Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10).
1 answer:
Answer:
y² / 81 - x² / 19 = 1
Step-by-step explanation: See Annex ( vertices and foci in coordinates axis)
The equation in standard form for the hyperbola is:
x² / a² - y²/b² = 1 or y²/a² - x² / b² = 1
In cases of transverse axis parallel to x axis or y axis respectively.
As per given information in this case hyperbola has a transverse axis parallel to y axis the equation is
y²/a² - x² / b² = 1
a is a distance between center and vertex therefore a = 9
c is a distance between center and a focus c = 10
and b will be:
c² = a² + b² ⇒ b² = c² - a² ⇒ b² = (10)² - (9)² ⇒ b² = 100 - 81
b = √19
And the equation in standard form is:
y² / a² - x² / b² = 1
y² / ( 9 )² - x² / √(19)² ⇒ y² / 81 - x² / 19 = 1
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Answer:
The general rule for the nth term of this sequence will be:
Step-by-step explanation:
Given the sequence
12a, 15a, 18a, 21a, 24a,...
An arithmetic sequence has a constant difference 'd' and is defined by
Here,
a₁ = 12a
computing the differences of all the adjacent terms
d = 15a-12a = 3a, d = 18a-15a=3a, d=21a-18a=3a, d=24a-21a=3a
using the nth term formula
substituting a₁ = 12a, d = 3a
Therefore, the general rule for the nth term of this sequence will be:
We are given:
The time t required to drive a certain distance varies inversely with the speed r.
According to the question t is inversely proportional to speed(r).
let us say distance (d) is constant of proportionality,
So the equation becomes,
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d=134 miles.
Now we have to find how long will it take to drive the same distance that is 134 miles at 55 miles per hour
so plugging the values, we have,
t=2.436
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Here you go. look for the simples method of elimination and solve.
