Answer:
R3 <= 0.083
Step-by-step explanation:
f(x)=xlnx,
The derivatives are as follows:
f'(x)=1+lnx,
f"(x)=1/x,
f"'(x)=-1/x²
f^(4)(x)=2/x³
Simialrly;
f(1) = 0,
f'(1) = 1,
f"(1) = 1,
f"'(1) = -1,
f^(4)(1) = 2
As such;
T1 = f(1) + f'(1)(x-1)
T1 = 0+1(x-1)
T1 = x - 1
T2 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2
T2 = 0+1(x-1)+1(x-1)^2
T2 = x-1+(x²-2x+1)/2
T2 = x²/2 - 1/2
T3 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2+f"'(1)/6(x-1)^3
T3 = 0+1(x-1)+1/2(x-1)^2-1/6(x-1)^3
T3 = 1/6 (-x^3 + 6 x^2 - 3 x - 2)
Thus, T1(2) = 2 - 1
T1(2) = 1
T2 (2) = 2²/2 - 1/2
T2 (2) = 3/2
T2 (2) = 1.5
T3(2) = 1/6 (-2^3 + 6 *2^2 - 3 *2 - 2)
T3(2) = 4/3
T3(2) = 1.333
Since;
f(2) = 2 × ln(2)
f(2) = 2×0.693147 =
f(2) = 1.386294
Since;
f(2) >T3; it is significant to posit that T3 is an underestimate of f(2).
Then; we have, R3 <= | f^(4)(c)/(4!)(x-1)^4 |,
Since;
f^(4)(x)=2/x^3, we have, |f^(4)(c)| <= 2
Finally;
R3 <= |2/(4!)(2-1)^4|
R3 <= | 2 / 24× 1 |
R3 <= 1/12
R3 <= 0.083
Boris buys candy that costs $7 per pound. He will spend at least $63 on candy. What are the possible numbers of pounds he will buy?
Answer:
Anything above 9
Step-by-step explanation:
63/7=9
The table below shows the number of miles Josh drives and the number of hours it takes to get there. What is the constant of proportionality in the table?
Answer:
B. 50
Step-by-step explanation:
2×50=100
3×50=150
4×50=200
5×50=250
If oranges cost 5 for 75cents how
many can you buy for $2.70?
Answer:
15 oranges
Step-by-step explanation:
Only if im correct in assuming you get 5 oranges per 75 cents if not then im not sure because im confused by the question
An object moving in a straight line passes through the points (3, 0) and (2, 2). The object also passes through the point (0, a).
Calculate the value of a.
Answer:
colinear pts (meaning gradient is same throughout)
Step-by-step explanation:
since grad is same,
(2-0)/(2-3) = (a-0)/(0-3)
-2 = a/-3
6 = a (multiply both sides by -3)
Simplify: 5^ -3 • 5^ 5
25^ 8
25^ -15
5^ -3
5^ 2
5^2
Step-by-step explanation:
You just add the exponents
-3 +5 =2
Answer:
5^2 .............................
Step-by-step explanation:
-3 + 5 = 2
Which one is the slope and which one is the y-intercept? Thank you for answering whoever answers.
Answer:
2.50 is the y-intercept, and 0.30 is the slope.
Step-by-step explanation:
y = 0.3x + 2.5
Answer:
Y intercept is the intercept that goes up and down on a graph. (x,y) Rise/run is the slope. Rise is how many y units one point is from the other and run is how many x units is away from one point to another on a graph. Hope this helped at all.
noah entered a bike race.He used his red bike because he read that red vehicles get speedjng tickets most often. He rode 32 miles in 160 minutes. How many minutes did it take him to cover 1 min?
Solve for k. simplify the answer
Answer:
c=5/2k+ −45/2
Step-by-step explanation:
Answer:
K= 9 + 2/5C
Step-by-step explanation:
1. Remove the parentheses
C= 5/2 x (k-9)
2. Multiply both sides
C= 5/2k- 45/2
3. Move the terms
2C= 5k- 45
4. Divide both sides
-5k= -45- 2C
5. Write in parametric form
k=9 + 2/5C
Find the slope of the following line: y=6x+1
Answer:
m=6 x-intercept = ( ---- ----1,0,6) y-intercept =(0,1)
Step-by-step explanation:
Slope= rise and run Since 6 is essentially 6-1 we know that the slope goes up to 6 units and right 1 unit on a graph.
Make sure to brainliest
which number is IRRATIONAL
Answer:
C the square root of 15
Step-by-step explanation:
sqrt of 15 = 3.87298335...
Brainliest?
Carlos is blowing air into a spherical soap bubble at the rate of 5 cm3/sec.
How fast is the radius of the bubble changing when the radius is 10 cm? (Round your answer to four decimal places.)
How fast is the surface area of the bubble changing at that time? (Round your answer to one decimal places.)
