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Ronch [10]
3 years ago
6

This table gives a few (x,y) pairs of a line in the coordinate plane

Mathematics
1 answer:
blagie [28]3 years ago
7 0

Answer:

The x-intercept of the line is the point (12,0)

Step-by-step explanation:

step 1

Find the slope of the lime

Take the points

(22,36) and (32,72)

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{72-36}{32-22}

m=\frac{36}{10}

m=3.6

step 2

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=3.6

point (22,36)

substitute

y-36=3.6(x-22)

step 3

Find the x-intercept

we know that

The x-intercept of a line is the value of x when the value of y is equal to zero

so

For y=0

substitute in the equation and solve for x

0-36=3.6(x-22)

0-36=3.6x-79.2

3.6x=79.2-36

3.6x=43.2

x=12

therefore

The x-intercept of the line is the point (12,0)

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The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs seven times as
lubasha [3.4K]

Answer:

l = \sqrt[3]{\frac{2V}{7}}     b = \sqrt[3]{\frac{2V}{7}}       h = \sqrt[3]{\frac{49V}{4}}

Step-by-step explanation:

Represent the volume of the box with V and the dimensions with l, b and h.

The volume (V) is:

V = l * b * h

Make h the subject of the formula

h = \frac{V}{lb}

The surface area (S) of the aquarium is:

S = lb + 2(lh + bh)

Where lb represents the area of the base (i.e. slate):

The cost (C) of the surface area is:

C = 7 * lb + 1 * 2(lh + bh)

C = 7lb + 2(lh + bh)

C = 7lb + 2h(l + b)

Substitute \frac{V}{lb} for h in the above equation

C = 7lb + 2*\frac{V}{lb}(l + b)

C = 7lb + \frac{2V}{lb}(l + b)

C = 7lb + \frac{2V}{b} + \frac{2V}{l}

Differentiate with respect to l and with respect to b

C_l=7b - \frac{2V}{l^2} =0

C_b=7l - \frac{2V}{b^2} =0

To solve for b and l, we equate both equations and set l to b (to minimize the cost)

7b - \frac{2V}{l^2}=7l - \frac{2V}{b^2}

7l - \frac{2V}{l^2}=7b - \frac{2V}{b^2}

By comparison:

l =b

C_l=7b - \frac{2V}{l^2} =0 becomes

7l - \frac{2V}{l^2}=0

7l = \frac{2V}{l^2}

Cross Multiply

7l^3 = 2V

Solve for l

l^3 = \frac{2V}{7}

l = \sqrt[3]{\frac{2V}{7}}

Recall that: l =b

b = \sqrt[3]{\frac{2V}{7}}

Also recall that:

h = \frac{V}{lb}

h = \frac{V}{\sqrt[3]{\frac{2V}{7}}*\sqrt[3]{\frac{2V}{7}}}

h = \frac{V}{\sqrt[3]{\frac{4V^2}{49}}}

Apply law of indices

h = \sqrt[3]{\frac{49V^3}{4V^2}}

h = \sqrt[3]{\frac{49V}{4}}

The dimension that minimizes the cost of material of the aquarium is:

l = \sqrt[3]{\frac{2V}{7}}     b = \sqrt[3]{\frac{2V}{7}}       h = \sqrt[3]{\frac{49V}{4}}

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Simplify -17.5 x 7 to -122.5

Switch sides

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