All categories

3 years ago

Find the domain and range

Mathematics

1 answer:

LiRa [457]3 years ago

6 0

Answer:

Domain: x = all reals

Range: y is less than or equal to -4

You might be interested in

A cylindrical can without a top is made to contain 25 3 cm of liquid. What are the dimensions of the can that will minimize the

Basile [38]

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= $\pi r^2h$

According to the problem,

$\pi r^2 h=25$

$\Rightarrow h=\frac{25}{\pi r^2}$

The surface area of the base of the can is = $\pi r^2$

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× $\pi r^2$ )

The lateral surface area of the can is = $2\pi rh$

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× $2\pi rh$ )

$=\$2.5 \pi r h$

Total cost of metal is C= 2.00 $\pi r^2$ + $2.5 \pi r h$

Putting $h=\frac{25}{\pi r^2}$

$\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}$

$\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}$

Differentiating with respect to r

$C'=4\pi r- \frac{62.5}{ r^2}$

Again differentiating with respect to r

$C''=4\pi + \frac{125}{ r^3}$

To find the minimize cost, we set C'=0

$4\pi r- \frac{62.5}{ r^2}=0$

$\Rightarrow 4\pi r=\frac{62.5}{ r^2}$

$\Rightarrow r^3=\frac{62.5}{ 4\pi}$

⇒r=1.71

Now,

$\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0$

When r=1.71 cm, the metal cost will be minimum.

Therefore,

$h=\frac{25}{\pi\times 1.71^2}$

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

6 0

3 years ago

Line m and point P are shown below. Part A: Using a compass and straightedge, construct line n parallel to line m and passing th

Morgarella [4.7K]

Answer:

The steps to construct a a line parallel to another line from a point includes

1) From the given line draw a transversal through the point

2) With the compass, copy the angle formed between the transversal and the given line to the point P

3) Draw a line through the intersection of the arcs of the angle construction to get the parallel line through the point P

Step-by-step explanation:

8 0

3 years ago

What is the "k" value of the following function? Is it 3, -2, -3, or 2?

snow_tiger [21]

Answer:

-3

Step-by-step explanation:

we khow that the vertex form of a function is written this way :

f(x)=a(x-h)²+k

the coordinates of the vertex are (h,k) so from the graph we can deduce that k = -3

5 0

3 years ago

There are 3 times as many students participating in the hiking trip this year than last year. There are 42 students on the trip

dalvyx [7]

Answer:

Step-by-step explanation:

42 divided by 3 is 14

8 0

3 years ago

Read 2 more answers

R is less than or equal to -9

Damm [24]

R<_-9

Hope this helps

5 0

3 years ago