Answer:
The answer is below
Step-by-step explanation:
a) dV/dt = 5 cm³/s
The volume (V) of the bubble is:
[tex]V=\frac{4}{3} \pi r^3\\\\Differentiating\ with\ respect\ to \ time(t)\\\\\frac{d}{dt}(V)=4\pi r^2 \frac{dr}{dt} \\\\Substituting\ \frac{d}{dt}(V)=5\ cm^3/s \ and\ r = 10\ cm\\\\5 = 4\pi *10^2*\frac{dr}{dt}\\\\5=400\pi *\frac{dr}{dt}\\\\\frac{dr}{dt}=0.004\ cm/s[/tex]
b) The surface area of the sphere (A) is:
[tex]A=4\pi r^2\\\\Differentiating\ w.r.t.\ t:\\\\\frac{dA}{dt}= 8\pi r\frac{dr}{dt} \\\\r=10, dr/dt=0.004\\\\\frac{dA}{dt}= 8\pi *10*0.004\\\\\frac{dA}{dt}=1\ cm^2/s[/tex]
The rate at which the radius of the bubble is changing at that time is [tex]0.0125 \pi cm^2/s[/tex]
The rate at which the surface area of the bubble is changing at that time is [tex]\pi^2 cm^2/s[/tex]
The formula for calculating the volume of a sphere is expressed as;
[tex]V =\frac{4}{3} \pi r^3[/tex]
r is the radius of the sphere
Differentiating the volume with respect to time;
[tex]\frac{dV}{dt} = \frac{dV}{dr} \times \frac{dr}{dt} \\\frac{dV}{dt} = 4 \pi r^2\frac{dr}{dt}[/tex]
Given the following parameters
dV/dt = 5 cm^3/sec.
r = 10 cm
Substitute into the formula to get dr/dt
[tex]\frac{dV}{dt} = 4 \pi (10)^2 \times \frac{dr}{dt}\\5 = 400 \pi \times \frac{dr}{dt}\\ \frac{dr}{dt}=0.0125 \pi cm/s\\[/tex]
The surface area of the bubble is expressed as:
[tex]S = 4 \pi r^2\\\frac{dS}{dt} = \frac{dS}{dr}\times \frac{dr}{dt}\\ \frac{dS}{dt} =8 \pi r \times 0.0125 \pi\\ \frac{dS}{dt} =\pi ^2 cm^2/s[/tex]
Hence the rate at which the surface area of the bubble is changing at that time is [tex]\pi^2 cm^2/s[/tex]
Learn more here: https://brainly.com/question/12663882
What is 0.87 is 10 times as much as?
Answer:
0.087
Step-by-step explanation:
So the equation would be:
x × 10 = 0.87
So you need to find what x is
An easy way to do this is to just to:
Move the decimal point twice to the left to get 0.087
Hope this helps!
Mr. Johnson listed each class’s average on a quiz in fraction form. Based on the chart, Which shows the classes ordered from the highest average to the lowest average?
A. C,D,A,B
B. C,A,D,B
C. B,D,A,C
D. B.A,D,C
Answer:
C
Step-by-step explanation:
I'm not sure if my picture made since because I'm not the best at drawing but that's how I'd explain it
To find the product of
3
7
×
5
9
, Cameron simplified
3
7
to
1
7
and then multiplied the fractions
1
7
and
5
9
to find the product
5
63
. What is Cameron's error?
Cameron divided a factor in one of the numerators by the GCF but did not divide a factor in one of the denominators by the GCF. He should have simplified
5
9
to and multiplied
1
7
and to find the product .
please i need help.
Answer:
.........................
Can someone help me plz
Answer:
i think the answer is 7
Solve the quadratic equation and give both solutions.
14x^2 − 29x − 15 = 0
Answer:
Step-by-step explanation:
[tex]x_{1,\:2}=\frac{-\left(-29\right)\pm \sqrt{\left(-29\right)^2-4\cdot \:14\left(-15\right)}}{2\cdot \:14}[/tex] so [tex]x=\frac{5}{2}[/tex] [tex]x=-\frac{3}{7}[/tex]
Adele made cupcakes and cookies. The number of cookies she made is five times as many as the number of cupcakes she made.
If she made 190 cookies, how many cupcakes did she make?
A. 190/5
B. 190+5
C. 190 times 5
D. 5/190
Answer:
A. 190/5.
Step-by-step explanation:
Adele made 190 cookies, which is five times the amount of cupcakes she made. To find the amount of cupcakes she made, we must divide 190 by 5. By doing this we get the answer: 38 cupcakes.
Hope this helps! Let me know!
you have a bill of $100. find a 10% tip?
