Answer:
2F /r = m
Step-by-step explanation:
F=1/2 mr
Multiply each side by 2
2F = 2*1/2 mr
2F = mr
Divide each side by r
2F/r = mr/r
2F /r = m
Answer:
(a) true
(b) true
(c) false; {y = x, t < 1; y = 2x, t ≥ 1}
(d) false; y = 200x for .005 < |x| < 1
Step-by-step explanation:
(a) "s(t) is periodic with period T" means s(t) = s(t+nT) for any integer n. Since values of n may be of the form n = 2m for any integer m, then this also means ...
s(t) = s(t +2mt) = s(t +m(2T)) . . . for any integer m
This equation matches the form of a function periodic with period 2T.
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(b) A system being linear means the output for the sum of two inputs is the sum of the outputs from the separate inputs:
s(a) +s(b) = s(a+b) . . . . definition of linear function
Then if a=b, you have
2s(a) = s(2a)
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(c) The output from a time-shifted input will only be the time-shifted output of the unshifted input if the system is time-invariant. The problem conditions here don't require that. A system can be "linear continuous time" and still be time-varying.
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(d) A restriction on an input magnitude does not mean the same restriction applies to the output magnitude. The system may have gain, for example.
Answer:
(-5, -8)
Step-by-step explanation:
Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex". If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point (h, k).
x^2 + 10x = - 17
x^2+10x+17=0
x^2+2*5x+25 - 8=0
(x+5)^2-8=0
h=-5, k= -8
vertex is (-5, -8)
Just use your equation and sub in 1.5 for x (thee time) to find y (the height at that time). You get a height of 15.5 when the time is 1.5 seconds
Answer:
27/ (4 x^6 y^8)
Step-by-step explanation:
4(3x^2y^4)^3/(2x^3y^5)^4
expand
4 (3^3 x^2^4 y^4^3) / (2^4 x^3^4 y^5^4)
power of the power rule , exponents to the power are multiplied
4 (3^3 x^(2*4) y^(4*3) / (2^4 x^(3*4) y^(5*4))
4 (27 x^(8) y^(12) / (16 x^(12) y^(20))
put like terms over each other
4 * (27/16) * x^8/x*16 * y^12/y^20
when dividing exponents , we subtract the powers
27 * 4/16 * x^ (8-14) * y^ (12-20)
27* 1/4 * x^(-6) * y^ (-8)
27/4 * x^(-6)(y)^ (-8)
negative terms go to the denominator
27/ (4 x^6 y^8)