Acceleration is the change in velocity over time. There's are formula's for such problems which are called kinematics equations. Look em up. One of them doesn't have t (time) in them you would normally use that one to solve this problem. 16/2/20=a=0.4m/s^2
I did it for you but please look it up, understand and memorize it ;)
Using Laplace transform we have:L(x')+7L(x) = 5L(cos(2t))sL(x)-x(0) + 7L(x) = 5s/(s^2+4)(s+7)L(x)- 4 = 5s/(s^2+4)(s+7)L(x) = (5s - 4s^2 -16)/(s^2+4)
=> L(x) = -(4s^2 - 5s +16)/(s^2+4)(s+7)
now the boring part, using partial fractions we separate 1/(s^2+4)(s+7) that is:(7-s)/[53(s^2+4)] + 1/53(s+7). So:
L(x)= (1/53)[(-28s^2+4s^3-4s^2+35s-5s^2+5s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]L(x)= (1/53)[(4s^3 -37s^2 +40s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]
denoting T:= L^(-1)and x= (4/53) T(s^3/(s^2+4)) - (37/53)T(s^2/(s^2+4)) +(40/53) T(s^2+4)-(4/53) T(s^2/s+7) +(5/53)T(s/s+7) - (16/53) T(1/s+7)
Step-by-step explanation:
When two statements are connected with an 'and,' you have a conjunction.
For conjunctions, both statements must be true for the compound statement to be true.
When the connector between two statements is "or," you have a disjunction. In this case, only one statement in the compound statement needs to be true for the entire compound statement to be true.
Answer:
Depends on which function is which...
Step-by-step explanation:
The blue graph is the same as the yellow graph but raised up 1 unit. That means either:
blue function rule = yellow function rule + 1
or
yellow function rule = blue function rule - 1
Your picture doesn't say which function is <em>f</em> and which is <em>g</em>.
If, just to pick a possibility, the blue function is <em>g</em>(<em>x</em>), then
g(x) = f(x) + 1
If the blue function is <em>f</em>(<em>x</em>), then
g(x) = f(x) - 1
Answer: Choice D.
Max: f (-1,-2)=4; min:f(3,5)=-11
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Work Shown:
Plug in (x,y) = (-1,3)
f(x,y) = -2x-y
f(-1,3) = -2*(-1)-3
f(-1,3) = 2-3
f(-1,3) = -1
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Plug in (x,y) = (3,5)
f(x,y) = -2x-y
f(3,5) = -2*3-5
f(3,5) = -6-5
f(3,5) = -11
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Plug in (x,y) = (4,-1)
f(x,y) = -2x-y
f(4,-1) = -2*4-(-1)
f(4,-1) = -8+1
f(4,-1) = -7
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Plug in (x,y) = (-1,-2)
f(x,y) = -2x-y
f(-1,-2) = -2*(-1)-(-2)
f(-1,-2) = 2+2
f(-1,-2) = 4
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The four outputs are: -1, -11, -7, and 4
The largest output is 4 and that happens when (x,y) = (-1,-2)
So the max is f(x,y) = 4
The smallest output is -11 and that happens when (x,y) = (3,5)
So the min is f(x,y) = -11
This all points to choice D being the answer.