Answer:
10 bucks
Step-by-step explanation:
Answer:
$10
Step-by-step explanation:
10%=0.1
100*0.1=10
$10
choose the letter that corresponds to the correct answer
Answer:
A
Step-by-step explanation:
If f(x)=3, what is the value of f(-7)?
What’s the slope of the line on the graph?
What is 15.23 rounded to the nearest hundredth
Answer:
15.20
Step-by-step explanation:
A child has fewer than 40 baseball cards. If he puts them in piles of 2, 4, 8, or 12 he has one card left over each time. How many baseball cards does he have?
The child has 25 baseball cards.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The total number of cards the child has can be calculated using the steps below.
We can use the following steps:
- Prime factorization of each number:
2= 2
4= 2²
8 = 2³
12 = 2² x 3
- For each prime factor, choose the maximum exponent in any row, and multiply those together to get the least common multiple.
i.e
The maximum exponent of 2 is 3 and the exponent of 3 is 1.
- The least common multiple.
= 2³ x [tex]3^1[/tex]
= 24
- Add one to get the total number of cards.
Now,
The child's baseball cards.
= 24 + 1
= 25
Therefore,
The child has 25 baseball cards.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
The table shows the mean number of basketball goals made by four random samples of players from the school team during this year’s season. Sample # Sample Mean Number of Goals 1 7 2 4 3 5 4 8 Is a valid prediction for the mean of the population possible using these samples? No, there are not enough samples. Yes, the sample means are all less than 10. Yes, the variation of the sample means is small. No, the variation of the sample means is too great.
Answer:
Answer is C
Step-by-step explanation:
There is not enough samples.
Answer:
Yes, the variation of the sample means is small.
Step-by-step explanation:
If a bag contains 12 quarters, 6 dimes and 18 nickels what is the part to whole ratio of nickels to all coins?
Answer:
18:36
Step-by-step explanation:
their are 18 nickels and 12+6+18=36 total coins
so the ratio is 18 to 36 or 18:36
How do you do this question?
Step-by-step explanation:
Start with the series representation for eˣ.
eˣ = ∑ₙ₌₀°° xⁿ / n!
Substitute -x².
e^(-x²) = ∑ₙ₌₀°° (-x²)ⁿ / n!
e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ) / n!
Multiply by x².
x² e^(-x²) = x² ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ) / n!
x² e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ⁺²) / n!
Integrate both sides (use power rule).
∫ x² e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ⁺³) / ((2n + 3) n!)
Evaluate between x=0 and x=0.5.
∫ x² e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (0.5²ⁿ⁺³) / ((2n + 3) n!)
This is an alternating series, so use alternating series estimation.
(0.5²⁽ⁿ⁺¹⁾⁺³) / ((2(n+1) + 3) (n+1)!) ≤ 0.001
(0.5²ⁿ⁺⁵) / ((2n + 5) (n+1)!) ≤ 0.001
n ≥ 1
So the estimate of the integral is the sum of the first two terms (n=0 and n=1).
I = (-1)⁰ (0.5³) / ((3) 0!) + (-1)¹ (0.5²⁺³) / ((2 + 3) 1!)
I = (0.5³) / 3 − (0.5⁵) / 5
I = 1/24 − 1/160
I = 17/480
I = 0.0354
A dog has three puppies. Spot weighs 12 ounces. Rascal weighs 9.5 ounces. Socks weighs 10.2 ounces. What is the total weight of the litter expressed to the correct number of significant figures?
a. 31.7 ounces
b. 31 ounces
c. 32 ounces
d. 30 ounces
e. 31.70 ounces
Answer:
c. 32 ounces
Step-by-step explanation:
Given that:
The weight of the Spot = 12 ounces
The weight of Rascal = 9.5 ounces; &
The weight of Socks = 10.2 ounces.
To find the litters' total weight, we will sum all the given number of the puppies.
i.e. Total weight of the litter = (12 + 9.5 + 10.2) ounces
Total weight of the litter = 31.7 ounces
Total weight of the litter [tex]\simeq[/tex] 32 ounces to the correct number of significant figures.
1) 3 is 50% of what?
Answer: 6
Step-by-step explanation:
Which of these shows the following expression factored completely? 6x2 – 13x +5
Answer:
B
Step-by-step explanation:
That's my guess.
Answer:
C
Step-by-step explanation:
If on a scale drawing 100 feet are represented by 15 inches, then a scale of 1/2 inches represents how many feet
Answer:
3 1/3 feet
Step-by-step explanation:
100 feet : 15 inches
3 1/3 feet : 1/2 inch
Answer:
[tex]3\frac{1}{3}[/tex] feet
Step-by-step explanation:
Inches : Feet = 15 : 100
Let 'x' be the feet required to find
15 : 100 :: 1/2 : x
Product of extremes = product of means
15 * x = 100 * (1/2)
15 * x = 50
x = 50/15
x = 10/3
x = [tex]3\frac{1}{3}[/tex]
