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.
Answer: 2 1/4
Step-by-step explanation:
Answer:
82
Step-by-step explanation:
Well since everything is already in order from least to greatest:
48, 56, 68, 72, 72, 78, 78, 80, 82, 84, 88, 88, 88, 90, 94, 98, 100
The median is the number in the middle
So 82 is the median
Hope this helps!
Feel free to comment any questions you have!
m = 36
<u>Work</u>
<em>45 + 2.50m = 3.75m</em>
<em> -3.75m -3.75m</em>
<em>45 - 1.25m = 0</em>
<em>- 45 - 45</em>
<u><em>-1.25</em></u><em>m = </em><u><em>-45</em></u>
<em>-1.25 -1.25</em>
<em> </em>m = 36
Answer:
2.5 ft.
Step-by-step explanation:
The area of the side of each smaller square = 100 / 16 sq ft.
= 6.25 sq feet.
So the length of each smaller square = square root of 6.25
= 2.5 ft.
