M ∠ 4 = ______ °<br> m ∠ 5 = ______ °<br> m ∠ 6 = _____

Sums of series, Maths. Any help appreciated.

Andrej [43]

Answer:

Step-by-step explanation:

Well, a series in math is simply the sum of the various numbers, or elements of a sequence. For example, to make a series from the sequence of the first five positive integers 1, 2, 3, 4, 5, just add them up. So, 1 + 2 + 3 + 4 + 5 = 15 is a series.

that all what i know i am really sorry bro but that is what i understand !

7 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

4) What is the total cost (tax and price) on a purchase of $108.50 if the sales tax is 8%?

vitfil [10]

Answer: C)$117.18

$108.50 X 1.08 = $108.50

4 0

3 years ago

What is the fraction of 2.6

Solnce55 [7]

2 3/5 or 2 6/10 is the answer

6 0

3 years ago

Read 2 more answers

Can someone please help :/ the people in my group are being mean,, ill mark you brainlest

Alex_Xolod [135]

You’re correct. its 6.25 oz, and bleep the people in ur group man

6 0

3 years ago

Read 2 more answers

M ∠ 4 = ______ ° m ∠ 5 = ______ ° m ∠ 6 = ______ °

M ∠ 4 = ° m ∠ 5 = ° m ∠ 6 = __ °