Answer:
Step-by-step explanation:
The equation for a tangent line of f(x) in the point (a,f(a)) can be calculated as:
L(x) = f(a) + f'(a)(x-a)
Where L(x) is also call a linear approximation and f'(a) is the value of the derivative of f(x) in (a,f(a)).
So, the derivative of f(x) is:
Then, to find the linear approximation we are going to use the point (16, f(16)). So a is 16 and f(a) and f'(a) are calculated as:
Then, replacing the values, we get that the equation of the tangent line in (16,4) is:
Finally, the approximation for 
is:
The value is 0.02
If it is a negative number, you move the decimal over to the left. :)
Answer:
Sharika needs 2.5 days to finish the remaining work
Step-by-step explanation:
Sharika can do a work in 6 days palkey can do it in 8 days
Then the amount of work sharika can do in 1 day = 1/6
And the amount of work palkey can do in 1 day = 1/8
The amount of work both of them can do together in 1 day = 1/6 + 1/8
= 7/24
The amount of work both of them can do together in 2 day = (2× 7/24)
= 7/12
Since Palkey left the work,the amount of
work remaining for Sharika to do alone = (1 - 7/12 )
= 5/12
The number of days Sharika take to finish the remainig work. = (5/12 ÷ 1/6 )
= 5/2 days
Therefore, Sharika needs 2.5 days to finish the remaining work.
The <em><u>correct answers</u></em> are:
The inequality is 75+4t ≥ 400, and they must sell at least 82 tickets.
Explanation:
t is the number of tickets sold. They start out with $75, so that is where our inequality begins. Each ticket is $4; this gives us the expression 4t. Together with the $75 carry over, we have 75+4t.
They must make at least $400 to pay for the dance. This means it must be more than or equal to 400; this gives us 75+4t ≥ 400.
To solve this, first subtract 75 from each side:
75+4t-75 ≥ 400-75
4t ≥ 325
Divide both sides by 4:
4t/4 ≥ 325/4
t ≥ 81.25
We cannot sell a portion of a ticket, so we round. While mathematically this number would "round down," if they only sell 81 tickets, they will not have enough money. Therefore we round up to 82.
It will be 0.0625 because you can use a calculator and do 14/224
