Answer:
91
Step-by-step explanation:
p^6×q^12 will have (6+1)(12+1) = 7×13 = 91 positive integer divisors.
The question is find the height of the tree, given that at two points 65 feet apart on the same side of the tree and in line with it, the angles of elevaton of the top of the tree are 21° 19' and 16°20'.
1) Convert the angles to decimal form:
19' * 1°/60' = 0.32° => 21° 19' = 21.32°
20' * 1°/60' = 0.33° => 16° 20' = 16.33°
2) Deduce the trigonometric ratios from the verbal information.
You can form a triangle with
- horizontal leg x + 65 feet
- elevation angle 16.33°
- vertical leg height of the tree, h
=> trigonometric ratio: tan (16.33) = h /( x + 65) => h = (x+65) * tan(16.33)
You can form a second triangle with:
- horizontal leg x
- elevation angle 21.32°
- vertical leg height of the tree, h
=> trigonometric ratio: tan(21.32) = h / x => h = x * tan(21.32)
Now equal the two expressions for h:
(x+65)*tan(16.33) = x*tan(21.32)
=> x*tan(16.33) + 65*tan(16.33) = x*tan(21.32)
=> x*tan(21.32) - x*tan(16.33) = 65*tan(16.33)
=> x = 65*tan(16.33) / [ tan(21.32) - tan(16.33) ] = 195.73 feet
=> h = 195.73 * tan(21.32) = 76.39 feet.
Answer: 76.39 feet
Answer:
y = 3x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
y - 3x = 4 ( add 3x to both sides )
y = 3x + 4 ← in slope- intercept form
with slope m = 3
Parallel lines have equal slopes, thus
y = 3x + c
The line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = 3x - 3 ← equation in slope- intercept form
To simulate the probability in a spinner divide the spinner into colors depending on the probability each color represents.
<h3>What does the word "probability" mean?</h3>
This word refers to the likelihood for an event to occur. Moreover, it is often expressed either as a fraction, a percentage, or a number.
<h3>How to create a spinner to simulate probability?</h3>
In this case, each of the colors represents a probability:
- Green 20%
- Blue 1/4 or 25%
- Yellow 2/5 oe 40%
- Orange 15%
Due to this, the best is to divide the spinner by colors and considering the percentanges of each color. For example 40% of the spinner should be red, while 15% should be orange.
Learn more about spinner in: brainly.com/question/24280611
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= 0.75