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4 years ago

What is the equation in point−slope form of the line passing through (1, 2) and (2, 5)? (5 points)

Mathematics

1 answer:

Jlenok [28]4 years ago

8 0

Slope is 3 so the equation is y-2=3(x-1) in point slope form as y-y1 =m (x-x1)

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A skating rink charges $75 for a nightly reservation as well as $5 per person skating. If n is the number of people skating, wri

Aleonysh [2.5K]

Answer:

75+5n

Step-by-step explanation:

3 0

3 years ago

1. Factor the expression 3x^3 + 4x^2 - 15x - 20 Please show work!

SOVA2 [1]

Do the split method, by splitting it in the middle

Factor 3x^3 + 4x^2 and -15x - 20 seperately

x^2 (3x + 4) - 5(3x + 4)

(x^2 - 5)(3x + 4) is your answer

hope this helps

7 0

3 years ago

Explicit formulas Write the first four terms of the sequence {an}n=1 infinity. 9. an=1/10n 11. an = 1 + sin(pin/2) Recurrence re

monitta

Answer:

Please see attachment

Step-by-step explanation:

Please see attachment

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

Find the value of x that makes the equation true.

Amiraneli [1.4K]

The correct answer is 8 because 8+4 equals 12

6 0

4 years ago