4th quadrant is positive x (cos) and negative y (sin)
Use the Pythagorean Theorem to calculate the value of y (sin).
x² + y² = c²
5² + y² = 13²
25 + y² = 169
y² = 144
y = 12
Since the y-value is negative in the 4th quadrant, then y = -12
10 , 20 , 30 , 40 , 50
8, 16 , 24, 32, 40
40 minutes
9514 1404 393
Answer:
- 13 ft
- (a) 1 second; (b) t = 0, t = 1/2
Step-by-step explanation:
<h3>1. </h3>
Let w represent the length of the wire. Then the height of attachment is (w-1). The Pythagorean theorem tells us a relevant relation is ...
5² +(w -1)² = w²
w² -2w +26 = w² . . . . . . . eliminate parentheses, collect terms
26 = 2w . . . . . . . . . . . . add 2w
13 = w . . . . . . . . . . . . divide by 2
The length of the wire is 13 feet.
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<h3>2. </h3>
(a) When h = 0, the equation is ...
0 = -16t^2 +8t +8
Dividing by -8 puts this into standard form:
2t^2 -t -1 = 0
Factoring, we get ...
(2t +1)(t -1) = 0
The positive value of t that makes a factor zero is t = 1.
It will take 1 second for the gymnast to reach the ground.
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(b) When h = 8, the equation is ...
8 = -16t^2 +8t +8
Subtract 8 and divide by 8 to get ...
0 = -2t^2 +t
0 = t(1 -2t) . . . . factor out t
Values of t that make the factors zero are ...
t = 0
t = 1/2
The gymnast will be 8 feet above the ground at the start of the dismount, and 1/2 second later.
Area of a Circle: The area of a circle is the amount of space the circle takes up. To compute the area of a circle, we use the formula a=πr^2 where r is the radius of the circle.
Radius: The radius of a circle is the distance from the center of the circle to any point on the circle.
Answer:
- 6.547
Step-by-step explanation:
Given that:
Sample size (n) = 1207
p = 0.85
p0 = 0.92
The test statistic :
Z = (p - p0) / √(p0(1 - p0) / n)
Z = (0.85 - 0.92) / √(0.92(1 - 0.85) / 1207)
Z = - 0.07 / √(0.92(0.15) / 1207)
Z = - 0.07 / √0.0001143
Z = - 0.07 / 0.0106926
Z = - 6.5465446
Z = - 6.547