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aniked [119]
3 years ago
11

Use the distance formula to show algebraically and graphically that the following two circles do not intersect. (x-1)²+(y+2)²=1

; (x+5)²+(y-4)²=4
Mathematics
1 answer:
lesya692 [45]3 years ago
3 0

Answer and Step-by-step explanation:

C1) (x-1)²+(y+2)²=1  C1 (1,-2) R1 = √1 = 1

C2) (x+5)²+(y-4)²=4 C2 (-5,4) R2 = √4 = 2

DISTANCE FORMULA: d² = (y₂-y₁)²+(x₁-x₂)²

calculating the distances between the 2 center:

d² = (4-(-2))²+(-5-1)² = (6)²+(-6)² = 36 + 36 = 72 ⇒ d = √72

√72 ≈ 8.49

R1 = 1 and R2 = 2

If the circles were secants, d would be < than R1 + R2.

If the circles were tangent, d would be = to  R1 + R2

As d > than R1 + R2, we know that the circles do not intercept.

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a rectangular prism has a square base with a side length of 10 inches. The volume of the prism is 1,600 cubic inches. Find the s
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Answer:

840 in^2

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If the base is square and the side length is 10 inches, the areas of the base and of the top combined is 2(100 in^2).

The height of the prism comes from dividing the volume, 1600 in^3, by the area of the base, 100 in^2:  It is 16 in.  Then the combined areas of the four sides of the prism is 4(160 in^2).

The total surface area of the prsim is then 640 in^2 + 200 in^2, or 840 in^2.

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Suppose that in a casino game the payout is a random variable X . If X is positive, you gain money, if negative, you lose.
Vanyuwa [196]

Answer:

the conditional probability that X = 1 , X = 2 and X = 3 is  0.7333 (73.33%) , 0.25 (25%) and 0.0167 (1.67%) respectively

Step-by-step explanation:

a player wins money when i>0 then defining event W= gain money , then

P(W) = p(i>0) = p(1)+p(2)+p(3)

then the conditional probability can be calculated through the theorem of Bayes

P(X=1/W)= P(X=1 ∩ W)/P(W)

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P(X=1 ∩ W)= probability that the payout is 1 and earns money

P(X=1 / W)= probability that the payout is 1 given money was earned

then

P(X=1/W)= P(X=1 ∩ W)/P(W) = P(X=1) / P(W) = p(1) /[p(1)+p(2)+p(3)] = 11/40 /(11/40+3/32+1/160 ) = 0.7333 (73.33%)

similarly

P(X=2/W)=p(2) /[p(1)+p(2)+p(3)] = 3/32 /(11/40+3/32+1/160 ) = 0.25 (25%)

P(X=3/W)=p(2) /[p(1)+p(2)+p(3)] = 1/160 /(11/40+3/32+1/160 ) = 0.0167 (1.67%)

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