(i) Velocity is the rate of change of position, so if
<em>r</em><em>(t)</em> = <em>b</em> cos(<em>ω t </em>) <em>i</em> + <em>b</em> sin(<em>ω t </em>) <em>j</em> + <em>v</em> <em>t</em> <em>k</em>
then
<em>v</em><em>(t)</em> = d<em>r</em>/d<em>t</em>
<em>v</em><em>(t)</em> = -<em>b</em> <em>ω </em>sin(<em>ω t</em> ) <em>i</em> + <em>b</em> <em>ω</em> cos(<em>ω</em> <em>t</em> ) <em>j</em> + <em>v</em> <em>k</em>
The speed of the particle is the magnitude of the velocity, given by
|| <em>v</em><em>(t)</em> || = √[(-<em>b</em> <em>ω </em>sin(<em>ω t</em> ))² + (<em>b</em> <em>ω</em> cos(<em>ω</em> <em>t</em> ))² + <em>v</em> ²]
… = √[<em>b </em>²<em>ω </em>² + <em>v</em> ²]
(ii) The path is a helix. Suppose you zero out the <em>k</em> component. Then the path is a circle of radius <em>b</em>, and the value of <em>ω</em> determines how quickly a particle on the path traverses the circle. Now if you reintroduce the <em>k</em> component, the value of <em>v</em> will determine how far from the plane <em>z</em> = 0 the particle moves in a helical path as <em>t</em> varies.
(iii) Acceleration is the rate of change of velocity, so
<em>a</em><em>(t)</em> = d<em>v</em>/d<em>t</em>
<em>a</em><em>(t)</em> = -<em>b</em> <em>ω </em>²<em> </em>cos(<em>ω t</em> ) <em>i</em> - <em>b</em> <em>ω</em> ² sin(<em>ω</em> <em>t</em> ) <em>j</em>
Answer:
The answer is
6.25×30= 18.75
I'm not sure but this is what I think
Answer:
Events A and B are independent if and only if P(A and B) = P(A)P(B). If you know these probabilities, you can check to see if this holds.
Step-by-step explanation:
:)
gcf = 8 lcm= 5
gcf means greatest common facter. 8 goes into 8 1 time and 32 4 times. therefor 8 is the gcf. lcm means least common multiple. and 5 is the lowest number that goes into 20 and 40
Remember to follow the order of operation, PEMDAS. PEMDAS stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
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5. 9(7x - 4) = 27
First, distribute 9 to all terms within the parenthesis:
9(7x - 4) = 27
(9 * 7x) - (9 * 4) = 27
63x - 36 = 27
Next, isolate the variable, x. Do the opposite of PEMDAS.
First, add 36 to both sides:
63x - 36 (+36) = 27 (+36)
63x = 27 + 36
63x = 63
Isolate the variable, x. Divide 63 from both sides:
(63x)/63 = (63)/63
x = 63/63 = 1
x = 1
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6. 5(3x + 8) = 175
First, distribute 5 to all terms within the parenthesis:
5(3x + 8) = (5 * 3x) + (5 * 8) = 15x + 40
15x + 40 = 175
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 40 from both sides:
15x + 40 (-40) = 175 (-40)
15x = 175 - 40
15x = 135
Next, divide 15 from both sides of the equation:
(15x)/15 = (135)/15
x = 135/15 = 9
x = 9
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