Write the equation of the line
2 answers:
Answer:
The equation of the line in the form y= mx + C, which passes through
(1,4) and has gradient 9 is
Step-by-step explanation:
We need to write the equation of the line in the form y= mx + C, which passes through (1,4) and has gradient 9
The equation of form has m equals to slope and c equals to y-intercept
So, we need to find slope and y-intercept.
Finding Slope
We are given gradient = 9
Gradient is also known as slope, so m = 9
Finding y-intercept
Using point (1,4) and slope m = 9, we can find y-intercept
So, y-intercept is: c = -5
Equation of line
Now, the equation of line having slope m = 9 and c= -5 is:
So, the equation of the line in the form y= mx + C, which passes through
(1,4) and has gradient 9 is
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Answer:
height = 14.5 ft
width = length = 3.2 ft
Step-by-step explanation:
Let the side of the square base is a and the height of the box is h.
The material required to make the box is equal to the total surface area of the box.
Area of base = a²
Cost of square base is $ 2 per ft²
So, the cost of making base = 2a²
Area of four walls + area of top = 2 (a² + ah + ah) + a² = 3a² + 2ah
Cost of making walls and the top is $ 1 per ft²
So, the cost of making walls and the top = 1 x ( 3a² + 2ah)
Total cost of making the box = 2a² + 3a² + 2ah = 5a² + 2ah
According to the question
144 = 5a² + 2ah
.... (1)
The volume of the box is V = length x width x height
V = a x a x h
V = 72 a - 2.5 a³ from equation (1)
Differentiate both sides with respect to a.
dV/da = 72 - 7.5 a²
Put, it equal to zero for maxima and minima
7.5 a² = 72
a = 3.2 ft
Put in equation (1)
h = 14.5 ft
So, the dimensions of the box are
height = 14.5 ft
width = length = 3.2 ft