Which statement is true about the underlined digit in the number 7,332? 3 hundreds = 3 ones
2 answers:
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Answer:
-0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.
Step-by-step explanation:
Let
x= distance between the wall and ladder
Ф = angle between the ladder and ground
The rate of change is: dx/dt = 0.8 ft/s
We need to find dФ/dt when x = 8 ft/s
From the triangle in the figure we see that:
cos Ф = x/10
=> x = 10 cosФ
Now, the rate of change will be
d(x)/dt = d/dt (10cosФ)
dx/dt = -10 sin Ф dФ/dt
dx/dt = 0.8 (given)
to find dФ/dt
we need to find sin Ф when x = 8
By Pythagoras theorem
(hypotenuse)^2 = (Perpendicular)^2+(base)^2
(10)^2 = (8)^2+ (Perpendicular)^2
100 = 64 + (Perpendicular)^2
=> (Perpendicular)^2 = 100-64
(Perpendicular)^2 = 36
Perpendicular = 6
sin Ф = Perpendicular/hypotenuse
sin Ф = 6/10 = 3/5
Putting values in:
dx/dt = -10 sin Ф dФ/dt
0.8 = -10(3/5) dФ/dt
0.8 = -6 dФ/dt
=> dФ/dt = 0.8 / -6
dФ/dt = - 0.133 radians/s
So, -0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.
Answer:
B. 1/8
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
<u>Algebra I</u>
- Function Notation
Step-by-step explanation:
<u>Step 1: Define</u>
<u /><u />
<u />
<u>Step 2: Evaluate</u>
- Substitute in <em>x</em>:
- Exponents:
- Multiply: