CPhill

The surface area is given by

SA= 2*pi*r*h + 2*pi*r^2      so we have

70 = 2*pi*r*h + 2*pi*r^2     divide by 2pi   and rearrange

r^2 + hr - 35/pi = 0              add 35/pi to both sides

r^2 + hr  =  35/pi                complete the square

r^2 + hr + (h^2/4) = 35/pi + (h^2/4)  factor

(r + h/2 )^2 = 35/pi + (h/2)^2   take the positive root of both sides

r + h/2 = √(35/pi + (h/2)^2)   subtract h/2 from both sides

r = √(35/pi + (h/2)^2) - h/2

6√20 + 8√5 - 5√45  =

6√(4*5) + 8√5 - 5√(9*5) =

6(2)√5 + 8√5 - 5(3)√5 =

12√5 + 8√5 - 15√5 =

20√5 - 15√5 =

5√5

x+10>10   subtract 10 from both sides

x > 0

x+10<9   subtract 10 from both sides

x < -1

If, by the word "and," you want the intersection of these two solutions......it doesn't exist.....there is no "overlap" on the number line of the two solutions......the answer is { }  = the empty set

-2x^3 - 2x^2 + 112x    take out the greatest common factor -2x.....so we have.....

-2x(x^2 + x - 56)      factor the expression in the parentheses

-2x(x + 8)(x - 7)

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

17<7p+3<24   subtract 3 from everything

14 < 7p < 21    divide everything by 7

2 < p < 14

On the number line, put circles at 2 and 14 and "shade" between them

(1/15)<((4-5x)/(15))<(2/3)   multiply everything by 15

1 < 4 - 5x < 10       subtract 4 from everything

-3 < -5x < 6          divide everything by -5 and reverse the inequality signs

3/5 > x > -6/5

On the number line, put circles at -6/5 and 3/5...."shade" between these

So we have

-42 < 7N < 42   divide by 7 on each term

-6 < N < 6

In interval notation, we have

(-6, 6)

If it's 8x⁰, the answer is 8

If it's (8x)⁰, the answer is 1

x^2-y^2=8
x-y=2            

Using the second thing, we can add y to both sides and subtract 2 from both sides....this gives

y = x - 2      and substituting this into the first equation, we have

x^2 - (x - 2)^2  = 8      expand   and simplify

x^2 - (x^2 - 4x + 4) = 8

x^2 - x^2 + 4x - 4 = 8

4x - 4  = 8      add 4 to both sides

4x = 12         divide by 4

x = 3

And, since y = x - 2. we have   y = 3 - 2 = 1

So....our solution is    (3, 1)

Nice, happy7.....this is always a "trick" question.......