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2 years ago

A laptop computer originally priced at $1,200 now sells for $1,600 what is the percent of increase

Mathematics

1 answer:

jolli1 [7]2 years ago

6 0

well, the increase from 1200 to 1600 is just 400.

if we take the 1200 to be the 100%, what is 400 off of it in percentage?

$\begin{array}{ccll} amount&\%\\ \cline{1-2} 1200&100\\ 400&x \end{array}\implies \cfrac{1200}{400}=\cfrac{100}{x}\implies 3=\cfrac{100}{x}\implies 3x=100 \\\\\\ x=\cfrac{100}{3}\implies x=33.\overline{3}$

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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 angle measures given the figure is a rhombus

IrinaK [193]

Answer:

74°

Step-by-step explanation:

A rhombus is a quadrilateral that has its opposite sides to be parallel to be each other. This means that the two interior opposite angles are equal to each other. Since the sum of the angles of a quadrilateral is 360°.

According to the triangle, since one of the acute angle is 32°, then the acute angle opposite to this angle will also be 32°.

The remaining angle of the rhombus will be calculated as thus;

= 360° - (32°+32°)

= 360° - 64°

= 296°

This means the other two opposite angles will have a sum total of 296°. Individual obtuse angle will be 296°/2 i.e 148°

This means that each obtuse angles of the rhombus will be 148°.

To get the unknown angle m°, we can see that the diagonal cuts the two obtuse angles equally, hence one of the obtuse angles will also be divided equally to get the unknown angle m°.

m° = 148°/2

m° = 74°

Hence the angle measure if m(1) is 74°

4 0

3 years ago

Hey guys help my please !!Q 4,6,7

padilas [110]

Q4, 4y²=60
y=√15 ( i am not sure)
q6, (5+y) ²=81
5+y=9
y=4
q7 (x+4) (x) =77
x²+4x-77=0
(x+11) (x-7) =0
x=-11(rej) or x=7
therefore ,length= 7+4=11cm
breadth=7cm

6 0

3 years ago

Is it possible to have a playground area made from 70 yards of fencing with an area of 324 square yards? Explain with

cricket20 [7]

Answer:

Yes: The answer would be 113.04 cubic feet

7 0

3 years ago

What part of 3 12 is 1/2 ? I need this asap

Aliun [14]

I assume you are asking one of three things, so I will answer all of them.

if you are asking what is 1/2 of 312, then multiply 312 by 1/2. 312 is really just 312/1, so
$312 \times \frac{1}{2} = \frac{312}{1} \times \frac{1}{2}$
we multiply fractions by multiplying straight across
$\frac{312 \times 1}{1 \times 2} = \frac{312}{2} = 156$

if you were asking what part of 3 1/2 is 1/2 then we have to recognize what 3 1/2 is as an improper fraction. to do this, we convert 3 into halves. how many halves of pizza are there in 3 whole pizzas? 6. so we have 6 halves and one half, which is a total of 7 halves.
$\frac{6}{2} + \frac{1}{2} = \frac{7}{2}$
now, we do the same thing as the first problem
$\frac{7}{2} \times \frac{1}{2} = \frac{7 \times 1}{2 \times 2} = \frac{7}{4}$

if you were asking what is half of 3.12, then we convert 1/2 to a decimal and multiply
$\frac{1}{2} = .5 \\ 3.12 \times .5 = 1.56$

6 0

3 years ago