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3 years ago

Graph Data ALG 2 Please Help!

Mathematics

1 answer:

Sergio039 [100]3 years ago

5 0

Answer:

1. Figure 3

2. 2881.4 cm³

Step-by-step explanation:

The graph in figure 3 has a curve that fits the data best because it captures most of the points unlike the other two curves.

The curve in figure 3 has the equation;

$y=-16.9x^2 +430x+523$

When using x=8, substitute the value of x in the equation with 8 to get

y = -16.9*64 + 430*8 + 523

y= 2881.4

= 2881.4 cm³

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10.05+50.25= 60.30

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3 years ago

an open rectangular cardboard box with a square base is to have a volume of 256cm^3. Find the dimensions of the box if the area

Anit [1.1K]

Let
x------> the length side of the square base of the box
y-------> the height of the box

we know that
volume of the box=b²*h
b=x
h=y
volume=256 cm³
so
256=x²*y------>y=256/x²--------> equation 1

The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.

surface area of the cardboard=area of the base+perimeter of base*height
area of the base=x²
perimeter of the base=4*x
height=y
surface area=x²+4x*y-----> equation 2
substitute equation 1 in equation 2
SA=x²+4x*[256/x²]-----> SA=x²+1024/x

step 1
find the first derivative of SA and equate to zero
2x+1024*(-1)/x²=0------> 2x=1024/x²----> x³=512--------> x=8 cm
y=256/x²------> y=256/8²-----> y=4 cm

the answer is
the length side of the square base of the box is 8 cm
the height of the box is 4 cm

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3 years ago

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Answer:

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We want to know when Paulo will have "more than" 50 coins in his collection. Therefore, we will use the "greater than" sign. Thus, our inequality will be:

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