Answer:
To figure out the common denominator for these fractions, I'll first need to factor that quadratic in the denominator on the right-hand side of the rational equation. This will also allow me to find the disallowed values for this equation. Factoring gives me:
x2 – 6x + 8 = (x – 4)(x – 2)
The factors of the quadratic on the right-hand side "just so happen" to be duplicates of the other denominators. This often happens in these exercises. (So often, in fact, that if you get completely different factors, you should probably go back and check your work.)
Step-by-step explanation:
Answer:
the bottom left one
Step-by-step explanation:
Answer:
cos 37=x/b (second one)
sin 37= a/b (third one)
tan 37=a/x (sixth one)
Step-by-step explanation:
Cos is defined by the adjacent side over the hypotenuse. Cos 37 would be x/b. Clearly, that is option 2. Sin is defined by opposite over hypotenuse. Sin 37 would be a/b. That is the 3rd option. Tan is defined by opposite over adjacent. Tan 37 would be a/x or the 6th option.
36 is a perfect square, but its factors include 1 and 36, 6 and 6, 4 and 9, 3 and 12, and 2 and 18. that's 9 factors, not 3.
Volume of cylinder:
V = πr²h
The desired volume is 1 Liter = 1000 cm³
1000 = πr²h
h = 1000/πr²
Surface area of cylinder:
S.A = 2πr² + 2πr²h
We substitute the value of h from the first equation:
S.A = 2πr² + 2πr(1/πr²)
S.A = 2πr² + 2/r
Now, to minimize surface area, we differentiate the expression with respect to r and equate to 0.
0 = 4πr - 1000/r²
4πr³ - 1000 = 0
r = 4.3 cm
h = 17.2 cm
