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.
% means per 100
so when figuring out percents it's good to use 100
so
on $100 7% would mean $7
on $50 7% would mean $3.5
in $200 7% would mean $14
Answer:
1/6
Step-by-step explanation:
Make the denominators the same by finding the lcm(least common denominator). The least common demominator would be 24. So multiply both numbers in 1/8 by 3. This would eaqual 3/24. Multiply both numbersin 4/3 by 8. This would equal 
= 
. Simplify 96/576 by dividing both numbers by 96.
<u>96</u> ÷ 96 = <u> 1 </u> 576 ÷ 96 = 6 and that becomes 1/6.
You leave at 1 P.M., the wedding ceremony starts at 5 P.M.
This gives you a 4 hour gap, the Wedding is 350 miles away, and you're traveling at 65 miles an hour.
Simply you can use two methods, (65 * 4) to verify if you'd make it or not or (350/65) to ensure how many hours it would take in total.
65 * 4 = 260 | Since this is not 350, we can verify that you'd be late.
350/65 = 5.4 (estimated) | Meaning it'd take about 5.4 hours.
To know how long that is we'd have to convert over.
5.4 = 5 2/5ths, 60 minutes are in an hour. Divide 60 by 5 to get 12, meaning:
1/5ths = 12/60ths, with that said multiply that by 2 to get your answer.
2/5ths = 24/60ths or 24 minutes.
This means you'd take 5 hours and 24 minutes to get there.
Originally we stated that the process would take 4 hours. Subtract:
(5 hours and 24 minutes) - (4 hours) = (1 hour and 24 minutes)
Concluding that you'd be late by an hour and 24 minutes.
I hope this helps, have a great rest of your day! ^ ^
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Answer:
6
Step-by-step explanation:
a right triangle's area is half of a square's.
(4*3)/2
6
