Write the equation of the line that represents the linear approximation to the following function at the given point a. b. Use the linear approximation to estimate the given quantity. c. Compute the percent error in the approximation, , where the exact value is given by a calculator. at a0; f() a. L(x) nothing
Answers
Answer:
(a) 15 - 4x
(b) 6.6
(c) 5.7143%
Step-by-step explanation:
The given problem is incomplete. Please find attachment of the complete description.
According to the question:
[tex]f(x)=11-x^2[/tex]
now,
(a)
[tex]f(a)=11-2^2[/tex]
[tex]=7[/tex]
[tex]f'(x)=-2x[/tex]
[tex]f'(2)=-4[/tex]
[tex]f(x)=f(a)+f'(a)(x-a)[/tex]
[tex]=7-4(x-2)[/tex]
[tex]=7-4x+8[/tex]
[tex]=15-4x[/tex]
(b)
[tex]f(2.1)=15-4\times 2.1[/tex]
[tex]=6.6[/tex]
(c)
[tex]Error=\frac{100\times \left | 6.6-7 \right |}{7}[/tex]
[tex]=5.7143[/tex]%
Related Questions
The Insurance Institute for Highway Safety publishes data on the total damage suffered by compact automobiles in a series of controlled, low-speed collisions. The cost for a sample of 9 cars, in hundreds of dollars, is provided below: 10,6,8,10,4,3.5,7.5,8,9 (a) What is the median cost of the total damage suffered for this sample of cars? (b) What is the first quartile for the above data? (c) What is the interquartile range of the above data? (d) What is the mean of the total damage suffered for this sample of cars? (e) Using the correct units, what is the value of the variance?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the cost data: 10,6,8,10,4,3.5,7.5,8,9
A.) Median cost :
Sorted data:
3.5, 4, 6, 7.5, 8, 8, 9, 10, 10
0.5(n + 1)th term ; n = number of samples
0.5(9 + 1)th term
= 0.5(10)th term = 5th term
Median = 5th term = 8
B.) First quartile (Q1) :
0.25(n + 1)th term ; n = number of samples
0.25(9 + 1)th term
= 0.25(10)th term = 2.5th term
Q1 = (2nd term + 3rd term) / 2 = (4+6)/2 = 10/2 = 5
Q1 = 5
C.) interquartile range = (Q3 - Q1)
Q3 = 0.75(n + 1)th term ; n = number of samples
0.75(9 + 1)th term
= 0.75(10)th term = 7.5th term
Q3 = (7th term + 8th term) / 2 = (9+10)/2 = 19/2 = 9.5
Q3 = 9.5
Q3 - Q1 = (9.5 - 5) = 4.5
D.) Mean (μ) :
μ = ΣX / n
n = sample size
μ =(10+ 6 + 8 + 10+ 4 + 3.5 + 7.5 + 8 + 9) / 9
μ = 66 / 9
μ = 7.33
3.) Population variance (s²)
Σ(x - μ)² / n - 1
=[(10 - 7.33)^2 + (6 - 7.33)^2 + (8 - 7.33)^2 + (10 - 7.33)^2 + (4 - 7.33)^2 + (3.5 - 7.33)^2 + (7.5 - 7.33)^2 + (8 - 7.33)^2 + (9 - 7.33)^2] / 9
= 45.5001 / 8
= 5.687
If a certain sum of money can become
5 times of its principal in 10 years, then
the rate of interest is
Answers
Question, simple interest or compounded?
Simple interest accumulated on a sum for 10 years will double in 10 years with an interest rate of 10%. Now, if you want it to accumulate five times principle, the interest rate will have to be: P(i)(10)=5P. Modifying the equation, we could get: (i)(10)=5. Alas, (.5)(10)=5. 50% is the rate for simple interest.
However, we started out with an amount, and your question asks at what rate will our original investment increase to five times the original amount. So, our equation must be modified: P(i)(10)= 5(P)-P. So, working the equation, i (10)=5(P)-P/P. 5xP-P= 4(P)/P. To restate, i(10)+P=5P. Also, i(10)=4P. Further, i =4P/10. I = .4, or 40%.
As proof, if a sum earns 4 each year for 10 years, the product is 40. If the investment earns 4 per year, at 40% interest, that investment must be 10. 40+10=50.
Compounding, we will have the following equation: P(1+i)^10=5P. P(i)^10=5.
Modified, 5=1(i)^10. \/5^10= 1.1746. Subtracting 1, results in 17.46% interest rate. (1.1746)^10=4.999. 4.999(1)=~5.
