The graph forms a straight line going downwards. The straight line means that the speed is constant. It is going downwards meaning it is stopping.
The best statement that represents the graph is:
<span>Each point shows the remaining distance, in feet, to the finish line of a race t seconds after a runner begins the final stretch and runs at a constant speed.</span>
Answer:
because the gross is the total amount of money they get without the subtraction of taxes that they have to pay
Step-by-step explanation:
200-50= 150
So you need to get 150 dollars in a month. If you get 20 dollars a week, then 150/20 will give you 7.5. So it will take you 7.5 weeks to get 150 dollars
<span>Understand that:
• the sum of two positive numbers is greater than either
number.
Understand that addition is the inverse of subtraction (addition
reverses subtraction and vice versa) and use this to check
results.
Respond rapidly to oral or written questions, explaining the
strategy used. For example:
• 654 add 50… Add 68 to 74…
• 7 add 12 add 9… Add 15, 6, 4, 15 and 1…
• What is the sum/total of 26 and 39? And of 13, 62 and 3?
• How many altogether are 121 and 35? And 61, 37 and 6?
• Increase 48 by 22.
• Which three numbers could have a total of 103?
Are there any others?</span>
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.
