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University of Texas at Austin

Michigan State University

01:15

Jinseop S.

$3-12=$ Using Models Use the model given to answer the questions about the object or process being modeled. The sales tax $T$ in a certain county is modeled by the formula $T=0.06 x .$ Find the sales tax on an item whose price is $\$ 120 .$

03:34

Kyle I.

Using Models Use the model given to answer the questions about the object or process being modeled. The distance $d$ (in mi) driven by a car traveling at a speed of $v$ miles per hour for $t$ hours is given by $$d=v t$$ If the car is driven at 70 milh for 3.5 $\mathrm{h}$ , how far has it traveled?

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?

02:33

Taylor S.

Using Models Use the model given to answer the questions about the object or process being modeled. The power $P$ measured in horsepower (hp) needed to drive a certain ship at a speed of $s$ knots is modeled by $$P=0.06 s^{3}$$ (a) Find the power needed to drive the ship at 12 knots. (b) At what speed will a 7.5 -hp engine drive the ship?

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Arco 2nd, 2nd and co tangent functions. Now the first thing to remember about the co second the second and the Tennco tangent functions is they are all reciprocal. For example, remember that sign is our Why over our whereas co second is the reciprocal, it's the are over the why the second the cosign is X over our and second is our over X and co tangent tangent, remember is why over X and co tangent is X over. Why? So they're all reciprocal and we're gonna use that in our graph and basically, how we're going to start. This is we're going to kind of start these little use shapes, and the first thing we're gonna do is we want to start off graphing these first. So like, here's a co second while I've got graft A sign graph. Here's the sign You wanna have that son graph draw just like for the second, we wanna have a co sign graph draw and then for co tangent, we wanna have a tangent graph draw. So it's really critical to go ahead and draw those. So when first thing we wanna do is we wanna place are asking heights where the sun crosses the center. Basically meaning on those, um, where it crosses that center line are basically where it crosses that X intercept. So on draw these dotted lines at these points. So for our coastline, we're gonna make thes use, and they're either gonna be upward or downward. They're gonna kind of look like parabolas, and they're gonna be going towards these dotted lines. So basically, for Kasab is gonna look like this right here. And even if the graph kept going, we would continue adding the Jews for a second. We're gonna kind of do the same thing for a second where we have those X intercepts, we're gonna draw these dotted lines and then we're gonna draw our use. And these years we're gonna be at these maximum and minimums. And so there's a second. So both of those show the reciprocal of our Coty, and it's basically it's showing where is going in the opposite directions from those points of those maximums and minimums Now, co change, it's gonna be a little bit different. We've already got these dotted lines, so we're gonna kind of basically draw them kind of going in the opposite direction. So, for example, for our first one, we would draw it going downward from here. Our lines would go in the opposite direction, and we would even have Are you here? But it would kind of just not be seen. So all of these showed the co tangent, which is like I said, It's basically the reciprocal, so it's gonna be going in the opposite direction with thes use.

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