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McMaster University

University of Michigan - Ann Arbor

00:55

Taylor S.

Using Models Use the model given to answer the questions about the object or process being modeled. The volume $V$ of a cylindrical can is modeled by the formula $$V=\pi r^{2} h$$ where $r$ is the radius and $h$ is the height of the can. Find the volume of a can with radius 3 in. and height 5 in.

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 $\$ 120 .$

01:11

Ruirui L.

Making Models : Write an algebraic formula that models the given quantity. 13. The number $N$ of cents in $q$ quarters

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?

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we're being asked to find each product. And as you can see, we have fractions here. So remember the general rule when you're multiplying fractions is they both have to be improper fractions. So you don't wanna have miss mixed numbers and then you can just multiply straight across. So, for example, if we go the part A. We have negative two thirds times five sevens, so we could just multiply straight across while two times five is 10, three times seven is 21 and to determine their sign because one sign was negative and the other was positive, Our result will be a negative value. Then always try and reduce if you can, but there is no number besides one that divides into 10 and 21 evenly. So our answer is simply, just negative 10/21. Now let's go to Part B. We have negative nine temps times negative, 20/21. Now we could just multiply straight across, but notice those values are kind of big. Remember, we can reduce before we multiply. There just needs to be a constant factor that goes into both numerator and either fraction and the denominator of evil fraction. So, for example, if I look at 20 and 10, I can divide those both by 10. Well, 20 divided by 10 is two and 10, divided by 10 is one. Then, if I look at nine and 21 I could divide those books by three nine. Divided by three is three and 21 divided by three or seven. So, really, what we're left with now is negative. 3/1 times negative to over seven. And though this is a lot easier numbers to multiply, so again, we'll play straight across three times to a six one time. Seven. It's seven. And because both numbers have the same sign, our result will be positive. So our final answer is 67 and that fraction can't be reduced. Now let's go to part C. First thing I notice is we have mixed numbers, so we have to change those into improper fractions. So let's start with you on one third. So remember, we're gonna multiply the denominator by the whole number and then add the numerator and that will give us our new numerator and we keep the denominator so three times to a six plus one is seven. So we have seven thirds. Now. We're gonna do the same thing for negative form one half. Two times four is a plus. One is nine. So we're gonna have negative night house. Now, let's see if we could reduce before we multiply. Well, I noticed that three goes into both three and nine, so I can divide both of them by three. Well, nine divided by three is three and three. Divided by three is one. So, really, we're just left with 7/1 times. Negative. Three over to now we can multiply well, seven times three is 21 one times two is two and ra multiplying two numbers with different sides. So the result will be negative. Now, unless you're directions. Told you otherwise, it's more likely than algebra that you're gonna leave. Your answer is improper fractions. So it's perfectly fine to stay that your answer is negative. 21/2

Linear Functions

Solve Linear Inequalities

Functions

Systems of Equations and Inequalities

Graph Linear Functions

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