Centimeter
Milimeter
Micrometer
Nanometer
Answer:
x ≈ 14.5
Step-by-step explanation:
A = x²√(25+10√5)/4
A = 1.72a²
x² = A/1.72
= 363.27/1.72
≈ 211
x = √211
≈ 14.5
Answer:
![\boxed{k = \frac{L^2 + p}{4t}}](https://tex.z-dn.net/?f=%5Cboxed%7Bk%20%3D%20%5Cfrac%7BL%5E2%20%2B%20p%7D%7B4t%7D%7D)
General Formulas and Concepts:
<u>Algebra I</u>
Basic Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify given.</em>
<em />![\displaystyle L = \sqrt{4kt - p}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20L%20%3D%20%5Csqrt%7B4kt%20-%20p%7D)
<u>Step 2: Solve for </u><u><em>k</em></u>
We can use equality properties to help us rewrite the equation to get <em>k</em> as our subject:
Let's first <em>square both sides</em>:
![\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cbegin%7Baligned%7DL%20%3D%20%5Csqrt%7B4kt%20-%20p%7D%20%26%20%5Crightarrow%20L%5E2%20%3D%20%5Cbig%28%20%5Csqrt%7B4kt%20-%20p%7D%20%5Cbig%29%20%5E2%20%5C%5C%26%20%5Crightarrow%20L%5E2%20%3D%204kt%20-%20p%20%5C%5C%5Cend%7Baligned%7D)
Next, <em>add p to both sides</em>:
![\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\& \rightarrow L^2 + p = 4kt \\\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cbegin%7Baligned%7DL%20%3D%20%5Csqrt%7B4kt%20-%20p%7D%20%26%20%5Crightarrow%20L%5E2%20%3D%20%5Cbig%28%20%5Csqrt%7B4kt%20-%20p%7D%20%5Cbig%29%20%5E2%20%5C%5C%26%20%5Crightarrow%20L%5E2%20%3D%204kt%20-%20p%20%5C%5C%26%20%5Crightarrow%20L%5E2%20%2B%20p%20%3D%204kt%20%5C%5C%5Cend%7Baligned%7D)
Next, <em>divide 4t by both sides</em>:
![\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\& \rightarrow L^2 + p = 4kt \\& \rightarrow \frac{L^2 + p}{4t} = k \\\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cbegin%7Baligned%7DL%20%3D%20%5Csqrt%7B4kt%20-%20p%7D%20%26%20%5Crightarrow%20L%5E2%20%3D%20%5Cbig%28%20%5Csqrt%7B4kt%20-%20p%7D%20%5Cbig%29%20%5E2%20%5C%5C%26%20%5Crightarrow%20L%5E2%20%3D%204kt%20-%20p%20%5C%5C%26%20%5Crightarrow%20L%5E2%20%2B%20p%20%3D%204kt%20%5C%5C%26%20%5Crightarrow%20%5Cfrac%7BL%5E2%20%2B%20p%7D%7B4t%7D%20%3D%20k%20%5C%5C%5Cend%7Baligned%7D)
We can rewrite the new equation by swapping sides to obtain our final expression:
![\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow \boxed{k = \frac{L^2 + p}{4t}}\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cbegin%7Baligned%7DL%20%3D%20%5Csqrt%7B4kt%20-%20p%7D%20%26%20%5Crightarrow%20%5Cboxed%7Bk%20%3D%20%5Cfrac%7BL%5E2%20%2B%20p%7D%7B4t%7D%7D%5Cend%7Baligned%7D)
∴ we have <em>changed</em> the subject of the formula.
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Learn more about Algebra I: brainly.com/question/27698547
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Topic: Algebra I
Answer:
m<BGC = 145°
Step-by-step explanation:
<AGC and <DGB are vertical angles. Vertical angles are congruent. Therefore:
m<AGC = m<DGB
(substitution)
Collect like terms
Divide both sides by -5
x = 5
m<BGC = 180 - (m<AGC) (linear pair)
m<BGC = 180 - (3x + 20)
Plug in the value of x
m<BGC = 180 - (3(5) + 20) = 180 - 35
m<BGC = 145°
Answer:
This is an ellipse.
Step-by-step explanation:
![z=5cos(\theta)+3isin(\theta)](https://tex.z-dn.net/?f=z%3D5cos%28%5Ctheta%29%2B3isin%28%5Ctheta%29)
Applying the angle values in intervals of right angles (90°), the resulting set of values for z are:
![\theta = 0,90,180,270,360](https://tex.z-dn.net/?f=%5Ctheta%20%3D%200%2C90%2C180%2C270%2C360)
(again)
If you look at the plot, you will observe how these values represent points in the xy plain. All of them belong to either the x or the y axis.
The resulting figure for the whole set of values of
is in fact an ellipse.