### Math homework help????/?

**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
thanks…**

**Solution: **

Ok lets see:

The angle of depression is given to be 12^{0} . The following picture shows the screen:

Now, as depression is 12, angle at C would also be 12^{0} (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 12^{0}

Please remember here that Perpendicular here would be AB and Base is BC:

**tan 12 ^{0 } = AB/BC**

**tan 12 ^{0 } = 120/BC**

**0.21 = 120/BC**

**BC= 571.42′**

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### 9i4qwzgasm

9i4qwzgasm

### Geometry help please………..!?

**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**

### What’s your answer?

### 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**

### help math problem ):?

Including 5% sales tax, a hotel charges $111.30 a night. How is it before tax?

(http://answers.yahoo.com/question/answer?qid=20090708080509AA5Wxso)

Solution:

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.

### Can someone help me with this algebra?

# July 3, 02: Jeff asked: solve the equation

**2y^2-35-7y=y^2-5y**

What is the solution set?

What is the solution set?

**Step 1:**Bring all the terms with variable y on left hand side of ‘equality’ sign:

**2y^2**- 35 –

*7y*-

**y^2**+

*5y*= 0

**Step 2:**Resolve similar terms: (terms with y^2 and terms with y)

**Step 3:**Now, it looks like a simple quadratic equation. So split the middle term in such a way that the product of the terms formed is equal to – 35 y^2

**- 2y**is written as

**- 7y + 5y**as

**-7y * 5y = -35y^2**

**Step 4:**Take things common fron first two terms and last two terms:

**(y – 7)**+ 5

**(y – 7)**= 0

**(y – 5) (y – 7) = 0**

**Step 5:**Now, either (y – 5) = 0 or (y – 7) = 0