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MAXImum [283]
3 years ago
8

Use linear approximation, i.e. the tangent line, to approximate √16.4 as follows: Let f(x)=√x. Find the equation of the tangent

line
Mathematics
1 answer:
Ivahew [28]3 years ago
6 0

Answer:

L(x)=\frac{1}{8}x+2\\ L(16.4)=4.05

Step-by-step explanation:

The equation for a tangent line of f(x) in the point (a,f(a)) can be calculated as:

L(x) = f(a) + f'(a)(x-a)

Where L(x) is also call a linear approximation and f'(a) is the value of the derivative of f(x) in (a,f(a)).

So, the derivative of f(x) is:

f(x)=\sqrt{x} \\f'(x)=\frac{1}{2\sqrt{x} }

Then, to find the linear approximation we are going to use the point (16, f(16)). So a is 16 and f(a) and f'(a) are calculated as:

f(16)=\sqrt{16}=4\\f'(16)=\frac{1}{2\sqrt{16} }=\frac{1}{8}

Then, replacing the values, we get that the equation of the tangent line in (16,4) is:

L(x)=4+\frac{1}{8}(x-16)\\L(x) = \frac{1}{8}x+2

Finally, the approximation for \sqrt{16.4} is:

L(16.4)=\frac{1}{8}(16.4)+2\\ L(16.4)=4.05

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Whats the awnser to the image that is selected?????
VikaD [51]

Answer:

30 units

Step-by-step explanation:

In order to find the length of the 3rd side of the triangle, the hypotenuse, you can use the Pythagorean Theorem. Using this method, you get 5^2+12^2=169. The square root of 169 is 13.

5 + 12 + 13 = 30 units.

7 0
1 year ago
13. If the following fractions were converted to decimals, which one would result in a repeating decimal? A. 3/4 B. 1/9 C. 5/11
Vladimir [108]
Hey there!

In order to find if a fraction would result in a repeating decimal, recall that a fraction is a division problem written vertically. All that you have to do is divide the numerator by the denominator. Also, remember that a repeating decimal will result in the same number after the decimal point as long as the calculator can handle. 

3 ÷ 4 = 0.75

1 ÷ 9 = 0.11111111...

5 ÷ 11 = 0.45454545...

3 ÷ 0.42857143...

As you can see, two out of your four answer choices give you a repeating decimal. B gives you a repeated number of "1" while C gives you "45". D doesn't count since there is no pattern of repeated numbers that it follows. 

Both B and C fall into the category of repeating decimal. If you're only able to choose one answer, I would ask your teacher, a parent, or a peer what they think. 

Hope this helped you out! :-)
5 0
3 years ago
Jamie went to the his 6 friends. For each friend, he spent $4.75 for a sandwich, $1.25 for a cold beverage, and $.56 for a piece
masha68 [24]

Answer:

Jamie spent $39.36 in total.

Step-by-step explanation:

First, add the money spent for the sandwich, beverage, and fruit together.

4.75 + 1.25 + .56 = 6.56

Then, multiply the amount spent for one friend by six to find the total.

6.56 x 6 =39.36

I hope this helped you!

8 0
3 years ago
what is the rate of change and initial value for this graph?
MAXImum [283]

Answer:

4/7

Step-by-step explanation:

the rate of change (aka slope) is the change in y over change in x and as y goes up 4 x goes up 7 so the rate of change is 4/7

have a great day :D

8 0
2 years ago
Please help me find the measure of
Yuri [45]

Answer:

hey here's your answer.

5 0
3 years ago
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