1st one
It all adds up and the first one would be the most educated answer
Mark brainliest please
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: 7.5 minutes (7 min 30 sec)
Step-by-step explanation: If it takes it 3 minutes to travel 2 km, it would take it 1.5 minutes to travel 1 km. So, 1.5 * 5 = 7.5, meaning it would take it 7.5 min to travel 5 km.
The answer to this problem is A
The length of one side of the square base is 8.5 centimeters.
<u>Given the following data:</u>
- Volume of cuboid = 867 cm
To find the length of one side of the square base:
Mathematically, the volume of a cuboid is given by the formula:
× 
Substituting the given values, we have:
× 
Base area = 72.225 
Now, we can find the length by using the formula:
<em>Length</em><em> = </em><em>8.5 centimeters</em>.
Therefore, the length of one side of the square base is 8.5 centimeters.
Find more information: brainly.com/question/11037225
