CPhill

This function is at its max when x = 0......then y = 1, i.e.,  b = 1

As x becomes greater and greater in  both positive and negative diections, the denominator  → ∞ and y → 0 =  a

So the range is (0, 1 ]

x = 7 is just a vertical line through the x axis at, surprise, (7, 0)  !!!

The slope of a vertical line is undefined...there is no y intercept...this line never intersects the y axis....

-3x^2+sqrt(2x)+1/2 ......when x = √2, we have

-3(√2)^2 + √(2√2) + 1/2 =

-3(2) + √(2√2) + 1/2 = about -3.818

Add the coins and currency in with the checks....this will be the gross deposit....doing a quick check with the calculator......this = the net deposit.......so no cash was given back.

$9998.67 is your answer

We have a right triangle where GI is the hypoteneuse and IH is one of the legs.....by the Pythagorean Theorem,

HG = √(52²- 21²)

And we can find angle I by using the tangent inverse

tan^-1 (√(52²- 21²) / 21) = about 66.18°

We have

sin(48) = c /3   just multiply both sides by 3....so we have

3 * sin(48)  =  c  

I'll let you evaluate that one !!!

Note, Anonymous 1.3333 is ok, but to be precise......1 + 1/3  (or 4/3) is better !!!

Yep.....

Since we can't take the square root of a negative quantity, we need to find where -10x^2 - 11x + 6 = 0

Set  it  = 0  and multiply through by a -1....so we have

10x^2 + 11x - 6 = 0    factor, if possible

(5x - 2)(2x + 3) = 0

Setting each to 0, we have that x = 2/5 and  x = -3/2

Now, we need to find the intervals where -10x^2 - 11x + 6 < 0

This will occur at either  x < -3/2  or     -3/2 < x  < 2/5       or     x > 2/5

Letting x = 0 we see that -3/2 < x  < 2/5  "works"

If you pick any point in the other two intervals, the expression inside the radical will be < 0.

So, our answer is  -3/2 ≤ x ≤ 2/5