What’s this formula used to calculate?
Answers
Answer : definitely sampling error
Please explain how to do this!!
Answers
9514 1404 393
Answer:
y = 55°
Step-by-step explanation:
You know the sum of angles in a triangle is 180°. So, ...
25° +30° +x = 180°
And, you know a linear pair of angles totals 180°:
x + y = 180°
Substituting for 180°, we have ...
25° +30° +x = x + y
Subtracting x from both sides, we get a relation that is useful to remember:
25° +30° = y
y = 55°
_____
This relation is usually described as ...
An exterior angle is equal to the sum of the remote interior angles.
200 students ate lunch today. 37% of the students ate soup how many students ate soup?
Answers
Answer:
74
Step-by-step explanation:
Answer:74 students ate soup
Step-by-step explanation:
37% of 200 = 74
or
.37 x 200 = 74
Thaw relationship between a distance in yards and the same distance in miles is described by the equation
Answers
Answer:
The relationship between a distance in yards (y) and the same distance in miles (m) is described by the equation y = 1760m.
Step-by-step explanation:
Jodi bought a new sofa for $1,430, plus fees and insurance. She made paid off the balance in 18 months at $89 per month. How much did she pay in insurance and fees?
Answers
Answer:
$172
Step-by-step explanation:
Ok, So $1430 is the total amount PLUS fees and insurance. So 18 months at $89 per month. so do 18*89=1602. $1602-$1430=$172.
So She paid insurance and fees $172.
Please answer ALL parts of the questions. is 3 divisble by 7
Answers
Answer:
no
Step-by-step explanation:
no
Answer:
no it is not
Step-by-step explanation:
Write 1.96 ...... as a mixed number in simplest form.
Answers
1.96= 196/100
196/100= 49/25
49-25= 24
1 24/25
what is the y intercept of a line that has a slope of -3 and passes through point 0.-7?
Answers
Answer:
-7
Step-by-step explanation:
(x,y) --> (0,-7) -7 is the y-intercept
Answer:the answer is -7
Step-by-step explanation:
To find the quotient Two-fifths divided by one-fourth,
multiply Two-fifths by 4.
multiply Two-fifths by One-fourth.
multiply Five-halves by One-fourth.
multiply Five-halves by 4.
Answers
Hope this helps:)
Answer:
above is right
Step-by-step explanation:
Isopropyl alcohol has a density of 0.786 grams per cubic centimeter (g/cm 3). An object has a mass of 13 grams (g) and a volume of 21 cubic centimeters (cm 3). What will happen when the object is placed into isopropyl alcohol?
Answers
Answer:
B, it will float bc it is less dence. give me brainliest ;)
Step-by-step explanation:
Think about the expansion for the binomial
(2x - y2)6.
The first term of this binomial is 2x.
The second term of this binomial is -y2.
What is the correct formula for the fifth term in this binomial expansion?
A)6C4(2x)4(-y2)2
B)6C4(2x)2(-y2)4
C)6C5(2x)(-y2)5
Answers
Answer: B
6C4(2x)2(-y2)4
Step-by-step explanation:
2020 edge
in the diagram of the collinear points, PT=20 QS=6 and PQ= QR= RS. find each lenght
Answers
Answer:
QR=3, PQ=3, RP=6, SP=9, RS=3, ST=11, RT=14, QR=3
Step-by-step explanation:
HELP ME PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Left: -1 2/3
Right: -1 1/4
What is the perimeter of a rectangle whose width is (x - 7) units and whose length is (3x + 10) units?
Answers
Answer:
The answer is "(8x + 6) units".
Step-by-step explanation:
Formula of perimeter is:
[tex]\to \bold{P=2 \text{(Length +width)} }[/tex]
[tex]=2((3x+10)+(x-7))\\\\=2(4x+3)\\\\= 8x+6[/tex]
How many four-digit whole numbers contain the digit pair "17" without other intervening digits? (Note that 2017 is one such example but 2107 is not.)
Answers
Answer:
There are 209 4-digit nu numbers with 17 as consecutive digits
Step-by-step explanation:
17xx xx represent 00 through 99, a set of {100} members.
y17z. y can be 1 through 9 {9}. z can be 0 thru 9 {10}
ww17 which includes 10 thru 99, a set of {90}
Add 100+90+10+9 to get 209 possible combinations.
Belindas blossom boutique is having a one day sell. Any two daisies cost $1.50. How many daisies could you buy for 8.25
Answers
Answer:
11
Step-by-step explanation:
Divide 8.25 by 1.50:
8.25/1.50
= 5.5
Since any two daises cost 1.50, multiply this amount by 2:
5.5(2)
= 11
So, you could buy 11 daisies.
