It would be the first one because it’s going up by a constant rate
Answer:
C. The 6th term is positive/negative 80
Step-by-step explanation:
Given
Geometric Progression


Required

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;
To solve the common ratio;
Divide the 7th term by the 5th term; This gives

Divide the numerator and the denominator of the fraction by 40
----- equation 1
Recall that the formula of a GP is

Where n is the nth term
So,


Substitute the above expression in equation 1
becomes


Square root both sides

r = ±
Next, is to solve for the first term;
Using 
By substituting 160 for T5 and ±
for r;
We get


Multiply through by 16



Now, we can easily solve for the 6th term
Recall that the formula of a GP is

Here, n = 6;



r = ±
So,
or 
or 
or 
±80
Hence, the 6th term is positive/negative 80
7/12 because it would come out to be 21/36, and the simplified version of that is 7/12<span />
Answer: The equation of an ellipse:
(
x
−
h
)
2
a
2
+
(
y
−
k
)
2
b
2
=
1
;
a
>
b
Has vertices at
(
h
±
a
,
k
)
Has foci at
(
h
±
√
a
2
−
b
2
,
k
)
Use the vertices to write 3 equations:
k
=
4
[1]
h
−
a
=
−
6
[2]
h
+
a
=
10
[3]
Use equations [2] and [3] to solve for h and a:
2
h
=
4
h
=
2
a
=
8
Use the focus to write another equation:
8
=
h
+
√
a
2
−
b
2
Substitute values for h and a:
8
=
2
+
√
8
2
−
b
2
6
=
√
64
−
b
2
36
=
64
−
b
2
b
2
=
64
−
36
b
2
=
28
b
=
√
28
Substitute the values into the standard form:
(
x
−
2
)
2
8
2
+
(
y
−
4
)
2
(
√
28
)
2
=
1
<h2>

</h2>
Two cones have their heights in the ratio 1 : 3 and the radius of their bases in the ratio 3 : 1 show that their volumes are in the ratio 3 : 1.
<h2>

</h2>
⇒ Ratio of heights of two cones = 1 : 3
⇒ Ratio of radius of their bases = 3 : 1
⇒ We know that V = 1/3πr²h
⇒ Ratio of their volume = V1 : V2








