Answer:
Given statement: The number of gallons of water in the swimming pool x minutes after turning on the faucet is represented by :
.....[1]
The equation of straight line is represented by .....[2]
where
m represents the slope of line
and
b is the y-intercepts.
On comparing the equation [1] with [2] we get;
slope(m) = 24 and
y-intercept(b) = 285.
x-intercept defined as the graph crosses the x-axis i.e,
substitute the value of y =0 in [1] to solve for x;
0= 24x + 285
Subtract 285 from both sides we get;
-285 = 24x
Divide both sides by 24 we get;
x = -11.875
(a)
y= 24x + 285 where x is in minute.
You can see the graph of the equation as shown below.
(b)
Slope of the equation = 24
y-intercepts = 285
(c)
Since, x intercept is not applicable to this problem because value of x is negative as x represents the time(in minutes)
144
If you add 9+6+9 is will give you 24 than you would times that by 6. So 9+6+9= 24 next 24×6=144.
The circumferince of the circle is 2πR ;
The area of the circle is π
;
Then, 2πR = 704 ;
R = 352 / π ;
π
= π × ( 352 / π )^2 = ( 352^2) / π = 123904 / π ≈ 39459.87 ≈ 39460 cm^2 ;
Answer:
<u>Up</u>. The focus is above the vertex meaning the parabola will open up. If the focus was below the parabola then it would open down.
Step-by-step explanation:
Answer:
Step-by-step explanation:
From the given information:
a)
Assuming the shape of the base is square,
suppose the base of each side = x
Then the perimeter of the base of the square = 4x
Suppose the length of the package from the base = y; &
the height is also = x
Now, the restriction formula can be computed as:
y + 4x ≤ 99
The objective function:
i.e maximize volume V = l × b × h
V = (y)*(x)*(x)
V = x²y
b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):
y + 4x ≤ 99 --- (1)
V = x²y --- (2)
From equation (1),
y ≤ 99 - 4x
replace the value of y into (2)
V ≤ x² (99-4x)
V ≤ 99x² - 4x³
Maximum value V = 99x² - 4x³
At maxima or minima, the differential of
⇒ 198x - 12x² = 0
By solving for x:
x = 0 or x =
Again:
V = 99x² - 4x³
At x =
= -198
Thus, at maximum value;
Recall y = 99 - 4x
when at maximum x =
y = 33
Finally; the volume V = x² y is;
V = 8984.25 inches³