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vagabundo [1.1K]
3 years ago
5

A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by V = x2h

cm3. Find the rate at which the volume of the box is changing when the edge length of the base is 4 cm, the edge length of the base is increasing at a rate of 2 cm/min, the height of the box is 15 cm, and the height is decreasing at a rate of 3 cm/min.
Mathematics
1 answer:
Tanya [424]3 years ago
8 0

Answer:

  192 cm^3/min

Step-by-step explanation:

Differentiating the volume expression, we get ...

  dV/dt = 2xh(dx/dt) +x^2(dh/dt)

We are given that ...

  x = 4 cm, dx/dt = 2 cm/min, h = 15 cm, dh/dt = -3 cm/min

Putting these values into the formula for volume rate of change, we get ...

  dV/dt = 2(4 cm)(15 cm)(2 cm/min) +(4 cm)^2(-3 cm/min)

  = 240 cm^3/min -48 cm^3/min

  dV/dt = 192 cm^3/min

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Answer:

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Step-by-step explanation:

Allele frequency is how often an allele occurs in a gene pool relative to the other alleles for that gene

<u>Genotype</u>    <u> No. of Individuals</u><u> </u>     <u>No. of Allele </u><u>B</u>   <u>No. of Allele</u><u> b </u>                      

BB                    30                            30*2 =60                   30*0 =0

Bb                     10                            10*1 =10                       10*1=10

bb                     10                             10 *0 =0                      10*2=20

Total                 50                              70                                 30

Total no. of alleles = 70+30 =100

The frequency of allele B :\frac{\text{number of B alleles}}{\text{total number of alleles}}

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The frequency of allele b :\frac{\text{number of b alleles}}{\text{total number of alleles}}

:\frac{30}{100}

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Hence the frequency of allele B is 0.7 and allele b is 0.3 in population’s gene pool.

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