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SIZIF [17.4K]
3 years ago
10

The cost, C, in millions of dollars of producing T million tons of steel is modeled by the equation C = 220T + 1890.

Mathematics
1 answer:
kobusy [5.1K]3 years ago
7 0

C = 220T + 1890.

Solve the equation for T.

220T = C - 1890

T = C/220 - 8.6

The steel produced is expected to be sold at a price of $310 per ton.

310 $/ton is a rate or slope. Write a linear equation where x is tons of steel produced and y is selling price of the steel.

y = 310x

Write and solve an equation to find the amount of steel produced if the selling price is equal to the cost of production.

* Here, note that the cost of production and tons of steel in the first equation is in the millions.  The equation we just wrote for the selling price was in x tons of steel. This only matters in regards to the units you specify because; million/million = 1

The unit multiplier of all variables must be specified as same. Either everything is in millions or not.

Here, I'll leave everything in millions, change x (tons of steel) to T (mill tons steel) and "y" to "S" in million dollars selling price.

S = 310T

Set equal to Cost equation.

220T + 1980 = 310T

Solve for T, million tons of steel produced.

1980 = 310T - 220T

1980 = 90T

T = 1980/90

T = 22 million tons steel produced


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a. If the diameter of the wheel is 68 cm, write an equation that models the height of the gum in centimeters above the ground at any time, t, in seconds.

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Step-by-step explanation:

a)

We are being told that:

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if we replace t with 1.56 seconds ; we can determine the height of the gum when Lamaj gets to the end of the block .

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c)

When are the first and second times the gum reaches a height of 12 cm

This indicates the position of y; so y = 12 cm

From the same equation from (a); we have :

\mathbf {y = 34 cos(\pi (t-1.25))+34}

\mathbf{12 = 34 cos ( \pi(t-1.25))+34}

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\mathbf {y = 34 sin (\pi (t-1.25))+34}

\mathbf{12 = 34 sin ( \pi(t-1.25))+34}

\dfrac {12-34}{34} = sin (\pi(t-1.25))

\dfrac {-22}{34} = sin (\pi(t-1.25))

-0.703 = (\pi(t-1.25))

t = 2.527 seconds

Hence, the gum will reach 12 cm first at 2.527 sec and second time at 2.72 sec.

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