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ira [324]
3 years ago
12

A six-ounce paper cup has a hole in the bottom and leaks water. If it was originally full and has only two ounces after 40 minut

es, what is the rate of change of the amount of water in the cup per minute?
1/10 ounces per minute.

-1/10 ounces per minute.

10 ounces per minute

-10 ounces per minute
Mathematics
2 answers:
Sveta_85 [38]3 years ago
6 0
Hey there, 

Lets solve this problem together. 

We know that a <span>six-ounce paper cup has a hole in the bottom and leaks water. If it was originally full and has only two ounces after 40 minutes.
 
</span>(0,6)(40,2)&#10;&#10; (slope) = (2-6) / (40 - 0)&#10;&#10;slope = -4/40&#10;&#10;slope = -1/10 per minute
Pie3 years ago
5 0
(0,6)(40,2)
rate of change (slope) = (2-6) / (40 - 0)
slope = -4/40
slope = -1/10 per minute


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10 POINTS PLEASE HELP!
Cerrena [4.2K]

When the surrounding flaps are folded up, the base of the box will have dimensions 11-2x by 16-2x, and the box will have a height of x. So the box has volume, as a function of x,

V(x)=(11-2x)(16-2x)x=176x-54x^2+4x^3

I don't know what technology is available to you, but we can determine an exact value for x that maximizes the volume by using calculus.

Differentiating V with respect to x gives

\dfrac{\mathrm dV}{\mathrm dx}=176-108x+12x^2

and setting this equal to 0 gives two critical points at

x=\dfrac{27\pm\sqrt{201}}6\implies x\approx2.1\text{ or }x\approx6.9

For the larger critical point we would get a negative volume, so we ignore that one. Then the largest volume would be about 168.5 cubic in.

7 0
3 years ago
she is cutting pieces of ribbon 9 3/8 inches long. About how many pieces can she cut from a 2 yard length of ribbon
MatroZZZ [7]

Answer:

7 pieces

Step-by-step explanation:

Turn yards into inches (2 yards = 72 inches)

Divide: 72÷9\frac{3}{8}

=7.68

7 pieces

7 0
3 years ago
If each interior angle of a regular polygon is 144 degrees. Find the number of sides in it.
andrew11 [14]

Answer:

10

Step-by-step explanation:

In a polygon

interior angle + interior angle = 180°, thus

exterior angle = 180° - 144° = 36°

The sum of the exterior angles in a polygon = 360°, thus

number of sides = \frac{360}{36} = 10

8 0
3 years ago
Read 2 more answers
can anyone help and explain why this is either proportional or not? urgent!! (it needs an explanation too)
adoni [48]
This is not proportional because it does not go through the origin and if you were to draw a straight line it would not not go through all the points.
Hope this helps :)
7 0
3 years ago
The perimeter of the base of a right square pyramid is 48 cm. The height of the pyramid is 12 cm. What is the volume of the pyra
Dimas [21]
V = (1/3)(b^2)(h) 
<span>b = 48/4 = 12cm </span>
<span>h = 12cm </span>
<span>V = (1/3)(144)(12) = 576cm^3 (third choice) </span>

<span>3) </span>
<span>V = (pi)(r^2)(h) </span>
<span>V = (3.14)(64)(8) = 1608cm^3 (not one of the choices but I'm certain that this calculation is correct) </span>
8 0
4 years ago
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