All categories

3 years ago

Simplify sqrt(x^2-16)

1 answer:

4 0

Remember for this type of question.I'm guessing you make the equation equal to 0. Then square both sides the (X ^2-16) and 0. Then the square root goes away. Then you factor it according to the difference of squares method. By taking the square root of x^2 and 16. So ultimately it turns into 2 binomials according to the difference of squares method. The simplified answer would be (X-4)(X+4)=0. To solve for x in each case, take each respective equation separately and make it equal to 0. Solve for x.

You might be interested in

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago

On the 1st of November 2015 there were 4200 trees planted in a wood

gayaneshka [121]

Answer:On 1st November 2016, only 3948 of these trees were still alive.

Step-by-step explanation:

Sorry if it’s wrong

5 0

2 years ago

If you borrow $900 for 6 years at

attashe74 [19]

Answer:

$1278

Step-by-step explanation:

First you would need to find out how much the annual interest rate is so you would find out what 7% of $900 is which is 63 meaning that there is an annual fee of $63 and since it was for 6 years you would multiply $63 times 6 to get 378 and then to find the total amount you would pay you have to add the interest to what you borrowed so you would do $900 + $378

4 0

3 years ago

Evaluate the following expression when x=2 and y=3.<br> 6у/x

vfiekz [6]

Answer:

Step-by-step explanation:

6y/x

6*3/2

18/2

8 0

3 years ago

Read 2 more answers

Identify the slope and the y-intercept in the equation y = -3/4x + 3. Please make sure to say which is the slope and which is th

Liula [17]

Answer:

the y -intercpt is the 3

the slope is -3/4

Step-by-step explanation:

this is because the 3 is the starting point on the y-axis and the slope is -3/4 because you are going down 3 to the right 4 ---hope this helps

5 0

3 years ago

Read 2 more answers