Answer: 4,879,682
Step-by-step explanation:
Answer:
x = 13
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality<u>
</u>
<u>Algebra I</u>
<u>Trigonometry</u>
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
- a is a leg
- b is another leg
- c is the hypotenuse<u>
</u>
Step-by-step explanation:
<u>Step 1: Identify</u>
<em>a</em> = 12
<em>b</em> = 5
<em>c</em> = x
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in variables [PT]: 12² + 5² = x²
- Evaluate exponents: 144 + 25 = x²
- Add: 169 = x²
- [Equality] Square root both sides: ±13 = x
- Rewrite: x = ±13
Since we are dealing with positive numbers, we can disregard the negative root.
∴ x = 13
First you need to find the rate. This problem is based on the formula d = rt
d = distance
r = rate
t = time.
The question is asking how many miles will it travel in 8 hours so to find this out we need to find the rate when the car travels 240 miles in 4 hours. We use this information and plug it into the model d = rt
d = 240
r = don't know yet
t = 4 hr
d = rt
240 = 4r
240 / 4 = 4r / 4
60 = r
r = 60
So the car is going at a rate of 60 miles per hour. Now that we know this we can solve for how many miles the car will travel in 8 hours.
d = rt
d = r * t
d = 60 * 8
d = 480
So the car will travel 480 miles in 8 hours
Another way to think about this is that you know the car traveled 240 miles in 4 hours and the question is wanting to know how far the car will travel in 8 hours, which would be double the 4 hours so 240 + 240 = 480
The answer in itself is 1/128 and here is the procedure to prove it:
cos(A)*cos(60+A)*cos(60-A) = cos(A)*(cos²60 - sin²A)
<span>= cos(A)*{(1/4) - 1 + cos²A} = cos(A)*(cos²A - 3/4) </span>
<span>= (1/4){4cos^3(A) - 3cos(A)} = (1/4)*cos(3A) </span>
Now we group applying what we see above
<span>cos(12)*cos(48)*cos(72) = </span>
<span>=cos(12)*cos(60-12)*cos(60+12) = (1/4)cos(36) </span>
<span>Similarly, cos(24)*cos(36)*cos(84) = (1/4)cos(72) </span>
<span>Now the given expression is: </span>
<span>= (1/4)cos(36)*(1/4)*cos(72)*cos(60) = </span>
<span>= (1/16)*(1/2)*{(√5 + 1)/4}*{(√5 - 1)/4} [cos(60) = 1/2; </span>
<span>cos(36) = (√5 + 1)/4 and cos(72) = cos(90-18) = </span>
<span>= sin(18) = (√5 - 1)/4] </span>
<span>And we seimplify it and it goes: (1/512)*(5-1) = 1/128</span>
