A forest fire is spotted by a ranger from a 120′ tower. The angle of depression is 12 degrees. Find the distance from the tower to the fire.
if you can maybe help me on how to do it too that would be great
Ok lets see:
The angle of depression is given to be 120 . The following picture shows the screen:
Now, as depression is 12, angle at C would also be 120 (Alternate angles)
If the tower is AB and ranger stands at A, we need to find BC.
Lets take a trigonometric ratio which considers AB and BC in consideration.
As tan an angle is Perpendicular/Bases take tan 120
Please remember here that Perpendicular here would be AB and Base is BC:
tan 120 = AB/BC
tan 120 = 120/BC
0.21 = 120/BC
The dimensions of the smaller cylinder are three fifths the dimensions of the larger cylinder. The volume o the smaller cylinder is 2160pie cm*cubed. Find the volume of the larger cylinder.
Ok, lets see…
The dimensions of a cylinder are its height (h) and radius of the circular base (r).
So, lets assume that radius of larger cylinder is ‘R’ and smaller is ‘r’ and height of larger cylinder is ‘H’ and smaller is ‘h’
Now, we know that, dimensions of smaller cylinder are 3/5 of larger cylinder, that means:
r = 3/5 R and h = 3/5 H
Now, volume of a cylinder = pi * r^2 * h
pi * r^2 * h = 2160 * pi
r^2 * h = 2160
As r = 3/5 R and h = 3/5 H, we can replace r and h by 3/5 R and 3/5 H respectively
(3/5 R)^2 * 3/5 H = 2160
9/25 R^2 * 3/5 H = 2160
27/125 R^2 * H = 2160
R^2 * H = 2160 * 125/27
R^2 * H = 10000
Volume of larger cylinder = pi * R^2 * H
Therefore, the answer = 10000 pi cubic cm
find quadratic equation to tracking profits in text book strategies for problem solving workbook?
Alright Wil, lets see.
Retailer spent = $48 to buy x mugs
So, cost per mug would be = x/48
Two of them broke, so remaining = x – 2
Sold remaining mugs for $3 more each, so for each mug, the selling price would be = $(x/48 + 3)
Total selling price would be = (x – 2) * (x/48 + 3)
This would be equal to original cost + profit, therefore, we can say:
(x – 2) * (x/48 + 3) = 48 + 22
(x – 2) * [(x +144)/48] = 70
(x^2 + 144x – 2x -288)/48 = 70
(x^2 + 142x -288) = 70 * 48
x^2 + 142x -288 = 3360
So the answer is x^2 + 142x -288 = 3360
Including 5% sales tax, a hotel charges $111.30 a night. How is it before tax?
Lets assume that the charge excluding the tax is $x
Now, we know that the final charge, being $111.30, it would $x and 5% of $x. Lets write the equation for it:
x + 5% of x = 111.30
x + (5/100) * x = 111.30
x + (1/20) * x = 111.30
(21/20) * x = 111.30
x = 111.30 * 20/21
x = 2226/21
x = 106
So the answer is $106.
July 3, 02: Jeff asked: solve the equation
What is the solution set?