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Liula [17]
2 years ago
13

How can you use 1300 divided by 13 to help you find 1,287 divided 13

Mathematics
1 answer:
tiny-mole [99]2 years ago
6 0

Answer:

Step-by-step explanation:

This question is about the benefits of estimation.

1300/13 is easy and results in 100.

1287/13 can be approximated by 1300/13:  1287/13 ≈ 100.

Actually, 1287 = 1300 - 13 = 13(99); just subtract 1 from 100.  

So:  1287/13 = 1300 - 13 = 1287.  A nice bit of mental math!

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Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x. (
True [87]
So it tells us that g(3) = -5 and g'(x) = x^2 + 7.

So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))

now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16 

Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84

So we have our linear approximation for the two. 

If you wanted to, you could check your answer by finding g(x).  Since you know g'(x), take the antiderivative and we will get 
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35

So just to check our linear approximations use that to find g(2.99) and g(3.01)

g(2.99) = -5.1597
g(3.01) = -4.8397

So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer.  Not a bad method if you ever need to use it. 
5 0
3 years ago
What's the answer guys?
MAXImum [283]

Answer:

Step-by-step explanation:

Ask your parents

4 0
3 years ago
Read 2 more answers
Prove the following identity true. Show work.
yulyashka [42]

Answer:

The  Pythagorean identity states that

\sin^2 t + \cos^2 t = 1

Using that we can rewrite the left denominator as:

1 - \sin^2 t

Which can be factored as

(1 - \sin t)(1+ \sin t)

The numerator we can expand as:

(1 - \sin t)(1 - \sin t)

On the right hand side, let's multply numerator and denominator with (1 - sin t):

The total formula then becomes:

\dfrac{(1-\sin t)(1-\sin t)}{(1 - \sin t)(1 + \sin t)} = \dfrac{(1-\sin t)(1 - \sin t)}{(1+\sin t)(1 - \sin t)}

There you go... left and right are equal.

3 0
3 years ago
Read 2 more answers
A square is cut diagonally into two equal parts. If each part has an area of 50 cm^2, then what is the perimeter of each part?
AysviL [449]

Answer:

<u><em>30cm</em></u>

Step-by-step explanation:

Given data

When are square is cut diagonally into two parts

The resulting shape is a triangle

hence the area of the square = 50+50 = 100cm^2

The length of each side of the square = √100= 10cm

likewise the diagonal of the square = 10cm

<u><em>Hence the perimeter of the resulting triangle= 10+10+10= 30cm</em></u>

8 0
2 years ago
Help please.<br><br><br><br> Thank you.
Tom [10]

Answer:

A,D,C would be your answers

Step-by-step explanation:

8 0
3 years ago
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