Answer:
The answer is a= 128.95 and b = 14.75
Step-by-step explanation:
Solution
Given
let the equation of the hyperbola be denoted as x2/a2 - y2/b2 = 1 here, we will consider the foci on the x-axis. All units are considered to be in mm.
From question stated, with x and y coordinates represents height and radius respectively,
Then,
When x = 83 + a, y is = 45/2 = 22.5 and
At x = 180 + a, y is = 57/2 = 28.5
It is important to know that, the height is estimated from the focus so we a a is included to the heights.
Thus,
(83+a)2/a2 - 22.52/b2 = 1 and (180+a)2/a2 - 28.52/b2 = 1
By using a calculator we have, a = 128.95 and b = 14.75
Therefore a= 128.95 and b = 14.75
Answer:
Domain: 
Range: 
Step-by-step explanation:
Given

Required
Determine the domain and the range
Solving for domain:
From the question, we understand that t represent years.
Because years can't be negative;
Then, we can conclude that the domain, t is:

Solving for Range:
We solved domain to be 
This implies that the minimum value of t is
and the maximum is infinity
Substitute 0 for t in 



Hence;
The range is 
Answer:
The margin of error for the survey is 0.016
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 1024
Sample proportion:

We have to find the margin of error associated with a 90% Confidence interval.
Formula for margin of error:


Putting the values, we get:

Thus, the margin of error for the survey is 0.016
This question is not complete.
Complete Question
Major arc CBD measures 300°. Which is the radian measure of its corresponding central angle?
a)4pi/3 radians
b) 5pi/6 radians
c) 5pi/3 radians
d) 11pi/6 radians
Answer:
c) 5pi/3 radians = 5π/3 radians
Step-by-step explanation:
The corresponding central angle can be defined as the angle that is formed when there is a joining together of two radii at the center of the circle.
The circumference of a circle is given as
360° = 2πr
The major arc CBD is 300°
Therefore,
360° = 2πr , radius is not given hence , 360° = 2π
300° = Y (Unknown)
Cross multiply
360Y= (300× 2π)
Y = 600π ÷ 360
Y = (5π÷ 3) radians
Y = 5π/3 radians
Hence the radian measure for the corresponding angle is = 5π/3 radians
Answer: The required system of equations are
y = 30x
13x + y = 258
Step-by-step explanation:
Let x represent the number of hours
that the driver worked.
Let y represent the number of miles that the truck drove.
For every truck that goes out, Mason must pay the driver $13 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance. If on a particular day, his total expenses for the driver, gas and truck maintenance were $258, it means that
13x + y = 258
On that particular day, the driver drove an average of 30 miles per hour.
Speed = distance/time
It means that
y/x = 30
y = 30x