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Alex73 [517]
3 years ago
10

Write the equation of the circle graphed below

Mathematics
1 answer:
abruzzese [7]3 years ago
8 0
8,2 I it took me a while but yes That’s the answer
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Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B
Vilka [71]

Answer:

66.42°

Step-by-step explanation:

<u>Given:</u>

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

BA • BC = 4

|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}

|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}

2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4

10\cos{(m\angle{ABC})} = 4

\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}

m\angle{ABC} = cos^{-1}{(\frac{2}{5})}

m\angle{ABC} = 66.4218^{\circ}

Rounded to two decimal places:

m\angle{ABC} = 66.42^\circ

3 0
2 years ago
Can someone please answer this im stuck
Nastasia [14]
I think its A not sure though
5 0
3 years ago
Read 2 more answers
Consider △RST and △RYX.
astra-53 [7]

Answer:

B. StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction

i.e \frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}

Step-by-step explanation:

Two or more shape or figures are similar when their sides and angles can be compared appropriately.

In the given figure, ΔRXY is within ΔRST. Since the two triangles are similar, then their length of sides can be compared in the form of required ratios.

So that by comparison,

\frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}

Therefore, the correct option to the question is B.

8 0
2 years ago
Read 2 more answers
Please solve this question!!​
GaryK [48]

Answer:  (i) 1/221     (ii) 11/221      (iii) 95/663        (iv) 1/663

<u>Step-by-step explanation:</u>

(i) A deck of cards contains 4 Kings out of 52 total cards

1st draw: 4 Kings out of 52 total cards → 4/52 = 1/13

2nd draw: 3 remaining Kings out of 51 total remaining cards  →  3/51 = 1/17

  <u>1st Draw </u>                   <u>2nd Draw </u>                  <u>Outcome</u>         <u>Probability</u>

 King: P(K) = 1/13        King: P(K₂/K₁) = 1/17     King, King       (1/13) x (1/17) = 1/221

*************************************************************************************************

(ii) A deck of cards contains 4 Jacks, 4 Queens, & 4 Kings out of 52 total cards

1st draw: 12 Face cards out of 52 total cards → 12/52 = 3/13

2nd draw: 11 remaining Face cards out of 51 total remaining cards  →  11/51

<u>1st Draw </u>                 <u>2nd Draw </u>                  <u>Outcome</u>       <u>Probability</u>

 Face: P(F) = 3/13    Face: P(F₂/F₁) = 11/51   Face,Face     (3/13) x (11/51) = 11/221

*************************************************************************************************

(iiI) A deck of cards contains 26 black cards out of 52 total cards but there are 2 black Jacks, 2 black Queens, and 2 black Kings.

1st draw: 20 Black (not Face) cards out of 52 total cards → 20/52 = 5/13

2nd draw: 19 remaining Black (not Face) cards out of 51 total remaining cards  →  19/51

  <u>1st Draw </u>                 <u>2nd Draw </u>                       <u>Outcome</u>   <u>Probability</u>

Black: P(B~) = 5/13   Black: P(B~₂/B~₁) = 19/51    B~,B~    (5/13) x (19/51) = 95/663

*************************************************************************************************

(ii) A deck of cards contains 4 Aces out of 52 total cards

1st draw: 4 Aces out of 52 total cards → 4/52 = 1/13

2nd draw: 1 Queen of Hearts out of 51 total remaining cards  →  1/51

  <u>1st Draw </u>                 <u>2nd Draw </u>                   <u>Outcome</u>         <u>Probability</u>

 Ace: P(A) = 1/13      Qh: P(Qh₂/A₁) = 1/51   Ace,Queen(h)   (1/13) x (1/51) = 1/663

7 0
3 years ago
Suppose n represents an even number for a simplified expression that represents the product of the next two even numbers
Digiron [165]
N+1 x n+2 = whatever that first part means
3 0
3 years ago
Read 2 more answers
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