Show your work.
Answers
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
Given: Two-fifths of the fish in Gary's fish tank are guppies.One-fourth of the guppies are red.
To Find: What fraction of the fish in Gary's tank are red guppies.
Solution:
Let total number of fish in tank be [tex]=\text{x}[/tex]
Number of guppies in tank are [tex]=\frac{2}{5}\text{of total fish}[/tex]
Number of guppies in tank are [tex]=\frac{2}{5}\text{x}[/tex]
Number of red guppies in tank are [tex]=\frac{1}{4}\text{of total guppies}[/tex]
[tex]\frac{1}{4}\times\frac{2}{5}\text{x}[/tex]
[tex]\frac{1}{10}\text{x}[/tex]
Now,
fraction of the fish in Gary's tank that are red guppies
[tex]=\frac{\text{red guppies}}{\text{total fish in Gary's tank}}[/tex]
[tex]\frac{\frac{1}{10}\text{x}}{\text{x}}[/tex]
[tex]\frac{1}{10}[/tex]
Hence [tex]\frac{1}{10}[/tex] of total fish are red guppies.
A bus timetable states that the next bus leaving for holmfirth is at 16:40 what time is this in 12 hours time
Answers
i hope this helps and have a wonderful day!!!
A negative correlation between two variables x and y usually yields a negative p-value for r.
a. True
b. False
Answers
Step by step ways to solve 3.4 x 4.72
Answers
Final answer:
To solve 3.4 x 4.72, multiply the numbers as if they are whole, then place the decimal in the product so that it has the same number of decimal places as the sum of the decimal places in the factors, resulting in 16.048.
Explanation:
To solve the multiplication of 3.4 x 4.72, follow these steps:
Write down the numbers to be multiplied, one below the other, aligning the decimal points: 3.4x 4.72
Multiply as if you are dealing with whole numbers, ignoring the decimal points for now. Start by multiplying the digit in the ones place of the bottom number by each digit in the top number, then move to the next digit to the left. 342
x 472
-------
1368 (3.4 x 2)
17100 (3.4 x 70, shift one place to the left)
136800 (3.4 x 400, shift two places to the left)
-------
160704
Add up the results of each multiplication step.Now count the total number of decimal places in both of the original numbers (1 in 3.4 and 2 in 4.72, so 3 in total).Place the decimal point in the answer so that it has the same number of decimal places as the sum from step 4. Since you have 3 decimal places in total, you'll count three places from the right of the answer.160.704
The final result of multiplying 3.4 by 4.72 is 16.048.
Round each addend to the nearest ten thousand,and then find the estimated sum.?
337,961 + 482,746
_+_=_
Answers
To find the estimated sum, round each addend to the nearest ten thousand by looking at the digit in the ten thousand places. Then add the rounded numbers together.
Explanation:To round each addend to the nearest ten thousand, look at the digit in the ten thousand places. If the digit is 5 or greater, round up by increasing the number in the ten thousand place by 1. If the digit is less than 5, round down by keeping the number in the ten thousand places the same. For 337,961, the digit in the ten thousand places is 9, so it rounds up to 340,000. For 482,746, the digit in the ten thousand places is 7, so it rounds down to 480,000. Now, you can find the estimated sum by adding the rounded numbers, which would be 340,000 + 480,000 = 820,000.
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The cartesian coordinates of a point are given. (a) (2, −2) (i) find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.
Answers
In a standard deck of cards, the jack, queen, and king are "face cards." you draw a card from a standard deck. your friend peeks and lets you know that your card is a face card. what is the probability that it is not a king given that it is a face card? leave your answer as a fraction
Answers
If the Ace is NOT a face card, then the answer will be 12/52 or 3/13 simplified.
Answer: [tex]\dfrac{2}{3}[/tex]
Step-by-step explanation:
Total number of cards in a deck = 52
Number of face cards = 12 ( 4 King + 8 others)
The probability that a card is face card P(Face card)= [tex]\dfrac{\text{Number of face cards }}{\text{Total cards}}[/tex]
[tex]\\\\=\dfrac{12}{52}=\dfrac{3}{13}[/tex]
Number of cards are not king = 8
The probability that a card is face card are not King :
P( Face card and not king )= [tex]\dfrac{\text{Number of face cards are not King}}{\text{Total cards}}[/tex]
[tex]\\\\=\dfrac{8}{52}=\dfrac{2}{13}[/tex]
Using conditional probability formula ,
[tex]\text{P(Not king}|\text{ Face card})=\dfrac{\text{P( Face card and not king )}}{\text{ P(Face card)}}[/tex]
[tex]=\dfrac{\dfrac{2}{13}}{\dfrac{3}{13}}=\dfrac{2}{3}[/tex]
Hence, the probability that it is not a king given that it is a face card [tex]=\dfrac{2}{3}[/tex]
Brian drove 120 miles at a speed of 60 mph. He drove the same distance back home at an average speed of 40 mph. Brian adds the speeds and divides by two to come up with an average speed of 50 mph what is wrong with his reasoning? Find his average speed
Answers
the total distance in this case is 120+120=240
the total hours is 120/60 + 120/40 =2+3=5
so 240/5=48
48 miles per hour
The point P(8, 6) is on the terminal side of θ. Evaluate sin θ.
Answers
Which word best describes the range of a function?
A. input
B. output
C. independent
D. relation
Answers
Answer:
It is actually B output
Step-by-step explanation:
A pine tree grows at a rate of 1.5 feet per year. James plants a 2-foot tall pine tree in his yard. How many years will it take for the tree to be at least 14 feet tall?
Answers
Let hh be the set of all points in the second quadrant in the plane v=ℝ2v=r2. that is, h={(x,y)∣x≤0,y≥0}h={(x,y)∣x≤0,y≥0}. is hh a subspace of the vector space vv?
Answers
The set hh, which represents all points in the second quadrant of the Cartesian plane, is not a subspace of the vector space vv, because it does not contain the zero vector and is not closed under scalar multiplication.
Explanation:In vector space theory, a subset of a vector space forms a subspace if it satisfies three key properties: it contains the zero vector of the larger vector space, it is closed under vector addition, and it is closed under scalar multiplication.
In our case, the set hh represents all points in the second quadrant of the Cartesian plane, that is, hh={(x, y)∣x≤0, y≥0}. Since the zero vector is not included in this set of vectors, it does not meet the first requirement. Therefore, hh is not a subspace of the vector space vv.
To illustrate, let's consider the vectors A=(0, 1) and B=(-1, 0) that belong to set hh. The sum of these vectors is A + B = (0 - 1, 1 + 0) = (-1, 1), which also belongs to set hh. However, if we multiply vector A by the scalar -1, the result is -A = (0, -1), a vector that does not belong to set hh. Hence, the set hh is not closed under scalar multiplication.
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