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3 years ago

Find the sum 32.330 + 23.559

Mathematics

2 answers:

Pepsi [2]3 years ago

3 0

The answer is 55.889

Mariulka [41]3 years ago

3 0

Answer: 55.889

Do the problem without the decimals at first then towards the end of the problem, put them back in the equation:)

I hope this has helped! Brainliest? :)

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Which logarithmic equation is equivalent to the exponential equation below?<br><br> 7^x=21

Irina-Kira [14]

Log base 7 (21)=x
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7 0

3 years ago

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Graph the line with slope 1 passing through the point (-5,2).

Mars2501 [29]

Answer:

(-5,2) (-7,0)

Step-by-step explanation:

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2 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

Please help! Find the equation of the line (graph provided in attached picture) Use exact numbers. y =_ x+_ ( _ represent blanks

Dennis_Churaev [7]

Answer:

$y = \frac{3}{4}x - 2$

Step-by-step explanation:

Equation of a line is given as $y = mx + b$

Where,

m = slope of the line = $\frac{y_2 - y_1}{x_2 - x_1}$

b = y-intercept, which is the value at the point where the line intercepts the y-axis. At this point, x = 0.

Let's find m and b to derive the equation for the line.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Use the coordinate pair of any two points on the line. Let's use the following,

$(0, -2) = (x_1, y_1)$ => on the line, when x = 0, y = -2

$(4, 1) = (x_2, y_2)$ => on the line, when x = 4, y = 1

Plug in the values and solve for m

$m = \frac{1 - (-2)}{4 - 0}$

$m = \frac{1 + 2}{4}$

$m = \frac{3}{4}$

b = -2 (the line intercepts the y-axis at this point)

Our equation would be =>

$y = mx + b$

$y = \frac{3}{4}x + (-2)$

$y = \frac{3}{4}x - 2$

5 0

3 years ago

6+754+537+633+632+11+98+2

Mariana [72]

Answer:

2673

Step-by-step explanation:

7 0

2 years ago

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