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Naya [18.7K]
3 years ago
6

Four polynomials are shown below:

Mathematics
1 answer:
marishachu [46]3 years ago
6 0
A is a 5th degree polynomial.

You might be interested in
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
F(1) = -3<br> f(n) = 2 · f(n − 1) +1<br> f(2)=
raketka [301]

Answer:

-5

Step-by-step explanation:

f(2) = 2 * f(1) + 1

f(2) = 2 * -3 + 1

f(2) = -6 + 1

f(2) = -5

6 0
3 years ago
Write the equation of the circle centered at ( 7 , − 5 ) (7,-5) with diameter 16
galina1969 [7]
The equation of a circle is (x - h)² + (y - k)² = radius² where (h, k) is the center. 

If the diameter is 16, then the radius is 8. 

Your equation is:
(x - 7)² + (y + 5)² = 64
3 0
3 years ago
Select the correct answer.
Alex73 [517]
C. 7.2°F is warmer than 7.0°F but colder than 7.6°F.
4 0
3 years ago
The first table that Cory designs will seat 8 people. If the diameter is 5 feet, what is the area? The area in terms of pi is Pi
frutty [35]

Answer: 19.6

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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