4. The equation is an exponential function where all y coordinates are above 4 (range is y>4), so for y=4 (answer D) there are no solutions. y=4 is the asymptote.
5. In a formula ax^2 + bx + c the discriminant is b^2-4ac. In this example the discriminant is 9-4*3*6 = -63. The fact that this value is negative reveals that this equation has no (real) solutions, only imaginary.
6. y=2x^2-x-5. Trial and error.
Answer:
The volume of the solid is 19.
unit³
Step-by-step explanation:
The given function is y = x³
The solid is created by revolving R about the line y = 1
We have that when y = 1, x = 1
Taking the end point as x = 2, we have the volume given by the washer method as follows;
![V = \pi \cdot \int\limits^a_b {\left( [f(x)]^2 - [g(x)]^2 \right)} \, dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Ccdot%20%5Cint%5Climits%5Ea_b%20%7B%5Cleft%28%20%5Bf%28x%29%5D%5E2%20-%20%5Bg%28x%29%5D%5E2%20%5Cright%29%7D%20%5C%2C%20dx)
Where;
a = 1, and b = 2, we have;
g(x) = 1
![V = \pi \cdot \int\limits^{2}_1 {\left( [x^3]^2 - [1]^2 \right)} \, dx = \pi \cdot \left[\dfrac{x^7}{7} + x \right]_1^{2} = \pi \cdot \left[\dfrac{2^7}{7} +2 -\left( \dfrac{1^7}{7} + 1\right)\right] =19\dfrac{1}{7}](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Ccdot%20%5Cint%5Climits%5E%7B2%7D_1%20%7B%5Cleft%28%20%5Bx%5E3%5D%5E2%20-%20%5B1%5D%5E2%20%5Cright%29%7D%20%5C%2C%20dx%20%20%3D%20%5Cpi%20%5Ccdot%20%5Cleft%5B%5Cdfrac%7Bx%5E7%7D%7B7%7D%20%2B%20x%20%5Cright%5D_1%5E%7B2%7D%20%3D%20%5Cpi%20%5Ccdot%20%5Cleft%5B%5Cdfrac%7B2%5E7%7D%7B7%7D%20%2B2%20-%5Cleft%28%20%5Cdfrac%7B1%5E7%7D%7B7%7D%20%2B%201%5Cright%29%5Cright%5D%20%3D19%5Cdfrac%7B1%7D%7B7%7D)
The volume of the solid, V = 
unit³ = 19. unit³
A piece of wood 10 yards long
and
A piece of wood 5 feet long
He has two pieces of wood. How much does he have in all?
5+10 = 15
15 feet of wood
