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4 years ago

X+y=12 x-y=2 Solve by elimination

1 answer:

7 0

$x+y=12 \\
\underline{x-y=2} \\
x+x=12+2 \\
2x=14 \\
x=\frac{14}{2} \\
x=7 \\ \\
x+y=12 \\
7+y=12 \\
y=12-7 \\
y=5 \\ \\
\boxed{(x,y)=(7,5)}$

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1. Kyle and John are twins who decided to plan an imaginary trip that started with cliff jumping. There were two different spots

Vikki [24]

Answer:

a) Δx = -35ft

b) Δx = -25ft

c) Kyle traveled 10ft more than John

Step-by-step explanation:

We define a coordinate reference system() in which y = 0 corresponds to the water surface.

a) The initial position of Kyle in our coordinate reference system is:

$x_{o} = 20 ft$

and his final position is:

$x_{f} = -15 ft$

Therefore, he traveled

Δx = $x_{f} - x_{o} = -15 - 20 = -35 ft$

b) The initial position of John in our coordinate reference system is:

$x_{o} = 15 ft$

and his final position is:

$x_{f} = -10 ft$

Therefore, he traveled

Δx = $x_{f} - x_{o} = -10 - 15 = -25 ft$

c) Then, Kyle traveled 10ft more than John

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4 years ago

Write 12 ten thousands, 8 thousands,14 hundreds, 7 ones in standard form

Cloud [144]

The correct answer is: 
129,407.

Explanation: 
12 ten-thousands = 12*10000=120,000.
8 thousands = 8*1000=8000;
this gives us 120,000+8,000=128,000.

14 hundreds = 14*100=1400;
this gives us 128,000+1,400=129,400.

7 ones = 7*1=7;
this gives us 129,400+7=129,407.

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4 years ago

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if 500 is deposited into an account earning 6 percent simple interest what is the future value in 6 years how do you work it put

djverab [1.8K]

$\bf \qquad \textit{Simple Interest Earned Amount}\\\\
A=P(1+rt)\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to& \$500\\
r=rate\to 6\%\to \frac{6}{100}\to &0.06\\
t=years\to &6
\end{cases}
\\\\\\
A=500(1+0.06\cdot 6)$

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4 years ago

Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3

Alex

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

$\frac{dV}{dt} = -kA$

Using Euler's method

$\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i} \\$

Where initial droplet volume is:

$V(0) = \frac{4pi}{3} * r(0)^3 = \frac{4pi}{3} * 2.5^3 = 65.45 mm^3$

Hence, the iterative solution will be as next:

i = 1, ti = 0, Vi = 65.45

$V'_{i} = -k *4pi*(\frac{3*65.45}{4pi})^(2/3) = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88$

i = 2, ti = 0.5, Vi = 63.88

$V'_{i} = -k *4pi*(\frac{3*63.88}{4pi})^(2/3) = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33$

i = 3, ti = 1, Vi = 62.33

$V'_{i} = -k *4pi*(\frac{3*62.33}{4pi})^(2/3) = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813$

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

$r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\$

The average change of droplet radius with time is:

Δr/Δt = $\frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min$

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

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4 years ago

(06.05) Neil is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect? graph of the function f of

schepotkina [342]

Given the stated equation we know that that quadratic formula has 2 as its degree. This meats it has 2 roots. A linear equation has a degree of 1. A linear equation has 1 root. To know if they intersect, the must have one root in common. To know this, solve the two equation simultaneously. If they result to an answer then they intersect.

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4 years ago

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