Answer:
Step-by-step explanation:
An ellipse with vertices (-8, 0) and (8, 0)
Distance between two vertices = 2a
Distance between (-8,0) and (8,0) = 16
2a= 16
so a= 8
Vertex is (h+a,k)
we know a=8, so vertex is (h+8,k)
Now compare (h+8,k) with vertex (8,0) and find out h and k
h+8 =8, h=0
k =0
a minor axis of length 10.
Length of minor axis = 2b
2b = 10
so b = 5
General formula for the equation of horizontal ellipse is
a= 8 , b=5 , h=0,k=0. equation becomes
Answer:
5507.79 feet
Step-by-step explanation:
To find the height of the mountain, we can draw triangles as in the image attached.
Let's call the height of the mountain 'h', and the distance from the first point (31 degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(34) = h/x
tan(31) = h/(x+1000)
tan(31) is equal to 0.6009, and tan(34) is equal to 0.6745, so:
h/x = 0.6745 -> x = h/0.6745
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.6745 + 1000) = 0.6009
h = 0.6009 * (h/0.6745 + 1000)
h = 0.8909*h + 600.9
0.1091h = 600.9
h = 600.9 / 0.1091 = 5507.79 feet
Answer:
There is a linear correlation between chest size and weight,0.8482
Step-by-step explanation:
Given that for a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears.
the value of the linear correlation coefficient is r = 0.921.
i.e. there is a strong positive correlation from the value of r.
(Two tailed test at 5% level for correlation coefficient)
Test statistic t =
p value <0.00001
Since p is less than 0.05 we reject H0
a) There is a linear correlation between chest size andweight
b)-- R^2 = 0.8482 proportion of the variation in weight can be explainedby the linear relationship between weight and chest size