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3 years ago

Include work pleaseeeee

Mathematics

1 answer:

Angelina_Jolie [31]3 years ago

5 0

Okay so to represent juice we are going to use X, and to represent water we are going to use Y.

We also know that the first two starting equations are:

6x + y = 135

4x + 2y = 110

We can re-arrange the first equation so that it equals y (for now), so it is going to end up looking like this:

y = -6x +135

Now you can take that equation and plug into either one of the starting two equations. I chose the second equation. We just substitute what y equals in for y in the equation, so we have:

4x + 2(135 - 6x) = 110

Now solve

4x + 270 -12x = 110

-8x + 270 = 110

Subtract 270 from both sides

-8x = -160

Now divide by -8 on both sides

x = 20

We can now confirm that juice costs $20

Now lets plug that into the equation where we solved for y, to get the actual value of y.

y = 135 - 6(20)

y = 135 - 120

y = 15

The price of water costs $15

From this we can conclude that the cost of juice is $20 and the price of water is $15

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Find the uncertainty in a calculated average speed from the measurements of distance and time. Average speed depends on distance

maks197457 [2]

Answer:

The uncertainty in the average speed is 0.134 meters per second.

Step-by-step explanation:

Let be $v(t, x) =\frac{x}{t}$ the average speed function, we calculate the uncertainty in the average speed by total differentials, which is in this case:

$\Delta v = \frac{\partial v}{\partial x}\cdot \Delta x+\frac{\partial v}{\partial t}\cdot \Delta t$

Where:

$\Delta v$ - Uncertainty in the average speed, measured in meters per second.

$\frac{\partial v}{\partial x}$ - Partial derivative of the average speed function with respect to distance, measured in $s^{-1}$ .

$\frac{\partial v}{\partial t}$ - Partial derivative of the average speed function with respect to time, measured in meters per square second.

$\Delta x$ - Uncertainty in distance, measured in meters.

$\Delta t$ - Uncertainty in time, measured in seconds.

Partial derivatives are, respectively:

$\frac{\partial v}{\partial x} = \frac{1}{t}$ , $\frac{\partial v}{\partial t} = - \frac{x}{t^{2}}$

Then, the total differential expression is expanded as:

$\Delta v = \frac{\Delta x}{t}-\frac{x\cdot \Delta t}{t^{2}}$

If we get that $\Delta x = 2.3\,m$ , $t = 6.3\,s$ , $x = 6.1\,m$ and $\Delta t = 1.5\,s$ , the uncertainty in the average speed is:

$\Delta v = \frac{2.3\,m}{6.3\,m}-\frac{(6.1\,m)\cdot (1.5\,s)}{(6.3\,s)^{2}}$

$\Delta v = 0.134\,\frac{m}{s}$

The uncertainty in the average speed is 0.134 meters per second.

8 0

3 years ago

Linda worked 20 hours and earned $215.At this rate, how much would she earn if she worked 24 hours ?

Lostsunrise [7]

$215/20 hours= $10.75 per hr

$10.75 per hr*24 hours= $258

3 0

3 years ago

Read 2 more answers

a parabola has its vertex at 1,1 and passes through the point -2,-2. Find the equation of this parabola

Jet001 [13]

Answer:

The vertex form of the equation is $y = -\frac{1}{3}( x-1)^{2} +1$ .

Step-by-step explanation:

You will use the equation $y=a(x-h)^{2} +k$ to solve this parabola. (h, k) is the vertex. So, we plug this into the equation to get $y= a(x - 1)^{2} +1$ .

Then, we substitute the point as our x and y to get $-2 = 9a+1$ (a lot of simplifying was done here). Then, add 2 to the right side of the equation and isolate the $9a$ to get $9a = 3$ . Finally, divide by 9 on both sides to get $a=\frac{1}{3}$ .

Now, substitute your $a$ back into the equation to get y = $-\frac{1}{3}(x-1)^{2}+1$ .

This is in vertex form. If the answer is needed in standard form, simply distribute and simplify to get $y = -\frac{1}{3} x^{2} +\frac{2}{3} x+\frac{2}{3}$ .