CPhill

Just set both factors to 0 and solve.....so we have

c(7c – 1) = 0

c = 0      is one solution

And

7c - 1  = 0     add 1 to both sides

7c  = 1        divide  both sides by 7

c = 1/7      and that's the other solution

There is no hard and fast rule, here....it depends upon the situation......however.....remember that sin (theta)  = sin (180 - theta).... and the inverse sine only returns angle values from -90° to 90°....so that's the reason that 106.6° will not be returned as an answer

If you know all three sides of a triangle.....the Law of Cosines will always produce the correct result

For example  if you know sides a, b and c ......you can find angle A  thusly

a^2  =  b^2 + c^2  - 2(b)(c)cos A

So

cos^-1 [ ( a^2 - b^2  - c^2) / ( -2(a)(b)) ]   =   A

LOL, Melody !!!!

I think you mean the sine inverse......hit the "2nd" button.......the "asin" button is the sine inverse

The area  is given by :

30 * (1/2) * (7^2) * sin (12°)  ≈   152.8 mm^2  

[ I think geno's answer would be the same.....]

Tax on video game - Tax on book  =

.095 [ 45 - 12]  = about $3.14  more

The sum of the entries in row 10 of Pascal's Triangle  = 2^10  = 1024  where row "0"  = 1

log₄ 6 + log₄ (x + 1) = 2    

We can write

log₄ [6 * (x + 1) ]  = 2

In exponential form, we have

4^2   =  6 (x + 1)    simplify

16 = 6x + 6      subtract 6 from both sides

10  = 6x      divide both sides by 6

10/ 6  = x  =   5/3

Since the area of the lawn = area of the store.... the area of the store must occupy 1/2 of the lot = (1/2)(70 * 45)  = 1575m^2

So....let x  be the width of the walk...so  the area of the store can be represented by

(70 - 2x) (45 - 2x)  = 1575

Solving this for x we have that x ≈ 7.9459 m  = the width of the walk

The dimesions of the store are :

70 - 2(7.9459) = 54.1082 m

45 -2(7.9459)  = 29.1082 m

So the dimensions of the store are   54.1082m x 29.1082m

We can use logic here :

Note that when Car B started......Car A has already traveled 30 miles.......so.....Car B must make up a 30 mile gap

And the difference in speeds  is  40 - 30  = 10 mph

So.....Car B  makes up a 10 mile gap every hour.....so.....it must take Car B  3 hours to catch Car A, i.e, at  1 PM