Which choice correctly shows the solution(s) of the equation x2 = 400?

A 25/9 <br> B 125/9<br> C 32 <br> D 64

andrezito [222]

Answer:

Length = 5 feet

Breadth = (5/3) feet

Height(depth) = 2 feet

Volume of the entire tank = Length x Breadth x Height

= $5 \times \frac{5}{3} \times2 = \frac{50}{3}$ ----------(1)

Water is filled upto a height of (1/3) feet

Volume of water in the tank = Length x Breadth x Height

= $5 \times \frac{5}{3} \times \frac{1}{3} = \frac{25}{9}$ -------------(2)

Volume of space needed to be filled = (1) - (2)

= $\frac{50}{3} -\frac{25}{9} = \frac{150-25}{9} = \frac{125}{9} cubic feet$

OR

Height of tank needed to be filled = 2 - (1/3) = (5/3) feet

Volume of space = Length x Breadth x Height of empty tank

= $5 \times \frac{5}{3} \times \frac{5}{3} = \frac{125}{9} cubic \ feet$

8 0

3 years ago

A hotel chain charges $75 each night for the first two nights and $50 for each additional night’s stay. the total cost t is a fu

g100num [7]

you would need a function to determine whether to use a formula for 1 or 2 nights or a formula for more than 2 nights

T(x)={a if x <_ 2, b if x > 2}

if it's 2 nights or less use option a, a = 75x

if its longer than 2 days use option b, b= 50x + 50

5 0

3 years ago

Read 2 more answers

Integers between -2 and +3

saveliy_v [14]

Answer:

-1, 0, 1, 2,

Step-by-step explanation:

8 0

3 years ago

Melissa’s birthday is next week and she has been receiving cards in the mail with different amounts of money. She has received 5

hoa [83]

Adding another card with value $25 would decrease the standard deviation because it is closer to the mean the the current standard deviation.

3 0

3 years ago

Read 2 more answers

A model for tumor growth is given by the Gompertz equation dV dt = a (In b-, In V) V where a >0 and b >0 are constants and

Xelga [282]

Answer:

$V(t) = b^{(1-e^{-at})}$

Step-by-step explanation:

We are given the following information in the question:

$\displaystyle\frac{dV}{dt} = a (In b - In V) V$

where a > 0 and b > 0.

$\displaystyle\frac{dV}{dt} = a (In b-In V) V\\\\\displaystyle\frac{dV}{dt} = -aV(ln\frac{V}{b})\\\\\frac{dV}{V(ln\frac{V}{b})} = (-a)dt\\\\\text{Put } ln\frac{V}{b} = z\\\\\text{Integrating both sides}\\\\\int \frac{dV}{V(ln\frac{V}{b})} = \int (-a)dt\\\\\text{We get}\\\\\int \frac{dz}{z} = \int (-a)dt\\\\\\\text{where C is the constant of integration}$

$V(0) = 1~ mm^3\\V(t) = b.e^{e^{-at+C}}\\\text{Putting t =0, V(0) = 1}\\\\V(0) = 1 = b.e^{e^{C}}\\\\V(t) = b^{(1-e^{-at})}$

where v(t) is the required tumor volume as a function of time that has an initial tumor volume of V(0) = 1 cubic mm.

5 0

3 years ago