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Grace [21]
4 years ago
9

a female bunny gained one pound per week for six weeks. a male bunny gained two pounds per week for six weeks. how many more pou

nds did the male bunny gain than the female bunny. two pieces of information are missing
Mathematics
1 answer:
tester [92]4 years ago
3 0
6 more
What was the start and end weight
Did they start at the same time maybe
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2.66a-6b

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The base and sides of a container is made of wood panels. The container does not have a lid. The base and sides are rectangular.
vfiekz [6]

Answer:

Minimum surface area =70.77 cm^2

Step-by-step explanation:

We are given that

Width of container=x cm

Length of container=2x cm

Volume of container=54 cm^3

We have to find the minimum surface areas that this container will have.

Volume of container=l\times b\times h

x\times 2x\times h=54

2x^2h=54

h=\frac{54}{2x^2}=\frac{27}{x^2}

Surface area of container=2(b+l)h+lb

Because the container does not have lid

Surface area of container=S=2(2x+x)\times \frac{27}{x^2}+2x\times x

S=\frac{162}{x}+2x^2

Differentiate w.r.t x

\frac{dS}{dx}=-\frac{162}{x^2}+4x

\frac{dx^n}{dx}=nx^{n-1}

Substitute \frac{dS}{dx}=0

-\frac{162}{x^2}+4x=0

4x=\frac{162}{x^2}

x^3=\frac{162}{4}=40.5

x^3=40.5

x=(40.5)^{\frac{1}{3}}

x=3.4

Again differentiate w.r.t x

\frac{d^2S}{dx^2}=\frac{324}{x^3}+4

Substitute x=3.4

\frac{d^2S}{dx^2}=\frac{324}{(3.4)^3}+4=12.24>0

Hence, function is minimum at x=3.4

Substitute x=3.4

Then, we get

Minimum surface area =\frac{162}{(3.4)}+2(3.4)^2=70.77 cm^2

8 0
3 years ago
Please help quick!!<br>​
Nataly [62]

Hi !

∫ \frac{t}{t + 1}dt

We need to prove that it is equal to

∫ \frac{u - 1}{u}du

As per given options, Substitute <em>u</em> by <em>t</em><em>+</em><em>1</em><em> </em>

=  > ∫ \frac{u - 1}{t + 1} du

<em>Then</em><em> </em><em>given</em><em> </em><em>t</em><em> </em><em>=</em><em> </em><em>u</em><em>-</em><em>1</em>

=  > ∫ \frac{t}{t + 1} du

Then substitue the third given value also

=  > ∫ \frac{t}{t + 1} dt

Therefore, it's <u>proved</u>

~<em>Hop</em><em>e</em><em> </em><em>i</em><em>t</em><em> </em><em>h</em><em>e</em><em>l</em><em>p</em><em>s</em>

7 0
2 years ago
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