Provide an appropriate response.Use the Intermediate Value Theorem to prove that x(x - 6)2 = 6 has a solution between 5 and 7.
What will be an ideal response?
Let f(x) = x(x - 6)2 and let y0 = 6. 
and 
Since f is continuous on 
and since 
is between 
and 
by the Intermediate Value Theorem, there exists a c in the interval 
with the property that 
Such a c is a solution to the equation 
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Solve the problem.Find the volume of the region bounded by the cylinder 
and the planes 
and 
.
A. 6? B. 12? C. 36? D. 18?
Find the length and direction (when defined) of u × v.u = - 
i + 
j + k, v = i + j + 2k
A. 2
; - 
i + 
j - 
k
B. 8; 
i - 
j + 
k
C. 2
; 
i + 
j - 
k
D. 8; 
i - 
j - 
k
Solve.A comet has an orbit that is hyperbolic in shape with Mars as the focus of the hyperbola. The comet heads towards Mars, comes within 310 million miles of Mars, but then veers off as shown in the picture. As it travels into the distance, it moves closer and closer to the line y = 4x. Find the equation that describes the path of the comet. 
A. The equation is 
- 
= 1, where x and y are measured in millions of miles.
B. The equation is 
- 
= 1, where x and y are measured in millions of miles.
C. The equation is 
- 
= 1, where x and y are measured in millions of miles.
D. The equation is 
- 
= 1, where x and y are measured in millions of miles.
Solve.
x - 7 = 25
A. x = 31.25 B. x = 48.75 C. x = 22.5 D. x = 40