Is -94 a rational number

A cylinder shaped can needs to be constructed to hold 300 cubic centimeters of soup. The material for the sides of the can costs

oksano4ka [1.4K]

Answer:

Step-by-step explanation:

Cost = Area Cylinder body* cost * 0.03 cm^3 + Area of 2 lids*cost 0.06 of cm^3

Volume = 300 cm^3

Volume = Base *h

Volume = pi * r^2 * h = 300

h = 300/(pi * r^2 )

Area material = 2*pi * r * h * 0.03 + 2 pi r^2 * 0.06

Area material = 0.06*pi * r * 300/(pi* r^2) + 0.12 * pi * r^2

dmaterial/dr = (-1)18 r^-2 + 0.12 pi * 2*r

dmaterial/dr = -18 r^-2 + 0.24 pi * r

The minimum occurs when the right side = 0

18/r^2 = 0.24 *pi r

18 = 0.24*pi * r^3

18/(0.24 * pi) = r^3

23.89 = r^3

cube root (23.89) = cuberoot(r^3)

r = 2.88 cm

h = 300/pi * r^2

h = 300/(3.14 * 2.88^2)

h = 11.52

This isn't much of a check but we can try it.

Volume = 3.14 * 2.88^2 * 11.52

Volume = 302.01 which considering all the rounding is pretty close.

Here's a graph that confirms my answer.

3 0

3 years ago

If you work for an hourly wage, your gross pay is a function of the number of hours that you work. If you earn $8 per hour, comp

Gelneren [198K]

1. Let $x$ be the number of hours that you worked. We know from our problem that your hourly wage is $8, so your hourly wage will be given by the linear function: $y=8x$ .
where
$f(x)$ is your gross pay.
$x$ is the number of hours that you worked.

To complete the table, we just need to evaluate the function at the given hours; in other words, we are going to replace $x$ with the number of hours in our linear function:
$y=8(0)=0$
$y=8(3)=24$
$y=8(5)=40$
$y=8(7)=56$
$y=8(10)=80$
$y=8(12)=96$

We can conclude that yous should fill your table as follows:
<span>Number of Hours
0
3
5
7
10
12
</span><span>
Gross Pay
0
24
40
56
80
96

2. Remember that the domain of a function are the set of the x-values of the function; the range of a function are the set of y-values of the function. From our previous point, we can infer that the ordered pairs of the function are: (0,0), (3,24), (5,40), (7,56), (10,80), and (12,96). The y-values and hence the range of the function are: 0, 24, 40, 56, 80, 96. Remember that in the quadrant I both the x-coordinates and the y-coordinates are positive. Since all the coordinates of our points are positive, we can conclude that the correct answer is:
</span><span>d. 0, 24, 40, 56, 80, 96; Quadrant I</span>

6 0

3 years ago

Read 2 more answers

The height of a rectangular prism is 3 in.. The perimeter is 88 in. (4 in. wide and 11 in. long). What is the value of the base?

Mamont248 [21]

<h2>The base of a rectangular prism(b) = 41 in.</h2>

Step-by-step explanation:

Given,

The height of a rectangular prism(h) = 3 in and

The perimeter of a rectangular prism = 88 in

To find, the base of a rectangular prism(b) = ?

We know that,

The perimeter of a rectangular prism = 2l + 2b or 2b + 2h or 2h + 2l

∴ 2b + 2(3) = 88

⇒ 2b = 88 - 6

⇒ 2b = 82

⇒ b = 41 in

Thus, the base of a rectangular prism(b) = 41 in.

7 0

3 years ago

The length of a shadow of a tree is 150 feet when the angle of elevation of the sun is 39°. Approximate the height of the tree.

fomenos

Answer:

The height of tree is approximately 121.5 feet.

Step-by-step explanation:

We are given following in question:

Length of shadow = 150 feet

Angle of elevation of the sun =

$\theta = 39^\circ$

The tree and the shadow forms a right angled triangle.

Thus, with the help of trigonometric relation, we can write:

$\tan \theta = \dfrac{\text{Height of tree}}{\text{Length of shadow}}$

Let x feet be the height of tree.

Putting all the values, we get,

$\tan 39^\circ = \dfrac{x}{150}\\\\0.80978 = \dfrac{x}{150}\\\\\Rightarrow x = 150\times 0.80978\\\Rightarrow x = 121.467 \approx 121.5$

Thus, the height of tree is approximately 121.5 feet.

6 0

4 years ago

How many students choose strawberry kiwi

Akimi4 [234]

Answer:

15 students. 30%

Step-by-step explanation:

3 0

3 years ago