The height of the tree given the depression angle to the top and the base
is given by the tangent relationship of the two given angles.
Correct response:
- The height of the tree is approximately <u>79.58 feet</u>
<h3 /><h3>Methods used for the calculation of the height of the tree</h3>
Given:
Altitude of the hot air balloon = 800 feet
Angle of depression to top of tree = 43°
Angle of depression to base of tree = 46°
Required:
Height of tree
Solution:
The horizontal distance of the balloon from the tree is given as follows;
Therefore;
Therefore;
- Height of tree = Altitude of balloon - Height of balloon above tree
Therefore;
Learn more about angle of elevation and depression here:
brainly.com/question/1978238
Answer:
B. -1
Step-by-step explanation:
x^3-4x^2+2x+10=x^2-5x-3
We know it has 3 roots since it is a 3rd degree polynomial.
Two of the roots are (3+2i) and (3-2i)
Subtract x^2-5x-3 from both sides
x^3-4x^2+2x+10-(x^2-5x-3)=x^2-5x-3 -(x^2-5x-3)
Distribute the minus sign
x^3-4x^2+2x+10-x^2+5x+3=x^2-5x-3 -x^2+5x+3
x^3 -5x^2+7x +13 =0
Graphing this equation , we see that it crosses the x axis at x=-1
That covers the three roots, 1 real and two complex
Answer:
x ≥ 4
General Formulas and Concepts:
<u>Pre-Algebra</u>
Step-by-step explanation:
<u>Step 1: Define inequality</u>
-4(8 - 3x) ≥ 6x - 8
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute -4: -32 + 12x ≥ 6x - 8
- Subtract 6x on both sides: -32 + 6x ≥ -8
- Add 32 on both sides: 6x ≥ 24
- Divide 6 on both sides: x ≥ 4
Here we see that <em>x</em> can be any value greater than or equal to 4.
Answer:
Option D, 0.32 meters per second
Step-by-step explanation:
<u>Step 1: Find the unit rate at which Matt needs to swim</u>
Make an equation to represent the scenario.
<em>25m = 8</em>
<u>Step 2: Solve for m by dividing both sides by 25</u>
25m / 25 = 8 / 25
<em>m = 0.32</em>
<u>Step 3: Check</u>
To check, you can multiply the number of second, 25, by the meters per second to see if you get the total meters, 8.
0.32 * 25
<em>8</em>
So, the answer is correct :)
<u><em>0.32 means that Matt needs to swim 0.32 meters per second to qualify as a state swimmer.</em></u>
Answer: Option D, 0.32 meters per second