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3 years ago

Why Mathematics Is a Language

1 answer:

5 0

Because mathematics is the same all over the world, math can act as a universal language. A phrase or formula has the same meaning, regardless of another language that accompanies it. In this way, math helps people learn and communicate, even if other communication barriers exist.

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A movie theater is offering a special summer pass. Passholders pay $8 per movie for the first 5 movies and watch additional movi

jasenka [17]

Answer:

Step-by-step explanation:

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3 years ago

Each side length of the parallelogram at the right is multiplied by 4 describe the change into the perimeter.judtify your answer

Sloan [31]

Let's say we have a parallelogram that has sides of 2 and 3
perimeter = 2 * (side1 + side2)
perimeter = 2 * (2 + 3)
perimeter = 10

If the sides are increased by a factor 4, the sides are 8 and 12
perimeter = 2 * (side1 + side2)
perimeter = 2 * (8 + 12)
perimeter = 40

The perimeter increases by a factor 4.

5 0

3 years ago

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

3 years ago

Use the graph to solve the equation.<br> f(x) = 0<br> The solutions are x =

Sergeu [11.5K]

Answer: The graph intersects y = 0 at x = 2 and x = -6, so the answer is B

Step-by-step explanation:

5 0

3 years ago

Lena’s guest house is 15 m long and 12 m wide how long is the diagonal of the house?

miv72 [106K]

imagine the diagonal of a rectangle being the split between two triangles. you are trying to find the longest side of the triangle, which is the "diagonal" of the rectangle.

to find the length of a side of a triangle, use the Pythagorean theorem. it is : a^2 + b^2 = c^2

so... plug in your data like this...

15^2 + 12^2= c^2.

225 + 144 = the square root of 369.

that is rounded to 19.2

this is just how I would solve this problem, if I helped you out please just let me know by voting me brainliest! Haha just kidding :)

Click to let others know, how helpful is it

3 0

4 years ago