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3 years ago

Which of the following triangles are possible to draw?

Mathematics

1 answer:

Darina [25.2K]3 years ago

5 0

#1. Simply because those measurements are actual measurements and it is really easy if you use a protractor.

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The weekly salary of a store manager includes a $30 bonus plus the number of hours the manager works multiplied by the managers

just olya [345]

Answer:

Yes this is a linear function f(x) = ex+30

e = hourly rate

x=hours

f(x) = total earnings

6 0

4 years ago

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago

-9y - 2 (2 - 7y) + 4

poizon [28]

Answer:

-9y-2(2-7y)+4 expand the brackets using-2

Step-by-step explanation:

-9y-4+14y+4

arrange the like terms

-9y+14y-4+4

=5y becoz -4+4=0

ans=5y

7 0

3 years ago

Read 2 more answers

You need to buy four cards but only have seven dollars to spend. Which inequality can you use to find the amount that you can af

suter [353]

Answer:

Step-by-step explanation:

3 0

3 years ago

Find the equation of the line with a slope of 4 that goes through the following point: (6,2)

Rasek [7]

Answer:

y=4x-22

Step-by-step explanation:

4 0

3 years ago