Answer:
Step-by-step explanation:
x is positive and y is negative
9514 1404 393
Answer:
a) V = 4w²h
b) SA = 4w² +10wh
c) SA = 4w² +37.5/w
d) C = 40w² +225/w
Step-by-step explanation:
The relevant formulas are ...
V = LWH
base area = LW
lateral area = H(2(L+W))
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a) The length is 4 times the width, so the volume is ...
V = (4w)(w)(h)
V = 4w²h
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b) The total surface area is the sum of the base area and the lateral area:
SA = base area + lateral area
SA = (4w)(w) + 2h(4w +w)
SA = 4w² +10wh
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c) The volume is 15 m³, so the height in meters in terms of the width in meters is ...
15 = 4w²h
h = 15/(4w²)
Then the surface area is ...
SA = 4w² +10w(15/(4w²))
SA = 4w² +37.5/w
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d) The equation we have for surface area has one term for base area and a second term for lateral area. We can apply the cost factors to those terms to get the cost of materials:
C = 10(4w²) +6(37.5/w)
C = 40w² +225/w
<h3>
Answer: 3 units</h3>
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Explanation:
The y coordinates are identical, so we just need to focus on the x coordinates.
Going from 0 to -3 is a distance of 3 units. Drawing out a number line might help.
Or we could apply subtraction and absolute value
|x1-x2| = |0-(-3)| = |0+3| = |3| = 3
which is the same as
|x2-x1| = |-3-0| = |-3| = 3
The absolute value is to ensure the result is never negative. Distance is never negative.
Side note: if the y coordinates weren't the same, then we'd have to use either the pythagorean theorem or the distance formula.
