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Johns Hopkins University
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University of Michigan - Ann Arbor
00:57
Amy J.
The model $L=4 S$ gives the total number of legs that $S$ sheep have. Using this model, we find that 12 sheep have $L=$ __________ legs.
00:52
07:20
Alix S.
Using Models Use the model given to answer the questions about the object or process being modeled. The gas mileage $M($ in milgal) of a car is modeled by $M=N / G,$ where $N$ is the number of miles driven and $G$ is the number of gallons of gas used. (a) Find the gas mileage $M$ for a car that drove 240 mi on 8 gal of gas. (b) $A$ car with a gas mileage $M=25$ mi/gal is driven 175 mi. How many gallons of gas are used?
02:13
Taylor S.
Using Models Use the model given to answer the questions about the object or process being modeled. A mountain climber models the temperature $T$ ( in $^{\circ} \mathrm{F}$ ) at elevation $h$ (in ft) by $$T=70-0.003 h$$ (a) Find the temperature $T$ at an elevation of 1500 $\mathrm{ft}$ . (b) If the temperature is 64$^{\circ} \mathrm{F}$, what is the elevation?
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one, we're gonna use the equation. A equals one half H Tom's B one plus B two. So obviously this is an area formula and it is the area for a trapezoid. So for this area, we want to solve four B one or the base one. So here's how we're gonna This is gonna take several steps to Dio and we're gonna move everything one bit at a time. But we may have to do some other sets before we can move. Let's first thing we're gonna do is let's get rid of this fraction. So we're going to do that by multiplying both sides by the denominator. So we're gonna multiply the right side by two and the left side by two. And what that's gonna happen is on the left side, my denominator is gonna cancel out and on the right side, I'm gonna have to a So now I have two. A equals. That's one h. So I'm just gonna put h Tom's be one plus b two now because the be wanted to be too are in this parentheses. Let's do distributed property. So let's multiply everything in the parentheses by H and rewrite that out. So two a equals H B one plus h be to. So now that we have got that distribute it out, we don't have a parentheses. We can go ahead and we can move by any adding or subtracting anything away from the B one. Well, we can subtract h b two. You want to try to do any subtracting before you do that final division or multiplying. So that's going to get rid of on the left is gonna cancel out. I'm sorry. On the right on left, you're gonna be left with two a minus. H B two equals h B one. So now I see that on the right side where my be one is All I'm left with is my h times that be one. So in order to get that h over to the left side, I have to do the opposite. Well, the opposite of multiplication is always gonna be division. So we're going to divide both sides by h on the right side. That's gonna cancel the h is and leave me with my be one, which is exactly what I want on the left side. We're gonna leave it as to a minus H B two over H and another way of writing this would be B one equals to a minus H B two over h.
Linear Equations and Functions
Linear Equations and Inequalities
Matrices and Determinants
Quadratic Equations
Applications of Trigonometric Functions
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