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d1i1m1o1n [39]
3 years ago
12

Problem Page Charmaine needs to buy plastic forks. Brand A has a box of 42 forks for $2.17. Brand B has a box of 48 forks for $3

.97. Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent
Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
6 0

Brand A:

42 for $2.17 0.05

$2.17/42 = $0.05

Unit price - $0.05

Brand B:

48 for $3.97

$3.97/48 = $0.08

Unit price - $0.08

The better buy is Brand A because the unit price is $0.05 which is cheaper than Brand B which the unit price is $0.08.

Hope this Helps!!

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Answer: On a number line, 0 is in the middle, to the right , 7 is 7 spaces away from 0

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At 1 P.M., ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast i
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<span>The distance between the ships is changing at a rate of 21.393 km/h

</span><span>Step 1: First, you must draw an image to help better understand the problem 
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The reason that ship A is moving -35km/h is because ship B acts as an "origin" and as things move closer to the "origin" they become negative and as things move away from the "origin" they become positive.

We know that the rate of Ship A is expressed as <span><span><span>dA</span><span>dt</span></span>=−35</span> and the rate of Ship B is expressed as <span><span><span>dB</span><span>dt</span></span>=25</span>

Step 2: We want to figure out how many km Ship A and Ship B traveled in 4 hours

<span>ShipA:−35<span><span>km</span>h</span>⋅4hr=−140km</span>

Now if we take this <span>−140km</span> and add it to the <span>150km</span> we can see that Ship A is now only <span>10km</span> away from where Ship B began

<span>ShipB:25<span><span>km</span>h</span>⋅4hr=100km</span>

This means that Ship B is now <span>100km</span> from where it originally started

We can now redraw our information

Step 3: We must use the Pythagorean Theorem to find the third side of the triangle

<span><span>x2</span>+<span>y2</span>=<span>z2</span>→<span>102</span>+<span>1002</span>=<span>z2</span></span>

<span>z=<span>√<span><span>102</span>+<span>1002</span></span></span></span>

Step 4: Now that we know z, we must differentiate the original equation in order to find the rate at which z in changing

<span><span>x2</span>+<span>y2</span>=<span>z2</span>→2x<span><span>dx</span><span>dt</span></span>+2y<span><span>dy</span><span>dt</span></span>=2z<span><span>dz</span><span>dt</span></span></span>

We can simplify by canceling out the 2's

<span>x<span><span>dx</span><span>dt</span></span>+y<span><span>dy</span><span>dt</span></span>=z<span><span>dz</span><span>dt</span></span></span>

Step 5: Write down all the information and then plug into equation

<span>x=10and<span><span>dx</span><span>dt</span></span>=−35</span>
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<span>z=<span>√<span><span>102</span>+<span>1002</span></span></span>and<span><span>dz</span><span>dt</span></span>=?</span>

Now plug in the information

<span>x<span><span>dx</span><span>dt</span></span>+y<span><span>dy</span><span>dt</span></span>=z<span><span>dz</span><span>dt</span></span></span>

<span>10<span>(−35)</span>+100<span>(25)</span>=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>−350+2500=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>2150=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>21.393=<span><span>dz</span><span>dt</span></span></span>

The distance between the ships are increasing at a rate of 21.393 km/h

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