Answer: Elizabeth and Manuel have a distance of 4 meters between them.
Step-by-step explanation: Please refer to the picture attached.
From the information given, Elizabeth is directly behind Hannah and directly left of Manuel. That means we have three points which are HEM, that is, we now have triangle HEM. The longest side (hypotenuse) which is the distance between Hannah and Manuel is given as 5 meters while the other side the distance between Hannah and Elizabeth is given as 3 meters.
We shall apply the pythagoras theorem in solving for the unknown side, EM.
The Pythagoras theorem states thus;
AC² = AB² + BC²
Where AC is the hypotenuse, and AB and BC are the other two sides.
Substituting for the known values, we now have;
5² = 3² + EM²
25 = 9 + EM²
Subtract 9 from both sides of the equation
16 = EM²
Add the square root sign to both sides of the equation
√16 = √EM²
4 = EM
Therefore the distance between Elizabeth and Manuel is 4 meters
A = 8i + 6j
b = 4i + 5j
ab = (8i + 6j)(4i + 5j)
ab = 8i(4i + 5j) + 6j(4i + 5j)
ab = 8i(4i) + 8i(5j) + 6j(4i) + 6j(5j)
ab = 32i² + 40ij + 24ij + 30j²
ab = 32i² + 64ij + 30j²
ab = <32, 30>
The answer is D.
Answer:
Step-by-step explanation:
Directions
- Draw a circle
- Dear a chord with a length of 24 inside the circle. You just have to label it as 24
- Draw a radius that is perpendicular and a bisector through the chord
- Draw a radius that is from the center of the circle to one end of the chord.
- Label where the perpendicular radius to the chord intersect. Call it E.
- You should get something that looks like the diagram below. The only thing you have to do is put in the point E which is the midpoint of CB.
Givens
AC = 13 inches Given
CB = 24 inches Given
CE = 12 inches Construction and property of a midpoint.
So what we have now is a right triangle (ACE) with the right angle at E.
What we seek is AE
Formula
AC^2 = CE^2 + AE^2
13^2 = 12^2 + AE^2
169 = 144 + AE^2 Subtract 144 from both sides.
169 - 144 = 144-144 + AE^2 Combine
25 = AE^2 Take the square root of both sides
√25 = √AE^2
5 = AE
Answer
The 24 inch chord is 5 inches from the center of the circle.
