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2 years ago

Find the common ratio and an explicit form in each of the following geometric sequences.

Mathematics

1 answer:

Margaret [11]2 years ago

7 0

Answer:

The explicit form is $a_{n}=162(2/3)^{n-1}$

Step-by-step explanation:

The explicit form of a geometric sequence is given by:

$a_{n}=ar^{n-1}$

where an is the nth term, a is the first term of the sequence and r is the common ratio.

In this case:

a=162

The value of the common ratio is obtained by dividing one term by the previous term.

For the first and second terms:

108/162=2/3

For the second and third terms (In order to prove that 2/3 is the common ratio)

72/108=2/3

Therefore:

r=2/3

Replacing a and r in the formula:

$a_{n}=162(2/3)^{n-1}$

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Write an equivalent representation of the number 5.46 in word form

DerKrebs [107]

Answer:

five and forty-six hundredths

Step-by-step explanation:

3 0

2 years ago

Geometry please help!

ikadub [295]

Answer:

see explanation

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

The polygon here has 8 sides, that is n = 8, thus

sum = 180° × 6 = 1080°

Sum the given angles and equate to 1080, that is

14x + 133 + 167 + 138 + 18x + 115 + 151 + 120 = 1080

32x + 824 = 1080 ( subtract 824 from both sides )

32x = 256 ( divide both sides by 32 )

x = 8

Thus the 2 unknown angles are

14x = 14 × 8 = 112°

18x = 18 × 8 = 144°

8 0

2 years ago

1. S(–4, –4), P(4, –2), A(6, 6) and Z(–2, 4) a) Apply the distance formula for each side to determine whether SPAZ is equilatera

Aleksandr [31]

Answer:

a) SPAZ is equilateral.

b) Diagonals SA and PZ are perpendicular to each other.

c) Diagonals SA and PZ bisect each other.

Step-by-step explanation:

At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.

a) If figure is equilateral, then SP = PA = AZ = ZS:

$SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}$

$SP \approx 8.246$

$PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}$

$PA \approx 8.246$

$AZ =\sqrt{(-2-6)^{2}+(4-6)^{2}}$

$AZ \approx 8.246$

$ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}$

$ZS \approx 8.246$

Therefore, SPAZ is equilateral.

b) We use the slope formula to determine the inclination of diagonals SA and PZ:

$m_{SA} = \frac{6-(-4)}{6-(-4)}$

$m_{SA} = 1$

$m_{PZ} = \frac{4-(-2)}{-2-4}$

$m_{PZ} = -1$

Since $m_{SA}\cdot m_{PZ} = -1$ , diagonals SA and PZ are perpendicular to each other.

c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:

$M_{SA} = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot A(x,y)$

$M_{SA} = \frac{1}{2}\cdot (-4,-4)+\frac{1}{2}\cdot (6,6)$

$M_{SA} = (-2,-2)+(3,3)$

$M_{SA} = (1,1)$

$M_{PZ} = \frac{1}{2}\cdot P(x,y) + \frac{1}{2}\cdot Z(x,y)$

$M_{PZ} = \frac{1}{2}\cdot (4,-2)+\frac{1}{2}\cdot (-2,4)$

$M_{PZ} = (2,-1)+(-1,2)$

$M_{PZ} = (1,1)$

Then, the diagonals SA and PZ bisect each other.

8 0

2 years ago

Andre builds a form for a new cement step in the shape of a rectangular prism. The form he builds is 40 and 1/2 inches long, 10

posledela

Answer:

3240 in^3

Step-by-step explanation:

Step one:

given data

The dimension of the form

Length 40 and 1/2 inches long,

Depth 10 inches deep,

The width and 8 inches high

Step two:

The amount of cement is equivalent to the volume of the form

$V=L*W*H\\\\V=40.5*10*8\\\\V=3240 in^3$

Hence the volume of cement is 3240 in^3

8 0

2 years ago

A mouse scurries across your kitchen floor at 2.0 feet per second. How many miles can the mouse travel in 1.5 hours (rounded to

Mila [183]

Given

A mouse scurries across your kitchen floor at 2.0 feet per second.

Find out the mouse travel in 1.5 hours.

To proof

FORMULA

Distance = speed × time

$1foot = \frac{1}{5280} miles$

Convert feet per second into miles per second

$= \frac{2.0}{5280}$

As given in the question

Time = 1.5 hours

1 hours = 3600 second

Time convert in the second

Time = 1.5 × 3600 second

= 5400 second

put all these value in the above formula

we get

$Distance= \frac{2.0\times 1.5 \times 3600}{5280}$

$Distance= \frac{10800}{5280}$

= 2.04 (approx) miles

= 2.0 miles

Hence proved

4 0

2 years ago

Read 2 more answers