Step-by-step explanation:
the introduction of a fraction tells us that we are dealing with multiplications, and therefore a geometric sequence (where every new term is created by multiplying the previous term by a constant factor, the ratio r).
I think your teacher made a mistake, or you made one when typing the question in here.
there is no factor r that creates
15×r = 9
and
9×r = 5/27
it would mean that
15 × r² = 5/27
r² = 5/27 / 15 = 5/27 × 1/15 = 5/405 = 1/81
r = 1/9
but 15 × 1/9 = 5 × 1/3 = 5/3 is NOT 9
and 9 × 1/9 = 9/9 = 1 is NOT 5/27
so, this can't be right.
on the other hand
15 × r = 9
r = 9/15 = 3/5
and then
9 × 3/5 = 27/5
so, either the sequence should have been
15, 5/3, 5/27
or (and I suspect this to be true)
15, 9, 27/5
under that assumption we have
s1 = 15
r = 3/5
sn = sn-1 × r = s1 × r^(n-1) = 15 × (3/5)^(n-1)
s10 = 15 × (3/5)⁹ = 15 × 19683/1953125 =
= 3 × 19683/390625 = 59049/390625 =
= 0.15116544 ≈ 0.151
Answer:
16.1157
Step-by-step explanation:
side = 8 m
the area of the rectangle = length × width = 16 × 4 = 64 m²
the area of the square = s² ( where s is the length of a side ), hence
s² = 64 ( since areas are equal )
take the square root of both sides
s = √64 = 8 m
Answer:
The center of the tetrahedron divides each of the four heights (or medians) in the ratio 1:3 (in an equilateral triangle the corresponding ratio is 1:2). The smaller part is also the radius of the inscribed sphere. Therefore the radius of this sphere is one quarter of the height or 9 in your case.
Answer:
Area of the image rectangle = 4(Area of the original rectangle)
Step-by-step explanation:
Length of the rectangle given in the graph = 4 units
Width of the rectangle = 2 units
Area of the rectangle = Length × Width
= 4 × 2
= 8 square units
Since, scale factor = 
2 = 
Length of the image rectangle = 2(4)
= 8 units
Similarly, width of the image rectangle = 2(2)
= 4 units
Area of the image rectangle = 8 × 4
Area of the image = Area of the original × 4
Area of the image = 4(Area of the original)
Area of the image rectangle = 4(Area of the original rectangle)
