A map is drawn to a scale of 1:50000.The distance between long mountain and plaine des papayes is 17.5 cm on the map.find the ac
1 answer:
Answer:
8.75 km.
Step-by-step explanation:
You can set up a ratio of the map to the actual distance of .
Then, this ratio can be used to cross multiply and divide to get an equivalent ratio for the distance:
=
By cross-multiplying we have x (in centimeters) = 17.5×50000. This tells us that x = 875,000 cm.
However, the answer asks for the distance in kilometers, so we need to convert it. There are 100,000 centimeters in a kilometer, so by dividing: 875000÷100000=8.75 kilometers.
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Yay, easy peasy, nice refresher
53. evaluate for x=infinity
we get 100/(infiniy^2-5) which is basically 100/infinity which is a very small number so about 0
54.
vertical assemtotes, neato
that is where the denomenator equals 0
but wait, simplify first
ok, fraction is simplified (anything factored out would be a hole)
so set the denom to 0 and solve
x^2-5=0
(x-√5)(x+√5)=0
x=-√5 and √5
vertical assemtotes at x=-√5 and x=√5
55. horizontal assemtotes
for the function p(x)/f(x)
if p(x) has lower degree than f(x) then y=0 is the horizontal assemtote
if p(x) has equal degree to f(x) then divide the leading coefients of p(x) and f(x)
if p(x) has greater degree than f(x) then we got slant assemtotes
100/(x^2-5)
100 has lower degree than x^2
y=0 is the horizontal assemtote
56. evalate for x=-5
we get -150/-10=150/10=15
the limit is 15
57. that negative on the right side means that we must approach it from the left
let's see if we can factor out the denomenator
nope
so go and evaluate values like 4, 4.5, 4.9, etc, approaching x=5 from the left
we keep getting smaller and smaller valuse
this make sense because as x approaches 5, we get 30(c)/(c-5) where c is close to 5, and as c appraoches 5 very close, the top part is appraoching 150 but the bottom approaches a very small negative number, and if we do something like 150/-0.00000000001, we get a very negative number
the limit is negative infinity
alternately, you could figure that there is a vertical assemtote at x=5 so we can see that if we aproximaate closer and closer values, we get smaller values. so from what we know about assemtotes, expecially vertical ones, we say that it approaches negative infinity
58.
evalauating we get infintity/inifinty, not helpful
hmmm, is there a horizontal assemtote to help us?
the degree of top is higher so we got a slant assemtote
the only way is to use long division to divide the top by the bottom (see attachment)
we get
the slant assemtote is
as you can see, as x approaches infinity, y also will approach infinity
ANSWERS:
53. 0
54. VA is x=-√5 and x=√5
55. HA is y=0
56. the limit is 15
57. the limit is -∞
58. the limit is ∞
53. evaluate for x=infinity
we get 100/(infiniy^2-5) which is basically 100/infinity which is a very small number so about 0
54.
vertical assemtotes, neato
that is where the denomenator equals 0
but wait, simplify first
ok, fraction is simplified (anything factored out would be a hole)
so set the denom to 0 and solve
x^2-5=0
(x-√5)(x+√5)=0
x=-√5 and √5
vertical assemtotes at x=-√5 and x=√5
55. horizontal assemtotes
for the function p(x)/f(x)
if p(x) has lower degree than f(x) then y=0 is the horizontal assemtote
if p(x) has equal degree to f(x) then divide the leading coefients of p(x) and f(x)
if p(x) has greater degree than f(x) then we got slant assemtotes
100/(x^2-5)
100 has lower degree than x^2
y=0 is the horizontal assemtote
56. evalate for x=-5
we get -150/-10=150/10=15
the limit is 15
57. that negative on the right side means that we must approach it from the left
let's see if we can factor out the denomenator
nope
so go and evaluate values like 4, 4.5, 4.9, etc, approaching x=5 from the left
we keep getting smaller and smaller valuse
this make sense because as x approaches 5, we get 30(c)/(c-5) where c is close to 5, and as c appraoches 5 very close, the top part is appraoching 150 but the bottom approaches a very small negative number, and if we do something like 150/-0.00000000001, we get a very negative number
the limit is negative infinity
alternately, you could figure that there is a vertical assemtote at x=5 so we can see that if we aproximaate closer and closer values, we get smaller values. so from what we know about assemtotes, expecially vertical ones, we say that it approaches negative infinity
58.
evalauating we get infintity/inifinty, not helpful
hmmm, is there a horizontal assemtote to help us?
the degree of top is higher so we got a slant assemtote
the only way is to use long division to divide the top by the bottom (see attachment)
we get
the slant assemtote is
as you can see, as x approaches infinity, y also will approach infinity
ANSWERS:
53. 0
54. VA is x=-√5 and x=√5
55. HA is y=0
56. the limit is 15
57. the limit is -∞
58. the limit is ∞
Answer:
1)
2)
We can find the individual probabilities and we got:
And the sum of the 3 values 0.6923+0.2307+0.0770= 1 so then we satisfy all the conditions and we can conclude that f(x) is a probability distribution.
Step-by-step explanation:
For this case we have the following density function:
In order to satisfty that this function is a probability mass function we need to check two conditions:
1)
2)
We can find the individual probabilities and we got:
And the sum of the 3 values 0.6923+0.2307+0.0770= 1 so then we satisfy all the conditions and we can conclude that f(x) is a probability distribution.
And if we want to find the following probabilities: