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topjm [15]
3 years ago
5

(6) (Bonus) A rectangular box has its edges changing length as time passes. At a particular instant, the sides have lengths a =

150 feet, b = 80 feet, and c = 50 feet. At that instant, a is increasing at 100 feet/sec, b is decreasing 20 feet/sec, and c is increasing at 5 feet/sec. Determine if the volume of the box is increasing, decreasing, or not changing at all, at that instant.
Mathematics
1 answer:
tamaranim1 [39]3 years ago
3 0

Answer:

Increasing,310000ft^3/s

Step-by-step explanation:

We are given that

a=150 feet

b=80 feet

c=50 feet

\frac{da}{dt}=100ft/s

\frac{db}{dt}=-20ft/s

\frac{dc}{dt}=5ft/s

We have to find the volume of the box  of the box increasing,decreasing or not changing at all at that instant.

We know that

Volume of box=lbh

Using the formula

Volume of box,V=abc

Differentiate w.r.t t

\frac{dV}{dt}=\frac{da}{dt}bc+\frac{db}{dt}(ac)+\frac{dc}{dt}(ab)

Substitute the values

\frac{dV}{dt}=100(80\times 50)-20(150\times 50)+5(150\times 80)

\frac{dV}{dt}=310000ft^3/s

Hence, the volume of the box is increasing .

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Drag the choices into the boxes to explain how all real numbers have a decimal expansion.
KATRIN_1 [288]

The decimal forms of some real numbers, like( 3/16), terminate, while the decimal forms of other real numbers, like(4 2/11 ), do not terminate, but have a repeating pattern. Still, other real numbers, like(5 squared ), have decimal forms that neither terminate nor repeat.

Step-by-step explanation:

1. The decimal forms of some real numbers, like( ), terminate

A number is terminating if it has decimal with finite number

So, \frac{3}{16}= 0.1875 as decimal stops after 4 digits so it is terminating.

2.  the decimal forms of other real numbers, like( ), do not terminate, but have a repeating pattern.

A number that do not terminate, but have a repeating pattern.

So, 4 \frac{2}{11} =\frac{44}{11}=4.1818181

3. have decimal forms that neither terminate nor repeat

5^2 = 25 it neither terminates nor repeat

So, answers will be:

The decimal forms of some real numbers, like( 3/16), terminate, while the decimal forms of other real numbers, like(4 2/11 ), do not terminate, but have a repeating pattern. Still, other real numbers, like(5 squared ), have decimal forms that neither terminate nor repeat.

Keywords: Decimals

Learn more about decimals at:

  • brainly.com/question/10941043
  • brainly.com/question/4390083

#learnwithBrainly

6 0
3 years ago
Figures A and B at right are similar. Assuming that figure A is the original figure, find the scale factor and find the lengths
AnnZ [28]

The scale factor is: 1/5.

The missing sides of figure B are: 2.4, 3.6, and 4.

<h3>How to find Scale Factor?</h3>

Scale factor = dimension of new figure / dimension of original figure

The polygons given are shown in the diagram attached below.

Figure A is the original figure

Figure B is the new figure.

x, y, and z has been used to mark the missing sides of figure B.

One dimension of original figure = 15

Corresponding dimension of the new figure = 3

Scale factor = new/original = 3/15

Scale factor = 1/5

To find the missing sides of figure B, multiply each corresponding side lengths of Figure A by the scale factor:

x = 12 × 1/5 = 2.4

y = 18 × 1/5 = 3.6

z = 20 × 1/5 = 4

In summary:

The scale factor is: 1/5.

The missing sides of figure B are: 2.4, 3.6, and 4.

Learn more about scale factor on:

brainly.com/question/2826496

3 0
3 years ago
Math halp please. Ty
77julia77 [94]
The 1st one is the right answer
4 0
3 years ago
Someone help me on this question..
inna [77]

Answer:

CD= 9

Step-by-step explanation:

AD and CD are the same length. The length of AD is 9. So the length of CD will also be 9. I hope that helps.

4 0
3 years ago
Please help! This is 6th grade math on surface area.
KatRina [158]

Answer:

<u>144</u>

Step-by-step explanation:

Ok. I love problems like this.

You just have to find the surface are of each part and add it up!

To find the surface area of a rectangle, you multiple the base and the height. To find the surface area of a triangle, you multiple the base and height, and divide by 2 (because its half of a rectangle).

<u>Left rectangle:</u> 3*ll=33

<u>Middle rectangle:</u> 4*ll=44

<u>Right rectangle:</u> 5*ll=55

<u>Top triangle:</u> 3*4=12

                      12/2=6

<u>Bottom triangle:</u> 3*4=12

                           12/2=6

<u>ADD THEM ALL!!!</u> 33+44+55+6+6=<u>144</u>

<u></u>

<u></u>

(Also can I please please please have brainliest? I need it to level up!)

5 0
3 years ago
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