CPhill

Just like this.......(4+5/8)/2

Then, hit "="

how many numbers between 1 and 100 (inclusive) are divisible by 3 and 5.

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Since 3 and 5 are relatively prime (they have no common divisors except 1) this should be easy to determine.

The first multiple of 3 and 5 is 15 = 3*5*1 = 15*(1)

The second one is 30 = 3*5*2 = 15*(2)

Then by solving this inequality....... 15(n) ≤ 100....you should be able to determine how many numbers between 1 and 100 (inclusive) are divisible by 3 and 5. If you get a "remainder," just ignore it - "n" is an integer.

a book falls off the top of an 8-foot shelf. Theodore is 4-feet tall. if is takes theodore 2 seconds to respond to the fall and get out of the way, does the book hit him?

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Let's see how much Physics I can remember.

The position "y"  of any object at time t is given by:

y = -16t² + v_ot + h

Where v_o is the original velocity ( 0, in our case) and h is the original height (8 ft.). Note that y = 4 feet above the ground. So we have...

4 = -16t² + 8  which simplifies to

0 = -16t² + 8  and solving for t, we get

t = ± (1/2) second

Rejecting the negative, we get that the book falls 4 ft. in (1/2) second !!

Move faster, Theodore !!

What is the quotient of (9.184×10−4)÷(2.87×10−2) written in scientific notation?

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So we really have  (9.184/2.87) X (10^-4/10^-2)

This simplifies to (3.2) X (10²) /(10⁴) =

(3.2) X 10^-2

And that's it.........

what is the next atep in solving this equation?.... 61=3341-2900cosX 

you are solving for X

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OK......first, let's subtract 3341 from each side   This gives

-3280 = -2900cosX

Divide both sides by -2900   We have

1.131 = cosX

Do you see the problem here??

The cosine function only returns values between -1 and 1, inclusive.

Thus, this problem has no solution !! 

60mm in cm

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There are 10 mm in each cm

Then

60mm x (1cm)/(10 mm) = 6 cm  (The mm units "cancel" each other out, and I'm just left with cm)

Greg made 9 gallons of chili dinner.Each bowl can hold 2 full ladles of chili.A full ladle holds 10 ounces. what is the greatest number of bowls he can fill with chili?

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Well....if he just dumped all of it into my SuperSized bowl, we wouldn't have to worry about it !!

OK....I'll get serious......

Let's see...each bowl holds 20 ounces (2 ladles full)

If we're in the U.S., we have 128 ounces to a gallon. So 9 gallons X nimber ounces in each gallon (128) = 1152 ounces. So dividing 1152 ounces by the number of ounces each bowl will hold (20), we get 57.6 bowls.

If we're in the U.K., we have 160 ounces to a gallon. So 9 gallons X nimber ounces in each gallon (160) = 1440 ounces. So dividing 1440 ounces by the number of ounces each bowl will hold (20), we get 72 bowls!!

Moral of the story........I'm moving to the U.K.    

csc138 degrees 23 inches

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I believe you have been asked to find this:   csc (138°0′23″)

The little   ″   means "seconds" (not "inches")......To be fair, I always wondered why this symbol was adopted, too!!  It IS a little confusing, if we don't know the context!!

Well, anyway....1 second = 1/3600th of a degree. We need to find a decimal value for 23 of them.

That's easy...it's just 23 x (1/3600) = .00639

Now....we're ready to rock and roll!!

So, we want to find csc(138.00639°)

And, using the on-site calculator, we have:

csc(138.00639°) ≈ 1.49

Also, note that the  ′ symbol means "minutes" (not "feet")    1 minute = 1/60th of a degree

Hey.....good thing they didn't divide degrees up into "yards," as well, huh??? I don't know what symbol we could have used for that !!

I think that's all ....  

a^b=b where a and b are different numbers

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Let a = √(2) .....let b = 2

Then....... (√(2))² = 2

Note that a, b ARE "different," since √(2) ≠ 2

(You didn't specify that "a" had to be an integer, only a "number"!!) 

the lateral area of a cone with radius 4 cm is 60 cm. a) Determine the slant height of the cone? b) Determine the height of the cone.

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The "formula" for the lateral surface area of a  cone is given by:

A = π * r * l

Where A is the area, r is the radius, and l is the slant height.  For convenience, I'll use 3.14 for π.  So we have....

60 = 3.14 * 4 * l   Solving for l, we have....

(60)/(3.13 * 4) = l  ≈ 4.77 cm.

Now, to find the height, we can note that the height and the radius form two legs of a right triangle, and the slant height, l, forms the hypoteneuse. Something like this:

So we have, using the Pythagorean Throrem, h = SQRT( l² - r²)

So we have:

h = SQRT(4.77² - 4²) ≈ 2.6 cm.

That makes sense. It should be less than the hypoteneuse.....and it is!! It's always good to check that your answer is "reasonable!!"  Also note, that it's a pretty "flat" cone!!!