Bosco

Catherine rolls a standard 6-sided die six times. If the product of her rolls is 2500 then how many different sequences of rolls could there have been? (The order of the rolls matters.)  

If you go to https://web2.0calc.com/questions/help-plz_51258

you can check out the earlier answer I gave, and GA's elaboration   

on the way to have done it using permutations.   

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I drove to the beach at a rate of 40 miles per hour.  If I had driven at a rate of 50 miles per hour instead, then I would have arrived 45 minutes later.  How many miles did I drive?   

You mean 45 minutes earlier.  Obviously, if you drive faster, you get there faster.  

This problem makes use of

the following relationship:                   Distance = Velocity x Time 

                                                           D  =  V • T  

case 1                                                 D  =  (40) • (T)  

case 2                                                 D  =  (50) • (T – 45)  

Since the Distance, D, is the  

same for both cases, let's set       

the "V•T"s equal to each other.             (50)(T – 45)  =  (40)(T)  

                                                               50T – 2250  =  40T  

Subtract 40T from both sides                  10T – 2250  =  0  

Add 2250 to both sides                                       10T  =  2250  

Divide both sides by 10                                           T  =  225   (this is in minutes)  

Divide minutes by 60 to get hours          225 minutes  =  3.75 hours  

Plug this T back into original equation                     D  =  (40 mi/hr) • (3.75 hr)  =  150 miles  

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Find the ordered triple (p,q,r) that satisfies the following system:  

p - 2q = 3  

q - 2r = -2 + q  

p + r = 9 + p  

This problem has no solution.  

One stipulation is   q - 2r = -2 + q    which means r = 1  

One stipulation is   p + r = 9 + p       which means r = 9  

You can't have both at the same time.  

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5x^4 * 5x^6  

To multiply exponential terms, IF the terms have the same base, simply add the exponents. 

Example.     5x⁴ • 5x⁶  

The base of each exponential term is x. 

So, we do see that the bases are the same. 

All you do is add the exponents.  4 + 6 = 10 

The "x" part of the product will be x¹⁰.  

That takes care of the x but we aren't through yet.    

There are coefficients.  

You have to multiply coefficients the regular way.    

In this case, the coefficients are 5 and 5.   

So, multiply 5 • 5 to obtain the resultant coefficient.  

This is a pretty easy one.  5 times 5 is 25.   

Combine the product of the coefficients   

with the product of the unknowns (the x).         5x⁴ • 5x⁶  =  25x¹⁰   

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Imitation is the sincerest form of flattery.  But, when you copy one of my answers and paste it in elsewhere, somewhere along the line the formatting gets dropped off.  So please use the formatting buttons this site provides, to make those exponents look like exponents. 

Example.  To make x4 look like a regular exponential expression:  Select the 4, then click the x² button in the coding buttons above, while you're on the editing screen.  

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Will and Grace are canoeing on a lake.  Will rows at 50 meters per minute and Grace rows at 20 meters per minute. Will starts rowing at 2 p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at 2 p.m. If they always row directly towards each other, and the lake is 3800 meters across from the west side of the lake to the east side, at what time will the two meet?

Will's rate is 50 m/min.  

Grace's rate is 20 m/min.  

They're rowing toward each other,  

so their rate of closure is 70 m/min.  

The lake is 3800 meters across.  

The time it will take them to meet is given by  

                                                                                    Distance  

                                                                            T  =  –––––––  

                                                                                       Rate  

                                                                                    3800 m  

                                                                            T  =  –––––––  

                                                                                    70 m/min  

The time it takes them to meet                             T  =  54.29 min  

Note that (0.29 min • 60 sec/min)  =  17 seconds

The time on the clock is                                             2:54:17 pm 

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In ab⁴, the exponent applies only to the b.  

What you're thinking about would be written (ab)⁴.  

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One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?  

To find b, consider                                                  ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

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Love your answer :-)  

what is the slope of a pipe that 120 feet long and drops 6 feet     

If you visualize a right triangle with one side 6 feet and the hypotenuse 120 feet  

then the sine of the angle opposite the 6 foot side is 6/120, which equals 0.05.  

Then use your calculator, or the tables, to find the arcsine of that ratio.   

          sin^–1(0.05) = 2.8659...  rounded to a reasonable number is 2.87.   

                                                                  The slope of the pipe is 2.87^o.  

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