dan picked 7 plums and 6 apples from the orchard. he gave 3 plums to sandy how many plums does he have left?
1 answer:
You might be interested in
Answer:
B. 585
Step-by-step explanation:
A graph of the scatter plot and line of best fit is attached.
The temperature in this problem will be the independent variable, or x. This is because we are assuming that the number of ice cream cones sold depends on the temperature; this means the number of ice cream cones will be the dependent variable, or y.
This means in our graphing calculator, we will enter temperature in the first list and the number of cones in the second.
After drawing the scatter plot, we run the linear regression; we get the values for a and b in our equation, y = ax+b:
a = 5.08
b = 46.59
This gives us the equation y = 5.08x + 46.59.
Entering our temperature, 106, in for x gives us
y = 5.08(106) + 46.59 = 585.07 ≈ 585
The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;
- Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.
- Maximum volume of the box is approximately 1048.6 in.³
The given dimensions of the cardboard are;
Width = 18 inches
Length = 35 inches
Let <em>x </em>represent the side lengths of the cut squares, we have;
Width of the box formed = 18 - 2•x
Length of the box = 35 - 2•x
Height of the box = x
Volume, <em>V</em>, of the box is therefore;
V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x
By differentiation, at the extreme locations, we have;
Which gives;
6•x² - 106•x + 315 = 0
Therefore;
x ≈ 4.55, or x ≈ -5.55
When x ≈ 4.55, we have;
V = 4•x³ - 106•x² + 630•x
Which gives;
V ≈ 1048.6
When x ≈ -5.55, we have;
V ≈ -7450.8
The dimensions of the box that gives the maximum volume are therefore;
- Width ≈ 18 - 2×4.55 in. = 8.89 in.
- Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.
- Height = x ≈ 4.55 in.
- The maximum volume of the box, <em>V </em><em> </em>≈ 1048.6 in.³
Learn more about differentiation and integration here:
#SPJ1