A boat leaves the dock and travels 9 miles due south, then 12 miles due west.

In circle pp, ad¯¯¯¯¯ad¯ is a diameter and bc¯¯¯¯¯bc¯ is perpendicular to ad¯¯¯¯¯ad¯ at ee. if pd=7pd=7 and ae=4ae=4, find cece.

kvv77 [185]

See the attached figure.

ad is a diameter of the circle with center p

∵ pd = radius = 7 ⇒⇒⇒ ∴ ad = 2 * radius = 2 * 7 = 14
∵ ae = 4 ⇒⇒⇒ ∴ ed = ad - ae = 14 - 4 = 10
∵ ad is a diameter
Δ acd is a triangle drawn in a half circle
∴ Δ acd is a right triangle at c
∵ bc ⊥ ad at point e
By applying euclid's theorem inside Δ acd
∴ ce² = ae * ed
∴ ce² = 4 * 10 = 40
∴ ce = √40 = 2√10 ≈ 6.325

3 0

3 years ago

On a quiz there are four-mulptiple choice questions worth 3 points each and two true/false questions worth 1 point

Scilla [17]

Answer:

15

Step-by-step explanation:

7 0

2 years ago

The following two sets of parametric functions both represent the same ellipse. Explain the difference between the graphs.

statuscvo [17]

The answer
ellipse main equatin is as follow:

X²/ a² + Y²/ b² =1, where a≠0 and b≠0

for the first equation: x = 3 cos t and y = 8 sin t
we can write x² = 3² cos² t and y² = 8² sin² t
and then x² /3²= cos² t and y²/8² = sin² t
therefore, x² /3²+ y²/8² = cos² t + sin² t = 1
equivalent to x² /3²+ y²/8² = 1

for the second equation, x = 3 cos 4t and y = 8 sin 4t we found
x² /3²+ y²/8² = cos² 4t + sin² 4t=1

7 0

3 years ago

Read 2 more answers

Point H is the midpoint of side FK. Triangles F G H and K J H are connected at point H. The lengths of sides F H and H K are con

earnstyle [38]

Answer:

the answer would be x=6

to find it you would set 3x-2 equal to 2x+4 and solve because the two sides would be equal if the triangles are congruent

hope this helps :)

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Describe the sample space for each of these experiments (a) A coin is tossed and a single die is rolled. (b) A paper cup is toss

kondor19780726 [428]

Answer:

a) S={(head,1),(head,2),(head,3),(head,4),(head,5),(head,6),(tails,1),(tails,2),(tails,3),(tails,4),(tails,5),(tails,6)}

b) S={top,bottom,side}

c) S={(Ace of diamonds),(Two of diamonds),(Three of diamonds),(Four of diamonds),(Five of diamonds),(Six of diamonds),(Seven of diamonds), (Eight of diamonds),(Nine of diamonds),(Ten of diamonds), (Jack of diamonds), (Queen of diamonds), (King of diamonds), (Ace of hearts),(Two of hearts),(Three of hearts),(Four of hearts),(Five of hearts),(Six of hearts),(Seven of hearts), (Eight of hearts), (Nine of hearts),(Ten of hearts), (Jack of hearts), (Queen of hearts),(King of hearts),(Ace of clubs),(Two of clubs),(Three of clubs),(Four of clubs),(Five of clubs),(Six of clubs),(Seven of clubs), (Eight of clubs), (Nine of clubs),(Ten of clubs), (Jack of clubs),(Queen of clubs),(King of clubs),(Ace of spades),(Two of spades),(Three of spades),(Four of spades),(Five of spades),(Six of spades),(Seven of spades),(Eight of spades), (Nine of spades),(Ten of spades),(Jack of spades),(Queen of spades),(King of spades)}

Step-by-step explanation:

The sample space is all the possible outcomes from each experiment:

a) The sample has the pairs of the result of the coin (head or tails) and the dice (a number from 1 to 6):

S={(head,1),(head,2),(head,3),(head,4),(head,5),(head,6),(tails,1),(tails,2),(tails,3),(tails,4),(tails,5),(tails,6)}

b) A paper cup can land in three different ways, on its top, bottom or side:

S={top,bottom,side}

c) The sample space is all the cards in the deck:

S={(Ace of diamonds),(Two of diamonds),(Three of diamonds),(Four of diamonds),(Five of diamonds),(Six of diamonds),(Seven of diamonds), (Eight of diamonds),(Nine of diamonds),(Ten of diamonds), (Jack of diamonds), (Queen of diamonds), (King of diamonds), (Ace of hearts),(Two of hearts),(Three of hearts),(Four of hearts),(Five of hearts),(Six of hearts),(Seven of hearts), (Eight of hearts), (Nine of hearts),(Ten of hearts), (Jack of hearts), (Queen of hearts),(King of hearts),(Ace of clubs),(Two of clubs),(Three of clubs),(Four of clubs),(Five of clubs),(Six of clubs),(Seven of clubs), (Eight of clubs), (Nine of clubs),(Ten of clubs), (Jack of clubs),(Queen of clubs),(King of clubs),(Ace of spades),(Two of spades),(Three of spades),(Four of spades),(Five of spades),(Six of spades),(Seven of spades),(Eight of spades), (Nine of spades),(Ten of spades),(Jack of spades),(Queen of spades),(King of spades)}

3 0

3 years ago