What is the exact volume of the cylinder radius is 4 inches height is 8 inches

Mathematics

1 answer:

Gelneren [198K]4 years ago

4 0

The Answer Is A 32n In^3

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Plz help

Len [333]

52x38=1976, 1976 is the answer

5 0

3 years ago

What solution is this w = 10

alina1380 [7]

Answer:

w = 10

Step-by-step explanation:

9(w - 9) -2 = -7 + 7(w -8)

Expand:

9w - 81 - 2 = -7 + 7w - 56

Rearrange:

9w - 7w = -7 - 56 + 81 + 2

2w = 20

w = 10

3 0

3 years ago

What’s the domain and range of:<br> log(√(2x-1) + 3 )<br> Please explain how you got it too!!

Radda [10]

Two main facts are needed here:

1. The logarithm $\log x$ , regardless of the base of the logarithm, exists for $x>0$ .

2. The square root $\sqrt x$ exists for $x\ge0$ .

(in both cases we're assuming real-valued functions only)

By (2) we know that $\sqrt{2x-1}$ exists if $2x-1\ge0$ , or $x\ge\dfrac12$ .

By (1), we know that $\log(\sqrt{2x-1}+3)$ exists if $\sqrt{2x-1}+3>0$ , or $\sqrt{2x-1}>-3$ . But as long as the square root exists, it will always be positive, so this condition will always be met.

Ultimately, then, we only require $x\ge\dfrac12$ , so the function has domain $\left[\dfrac12,\infty)$ .

To determine the range, we need to know that, in their respective domains, $\sqrt x$ and $\log x$ increase monotonically without bound. We also know that $x=\dfrac12$ at minimum, at which point the square root term vanishes, so the least value the function takes on is $\log3$ . Then its range would be $[\log3,\infty)$ .