Answer:velocity=185 m/s
Step-by-step explanation:
So make k the subject of the formula by divide both by sqrt(x)
h= k × sqrt(x)
k=h/sqrt(x)
k=256 / sqrt(256)
k=256 / 16
k=16
So now substitute the value of k :
h= 16 × sqrt (x)
Then differentiate:
=(1/2 × sqrt(x))× 16
=16/(2×sqrt(x)
=8/sqrt(x)
Then
= 8/sqrt(x) × 370
=8/ sqrt(256) × 370
=8/16 × 370
velocity=185 m/s
Let the number of children be c, and the number of adults be a.
c + a = 170 (total number of tickets)
Then the cost of each is: $5.90/child, $9.60/adult:
5.9c + 9.6a = 1269.40 (total sales)
Solving as 2 simultaneous equations, we first transform the first equation:
a = 170 - c
Substitute into the 2nd equation:
5.9c + 9.6(170 - c) = 1269.40
Solving gives c = 98, and a = 170 - 98 = 72. This means that 72 adult tickets were sold that day.
Answer:
4.41 feet per second.
Step-by-step explanation:
Please find the attachment.
We have been given that a man flies a kite at a height of 16 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. We are asked to find how fast must he let out the string when the kite is flying on 34 ft. of string.
We will use Pythagoras theorem to solve for the length of side x as:



Now, we will use Pythagorean theorem to relate x and y because we know that the vertical side (16) is always constant.

Let us find derivative of our equation with respect to time (t) using power rule and chain rule as:

We have been given that
,
and
.





Therefore, the man must let out the string at a rate of 4.41 feet per second.
Answer:
$23
Step-by-step
Johns debt is 70.00 dollars in 3 months. 70 divided by 3 is 23.