A triangle has three angles 1x, 11x and 8x. as described below. Find the value of x

Solve using the quadratic formula: 2x2-9x+12=0

marta [7]

Answer:

no solution

Step-by-step explanation:

For getting the nature of solution of the quadratic equation of the form:

ax² + bx + c = 0

We need to find Discriminant which is:

Discriminant (D) = b² - 4ac

If D < 0, there is no solution of equation.
If D = 0, there are two equal and real solution of equation
If D < 0, there are two real and distinct solution of equation

Here we have equation is:

2x² - 9x + 12 = 0

∴ a=2, b = -9, c = 12

⇒ D = 81 - 4 × 2 × 12 = -16 < 0

Hence, there is no solution of given equation.

5 0

3 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

The coordinates of parallelogram PVWZ are P(0, 0), V(-p, q), and W(-p - r, q). Find the coordinates of Z without using any new v

Drupady [299]

For the answer to the question above asking to f<span>ind the coordinates of Z without using any new variables.
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Vector WZ equals vector VP, which is (p, -q)
So Z is (-p - r + p, q - q) which is (-r, 0)
I hope my answer helped you.

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