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3 years ago

Simplify 3 Square root of 3 multiplied by 6 square root 6

Mathematics

1 answer:

kvasek [131]3 years ago

7 0

Answer:

54√2

Step-by-step explanation:

3√3 * 6√6

number x number = 6 * 3 = 18

root * root = √18 = √3^2 *.2 = 3√2

18 * 3 = 54

54√2

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Simplify this expression.

Tresset [83]

Answer:

Step-by-step explanation:

Second option correct

6 0

3 years ago

Find the absolute maximum and minimum values of the function below. f(x) = x3 − 9x2 + 3, − 3 2 ≤ x ≤ 12 Solution Since f is cont

Neko [114]

Answer:

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

Step-by-step explanation:

The correct statement is described below:

Find the absolute maximum and minimum values of the function below:

$f(x) = x^{3}-9\cdot x^{2}+ 3$ , $2 \leq x \leq 12$

Given that function is a polynomial, then we have the guarantee that function is continuous and differentiable and we can use First and Second Derivative Tests.

First, we obtain the first derivative of the function and equalize it to zero:

$f'(x) = 3\cdot x^{2}-18\cdot x$

$3\cdot x^{2}-18\cdot x = 0$

$3\cdot x \cdot (x-6) = 0$ (Eq. 1)

As we can see, only a solution is a valid critical value. That is: $x = 6$

Second, we determine the second derivative formula and evaluate it at the only critical point:

$f''(x) = 6\cdot x -18$ (Eq. 2)

x = 6

$f''(6) = 6\cdot (6)-18$

$f''(6) =18$ (Absolute minimum)

Third, we evaluate the function at each extreme of the given interval and the critical point as well:

x = 2

$f(2) = 2^{3}-9\cdot (2)^{2}+3$

$f(2) = -25$

x = 6

$f(6) = 6^{3}-9\cdot (6)^{2}+3$

$f(6) = -105$

x = 12

$f(12) = 12^{3}-9\cdot (12)^{2}+3$

$f(12) = 435$

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

6 0

3 years ago

A camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. If the rope is 8 feet long,

irina [24]

Using the Pythagorean theorem 4 would be the height and 8 would be the hypotenuse, you need to find the base

4^2 + X^2 = 8^2

16 x x^2 = 64

x^2 = 64-16
x^2 = 48

x = sqrt(48) = 6.92 feet ( round answer as needed )

6 0

3 years ago

PLEASE HELPPPP I NEED THIS FASTTTTT

rusak2 [61]

Answer:

$there \: are \: 8 \: values \\ = \frac{8}{17} \times 100\% \\ = 47\%$

6 0

2 years ago

∠1 and ∠2 are supplementary angles. If m∠1 = 77°, then m∠2 =

posledela

Answer:

B. 103°

Step-by-step explanation:

Supplementary angles add up to 180°, so we can find the measure of angle 2 by subtracting 77 from 180

180 - 77

= 103

So, m∠2 is 103°

7 0

2 years ago