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3 years ago

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a scientist if using a tracking device to measure how fast a blue whale swims. Data from the device show that the whale swam a c

onstant rate for 5 minutes and covered 2.5 miles in that time. make sure a graph showing the change the whales distance over time. how far does a blue whale swim in one minute ?

1 answer:

Dahasolnce [82]3 years ago

6 0

Answer:

it would be 423849+2364355-3213123122+232424-213123:222.222222222222

Step-by-step explanation:

mark it brainliest if it helps you ❤️

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A large tank is filled to capacity with 300 gallons of pure water. Brine containing 5 pounds of salt per gallon is pumped into t

Gwar [14]

Answer:

(a) $A = 1500(1 - e^{-0.01t})$

(b) $t = 0$

Step-by-step explanation:

Given

$V= 300gal$ --- Volume of tank

$B = 5lb/gal$ --- Brine solution

$R_1 = 3gal/min$ --- Rate in, in gallon/min

$R_2 = 6gal/min$ --- Rate out, in gallon/min

Required

Determine A(t)

First, calculate the rate in (R in) and (R out) in lb/min

$R_{in} = B * R_1$

$R_{in} = 5lb/gal * 3gal/min$

$R_{in} = 15lb/min$

R(out) is calculated by multiply the rate at which brine leaves the tank (lb/gal) * R2

So, we have:

$R_{out} = \frac{A(t)}{300} lb/gal * 3gal/min$

$R_{out} = \frac{3*A(t)}{300} lb/min$

$R_{out} = \frac{A(t)}{100} lb/min$

The change in the amount of brin e in the tank at time t is given as:

$A'(t) = R_{in} - R_{out}$

$A'(t) = 15 - \frac{A(t)}{100}$

Rewrite:

$\frac{dA}{dt} = 15 - \frac{A}{100}$

Multiply through by dt

$dA = [15 - \frac{A}{100}]* dt$

Make dt stand alone

$\frac{dA}{15 - \frac{A}{100}} = dt$

$ln|15 - \frac{A}{100}| = -0.01t + ln\ c$

Express as exponents

$15 - \frac{A}{100} = ce^{-\frac{t}{100}}$

Multiply through by 100

$1500 - A = 100ce^{-\frac{t}{100}}$

$A = 1500 - 100ce^{-\frac{t}{100}}$

$A = 1500 - 100ce^{-0.01t}$

Apply initial conditions

$A(0) = 0$

Substitute 0 for t in: $A = 1500 - 100ce^{-0.01t}$

$0 = 1500 - 100ce^{-0.01*0}$

$0 = 1500 - 100ce^{0}$

$0 = 1500 - 100c$

$100c = 1500$

$c = 15$

Substitute 15 for c in $A = 1500 - 100ce^{-0.01t}$

$A = 1500 - 100*15e^{-0.01t}$

$A = 1500 - 1500e^{-0.01t}$

Factorize:

$A = 1500(1 - e^{-0.01t})$

How long to empty the tank

Set A to 0

$1500(1 - e^{-0.01t}) = 0$

Divide through by 1500

$1 - e^{-0.01t} = 0$

Collect Like Terms

$e^{-0.01t} = 1$

Take ln of both sides

$ln\ (e^{-0.01t}) = ln\ 1$

$-0.0t = 0$

$t = 0$

8 0

3 years ago

LOOK BELOW PLEASE AM MARKING BAINLIST PLEASE GUYS

Harman [31]

Answer:

C) 10

Step-by-step explanation:

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Find the percent of decrease from 6 to 5.

lozanna [386]

Answer:

Use this

Step-by-step explanation:

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3 years ago

The diameter of a table tennis ball is 20 millimeters.

KiRa [710]

The surface area of the table tennis ball will be around 1256.64 mm².

<h3>What is the sphere?</h3>

A sphere is a 3D geometrical object which has a radius and becomes a point that revolves around a fixed point called the center.

A sphere has surface area and volume based upon the radius of the sphere.

For example, if you have a sphere of radius r then its surface area will be 4πr² and volume will be (4/3)πr³.

The table tennis ball is the form of a sphere.

Given that,

The diameter of a table tennis ball is 20

Radius(r) = 20/2 = 10 mm

Surface area of an sphere = 4πr²

So,

Area = 4π(10)² = 1256.64 mm².

Hence "The surface area of the table tennis ball will be around 1256.64 mm²".

For more about a sphere,

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What system of equations represents the graph?

il63 [147K]

B. Because of the slope and where it the lines intersect the y axis

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