Answer: The length of BD is 2.4
Step-by-step explanation: BD is a leg of a right triangle, so use the
Pythagorean Theorem a² + b² = c²
BC is the hypotenuse here, so that is c = 3
We can use the segment CD as side b = 1.8
We will call BD side a, and solve to find that length.
a² + (1.8)² = 3² Square the known values of b and c
a² + 3.24 = 9 Subtract 3.24 from both sides.
a² = 9 - 3.24 Simplify
a² = 5.76 Find the square root of both sides (Calculator time!)
a = 2.4
If you substitute each ordered pair for x and y the only ordered pair that works is (0,-3) .
First we must convert the mixed numbers to the improper fractions:
Answer:
Arc length XPY =28.26 m.
Step-by-step explanation:
Given : A circle with two arc XY and XPY and radius 6 m.
To find : Arc length XPY.
Solution : We have given that arc XY and XPY .
Radius = 6 m.
Central angle formed by arc XPY = 360 - 90 = 270.
Arc length = 2 *pi* r ( 
.
Plugging the values
Arc length = 2 *3.14 * 6 ( 
.
Arc length =37.68 ( 
.
Arc length =37.68 * 0.75
Arc length XPY =28.26 m.
Therefore, Arc length XPY =28.26 m.
Let <em>a</em> and <em>b</em> be the zeroes of <em>x</em>² + <em>kx</em> + 12 such that |<em>a</em> - <em>b</em>| = 1.
By the factor theorem, we can write the quadratic in terms of its zeroes as
<em>x</em>² + <em>kx</em> + 12 = (<em>x</em> - <em>a</em>) (<em>x</em> - <em>b</em>)
Expand the right side and equate the coefficients:
<em>x</em>² + <em>kx</em> + 12 = <em>x</em>² - (<em>a</em> + <em>b</em>) <em>x</em> + <em>ab</em>
Then
<em>a</em> + <em>b</em> = -<em>k</em>
<em>ab</em> = 12
The condition that |<em>a</em> - <em>b</em>| = 1 has two cases, so without loss of generality assume <em>a</em> > <em>b</em>, so that |<em>a</em> - <em>b</em>| = <em>a</em> - <em>b</em>.
Then if <em>a</em> - <em>b</em> = 1, we get <em>b</em> = <em>a</em> - 1. Substitute this into the equations above and solve for <em>k</em> :
<em>a</em> + (<em>a</em> - 1) = -<em>k</em> → 2<em>a</em> = 1 - <em>k</em> → <em>a</em> = (1 - <em>k</em>)/2
<em>a</em> (<em>a</em> - 1) = 12 → (1 - <em>k</em>)/2 • ((1 - <em>k</em>)/2 - 1) = 12
→ (1 - <em>k</em>)²/4 - (1 - <em>k</em>)/2 = 12
→ (1 - <em>k</em>)² - 2 (1 - <em>k</em>) = 48
→ (1 - 2<em>k</em> + <em>k</em>²) - 2 (1 - <em>k</em>) = 48
→ <em>k</em>² - 1 = 48
→ <em>k</em>² = 49
→ <em>k</em> = ± √(49) = ±7