Solve -2(2x + 5) - 3 = -3(x - 1).
Answers
The solution for the equation -2(2x + 5) - 3 = -3(x - 1) is x = - 16 which can be solved by the use the distributive property.
What is distributive property?Distributive Property that when we multiply a number by a group of numbers that are added together, we can multiply each value in the group separately, then add the products of the multiplications.
-2(2x + 5) - 3 = -3(x - 1)
To solve this equation, we need to first use the distributive property to expand the left side of the equation.
We have:
-4x-10-3 = -3(x - 1)
-4x-13 = -3(x - 1)
Now, we can group the like terms on the left side and the right side of the equation.
On the left side, we have -4x - 13 and on the right side, we have -3x + 3.
-4x-13 = -3x + 3
To solve for x, we can add 3x to left side of the equation and add 13 to the right side.
This results in the equation:
-4x+ 3x = 13 + 3
Now, we can add 3x with -4x of the equation to isolate the x-term.
We have:
-x = 16
x = - 16
For more questions related to equation
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A number decreased by twelve is forty-five.
helpp.
Answers
Answer:
57
Step-by-step explanation:
57-12=45. Simple subtraction/addition
maria has 15 fewer apps on her phone than orlando. if the total number of apps on both phones is 29, how many apps are on each phone
Answers
This is impossible because 15 fewer than 29 is 14 and then she would have to have negative apps.
Step-by-step explanation:
Orlando's number of apps = 22
Maria's number of apps = 7
Given,
Maria has 15 fewer apps on her phone than Orlando.
The total number of apps on both phones is 29.
We need to find out how many apps are on each phone.
What does the term mean?- M fewer than N by 2
This means if N = P then M = P - 2
- M more than N by 2
This means if N = P then M = P + 2
We have,
Total number of apps = 29 _____(1)
Maria has 15 fewer apps on her phone than Orlando.
We can write this as:
Orlando's number of apps = O.
Now,
Maria's number of apps = O - 15
Now,
From (1)
Orlando's number of apps + Maria's number of apps = 29
O + O - 15 = 29
2O - 15 = 29
2O = 29 + 15
20 = 44
O = 44/2
0 = 22
Orlando's number of apps = 22
Maria's number of apps = 22 - 15 = 7
Thus,
Orlando's number of apps = 22
Maria's number of apps = 7
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Add. 41.600 + 79.436
79.852 120.442 120.960 121.036
Answers
Answer:
2346
Step-by-step explanation:
alexis rolled a six sided die and recored the results of each roll as shown below. what is the probability of rolling a six
Answers
Answer:
1/6
Step-by-step explanation:
there is six sides so theres only a 1/6 chance it will land on 6
3-2/7 divided by 1-1/4
Answers
1-1/4 = 0/4
Which of the following is a binomial?
Answers
Answer:
B
Step-by-step explanation:
Initially a pool contains 340 gallons of water. A hose is placed in the pool, and the water is turned on. The hose adds 5.2 gallons of water per minute. Write an equation to represent the total amount V of water in the pool in terms of x, the number of minutes the hose has been on.
Answers
Answer: Amount of water that is turned in a minute is 5.2d. Given the fact that initially was 350 gallons of water everything you pour needs to be added to the initial amount. So the answer is V(x) = 350 + 5.2x
thank me plz brainliest
Step-by-step explanation:
Evaluate the expression when x=-4.
x2 +7x-6
Answers
• -18
-8+ -34
-42
I think this is right lol
Ryan buys 5 tickets for the school play, Each ticket costs $8.
How much does Ryan spend in all?
Answers
Answer:
$40
Step-by-step explanation:
1=8
5x8=40
Answer:
40 shillings.
Step-by-step explanation:
If 1 ticket=8 shillings, what about 5 tickets?
8 shillings multiplied by 5 it will be 40 shillings.
On a number line, what is the distance between -1.75 and 2.5 help meerr
Answers
Answer:
4.25
Step-by-step explanation:
-1.75+x=2.5
x=4.25
(7p² + 4p+3)-(4p²- 3p+1)
Answers
Answer:
Step-by-step explanation:
(7p² + 4p+3)-(4p²- 3p+1)
opening the brackets
7p² + 4p + 3 - 4p²+ 3p - 1
By grouping the like terms,
7p² - 4p² + 4p + 3p + 3 - 1
3p² + 7p + 2
Hope this helps
plz mark as brainlest!!!!!!!