MATHEMATICS COLLEGE

a.Find a linear approximation of 4√14 . b. Justify visually whether your approximation is an over- or underestimate.

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Let f(x) be the function

$\bf f(x)=√(x)$

A linear approximation of f is the Taylor polynomial of degree one:

$\bf f(x)\approx f(a)+f'(a)(x-a)$

Taking a = 16, and given that

$\bf f'(x)=\displaystyle(1)/(2√(x))$

we get

$\bf f(x)\approx f(16)+f'(16)(x-16)=√(16)+\displaystyle(1)/(2√(16))(x-16)=4+\displaystyle(x-16)/(8)$

$\bf √(14)=f(14)\approx 4+\displaystyle(14-16)/(8)=3.75\Rightarrow\n\n\Rightarrow 4√(14)\approx 4(3.75)=15$

Since 16 > 14, we can deduce that this is an overestimate.

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Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste?A. none of these
B. Let “1,2,3” represent preferring the toothpaste and “0,4,5,6,7,8,9” represent not recommending the toothpaste.
C. Let “1,2,3” represent preferring the toothpaste and “4,5,6,7,8,9” represent not recommending the toothpaste.
D. Let “0,1,2” represent preferring the toothpaste and “3,4,5,6,7,8” represent not recommending the toothpaste.
Reset Selection

Answers

Let favorable event“1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.

Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste to determine.

What is probability?

Probability can be defined as the ratio of favorable outcomes to the total number of events.

While going throughout the option in options C and D number so the sample is not equal to 10 so both the statement is false. Option B is the correct option because the sample space is also equal to 10 and the number of the favorable events is also 3 which is mentioned in the question.

Thus, let favorable event “1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.

Learn more about probability here:

brainly.com/question/14290572

#SPJ5

Answer:

Step-by-step explanation:

only b has 10 didgets. it could be a since the didgets aren't very random, but then again, i think it's b

The taxi driver charges $3.50 just to get in the cab and then $2.50 per mile. If Lisa travels m miles, which equationtells Lisa how much she will have to pay for her taxi ride, r?
A r = 2.5 +3.5
B = 3.5m + 2.5
r= 2.5m + 3.5
Dr= 2.5m - 3.5

Answers

Answer:r=2.5m+3.5

Step-by-step explanation:

the answer is 2.5m + 3.5 because we don't know how many miles the taxi driver drove

Find the product. write your answer in exponential form 9²•9-⁶

Answers

Answer:

9^8

Step-by-step explanation:

9²•9⁶ = 9^(2+6) = 9^8

Answer:

IF the 6 is negative : $9^(2)$ · $9^(-6)$ then the answer is 1/ $9^(4)$

If the 6 is positive then the answer is $9^(8)$

Step-by-step explanation:

Exponents are add when their bases are similar.

each day a bobcat drinks about 3 times as much water as a canada goose drinks. how much water can a bobcat drink in ① day?

Answers

56 gallons
I think..
Hope this will be helpful for you

the formula for this is b= bobcat and g=goose so if the bobcat is three times as much as the goose then b=3g now if you know b or g you can fill it in to find the other.

36 diveded to 68251500

Answers

Answer: do you mean divided

If so the answer is

1895875

Step-by-step explanation:

68251500÷36=1895875

An object is launched at 20 m/s from a height of 65 m. The equation for the height (h) in terms of time (t) is given by h(t) = -4.912 + 20t + 65. What is theobject's maximum height?

Answers

Answer:

The maximum height is the y-value of the vertex.

h(t) = -4.9t² + 20t + 65

a=-4.9 b=20 c=65

h(2) = -4.9(2)² + 20(2) + 65

= -19.6 + 40 + 65

= 85.4

Step-by-step explanation:

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