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3 years ago

Who created the pie symbol in math

Mathematics

2 answers:

lord [1]3 years ago

7 0

Answer:

William Jones

MArishka [77]3 years ago

5 0

William Jones created the pie symbol

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How can you factor out the coefficient of a variable? Please help , Thank you

Dvinal [7]

The coefficient of b (that is, 2) divides into 2b and also into 8, so it is a factor (a value that is multiplied by another value to produce a term in an expression)

7 0

3 years ago

Shay's net pay is $575.50 biweekly. If her gross annual income is $17,500, how much is deducted from each paycheck?

Delvig [45]

Answer:

6,906

Step-by-step explanation:

575.50× 12=6906

17500-6906=10,594

10,594-17500= 6906

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

Geometry ∠1 and ∠2 are vertical angles. If m∠1 = 17x + 1 and m∠2 = 20x – 14, find m∠2.

stiv31 [10]

Answer:

m∠2= 86

Step-by-step explanation:

since they are vertical angles, that means they are both equal to eachother.

so lets set them equal!

17x+1=20x-14

17x+15=20x

15=3x

x=5

now input x into m∠2

m∠2 = 20(5) – 14 = 86

7 0

4 years ago

What is the equation of the quadratic graph with a focus of (3, −1) and a directrix of y = 1?

Tomtit [17]

Use our brains and what we know
f(x)=a(x-h)²+k
vetex is (h,k)
and a is te leading coefient

if directix is below the focus, then it opens up and a is positive
if directix is above focus, then it opens down and a is negaitve

vertex is in between directix and focus

so
(3,-1) and y=1
-1<1
so directix is above
a is negative

directly in between
distance from -1 to 1 is 2
2/2=1

1 above (3,-1) is (3,0)
vertex is (3,0)

y=a(x-3)²+0
y=a(x-3)²

the only option with a negative 'a' value is B

answer is B

5 0

3 years ago

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