1. RS has endpoints R(2, 4) and S(-1, 7). What are<br> the coordinates of its midpoint M?

A water dispenser has a capacity of 20,000 milliliters. Use the facts to find how much this is in liters .

laila [671]

Answer:

The water dispenser's capacity in liters is 20liters

Explanation:

Given:

A water dispenser capacity = 20,000milliliters

To find

the capacity of the water dispenser in liters

To determine the capacity in liters, we will convert the capacity in ml to liters using the conversion:

1000ml = 1 liter

let the capacity of the water dispenser in Liters = y

$\begin{gathered} 1000ml\text{ = 1 L} \\ 20000ml\text{ = y} \\ cross\text{ multiply:} \\ y(1000)\text{ = 1\lparen20000\rparen} \\ 1000y\text{ = 20000} \end{gathered}$ $\begin{gathered} divide\text{ both sides by 1000:} \\ y\text{ = }\frac{20000}{1000} \\ y\text{ = 20} \end{gathered}$

The water dispenser's capacity in liters is 20liters

5 0

1 year ago

Use the grouping method to factor the polynomial below x^3 -4x^2+3x-12

olasank [31]

Answer:

x^2(x-4) + 3(x-4)

(x^2 + 3)(x-4)

Step-by-step explanation:

8 0

3 years ago

Assume z = x + iy, then find a complex number z satisfying the given equation. d. 2z8 – 2z4 + 1 = 0

kodGreya [7K]

Answer: complex equations has n number of solutions, been n the equation degree. In this case:

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i11,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i101,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i191,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i281,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i78,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i168,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i258,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i348,75°}$

Step-by-step explanation:

I start with a variable substitution:

$Z^{4} = X$

Then:

$2X^{2}-2X+1=0$

Solving the quadratic equation:

$X_{1} =\frac{2+\sqrt{4-4*2*1} }{2*2} \\X_{2} =\frac{2-\sqrt{4-4*2*1} }{2*2}$

$X=\left \{ {{0,5+0,5i} \atop {0,5-0,5i}} \right.$

Replacing for the original variable:

$Z=\sqrt[4]{0,5+0,5i}$

or $Z=\sqrt[4]{0,5-0,5i}$

Remembering that complex numbers can be written as:

$Z=a+ib=|Z|e^{ic}$

Using this:

$Z=\left \{ {{{\frac{\sqrt{2}}{2} e^{i45°} } \atop {{\frac{\sqrt{2}}{2} e^{i-45°} }} \right.$

Solving for the modulus and the angle:

$Z=\left \{ {{\sqrt[4]{\frac{\sqrt{2}}{2} e^{i45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i45}} } \atop {\sqrt[4]{\frac{\sqrt{2}}{2} e^{i-45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i-45}} }} \right.$