Answer:
7
Step-by-step explanation:
.
Given:
The power generated by an electrical circuit (in watts) as a function of its current x (in amperes) is modeled by
To find:
The current which will produce the maximum power.
Solution:
We have,
Differentiate with respect to x.
...(i)
To find the extreme point equate P'(x)=0.
Divide both sides by -30.
Differentiate (i) with respect to x.
(Maximum)
It means, the given function is maximum at x=4.
Therefore, the current of 4 amperes will produce the maximum power.
To answer this you have to use Pythagoras's theorem: a^2 + b^2 = c^2
Put in the values:
5^2 + 15^2 = c^2
Simplify it:
25 + 225 = c^2
Simplify again:
250 = c^2
Square root both sides:
15.8113883008 = c
So the ramp is:
15.8113883008 feet
Now round the number:
15.8ft
The above is the answer :)
(btw sorry in advance if you've spotted a mistake)
Answer:
y=mx+c
We have to find the value of m and c.
Let's substitute the value of x and y from the table.
When x=1, y=15,
15= m(1)+c
m +c= 15 ------(1)
Now substitute another set of x and y values.
When x=2, y=24,
24= m(2)+c
2m +c= 24
c= 24 -2m ------(2)
Let me rewrite the two equations so that it is clearer for you to see.
m + c= 15 -----(1)
c = 24 -2m -----(2)
subst. (2) into (1):
m+ 24-2m= 15
-m= 15-24 (bring constants to 1 side, m terms to the other)
-m= -9 (simplify)
m= 9 ( divide by -1 throughout)
subst. m=9 into (2):
c= 24 -2(9)
c= 24-18
c= 6
Thus, the equation is y=9x+6.
When the cat is 3 years old, x=3.
When x=3,
y= 9(3)+6
y= 33.
Hence, the cat is 33 years old in human years.
Yes.
9m-3m=1+19
6m=20
m=20/6=10/3
