Solve for h.-18 h = 28h =

The third term of the sequence is 120. The fifth term is 76.8 The explicit rule for the geometric sequence is an=?(?)n-1

gulaghasi [49]

Answer:

The explicit rule of the geometric sequence

aₙ = 187.5 (0.8)ⁿ⁻¹

Step-by-step explanation:

Step(i):-

Given that the third term of the sequence = 120

tₙ = a rⁿ⁻¹

t₃ = a r³⁻¹ = ar²

120 = ar² ..(i)

Given that the fifth term of the given geometric sequence = 76.8

tₙ = a rⁿ⁻¹

t₅ = a r⁵⁻¹ = a r⁴

76.8 = a r⁴...(ii)

Step(ii):-

Dividing (ii) and (i)

$\frac{ar^{4} }{ar^{2} } = \frac{76.8}{120}$

r² = 0.64

r =√ 0.64 = 0.8

Substitute r= 0.8 in equation (i)

120 = ar²

120 = a(0.8)²

⇒ $a = \frac{120}{0.64} =187.5$

Step(iii):-

The explicit rule of the geometric sequence

aₙ = a rⁿ⁻¹

put a= 187.5 and r = 0.8

aₙ = 187.5 (0.8)ⁿ⁻¹

7 0

2 years ago

The day length in Manila, Philippines, varies over time in a periodic way that can be modeled by a trigonometric function.

iris [78.8K]

Answer:

L(t) = 727.775 -51.875cos(2π(t +11)/365)
705.93 minutes

Step-by-step explanation:

a) The midline of the function is the average of the peak values:

(675.85 +779.60)/2 = 727.725 . . . minutes

The amplitude of the function is half the difference of the peak values:

(779.60 -675.85)/2 = 51.875 . . . minutes

Since the minimum of the function is closest to the origin, we choose to use the negative cosine function as the parent function.

Where t is the number of days from 1 January, we want to shift the graph 11 units to the left, so we will use (t+11) in our function definition.

Since the period is 365 days, we will use (2π/365) as the scale factor for the argument of the cosine function.

Our formula is ...

L(t) = 727.775 -51.875cos(2π(t +11)/365)

__

b) L(55) ≈ 705.93 minutes

8 0

3 years ago

PLEASE HELP ME

vazorg [7]

Answer:

For the first one, just make sure the sides add up correctly and include the sides it gives. The prism will be 9x1x8 = 82 inches cubed.

Step-by-step explanation:

Insta: lankey.t

6 0

2 years ago

(x+4)(x+2) in quadratic form

Marysya12 [62]

2x+6 is the answer
you have to combine like terms

6 0

3 years ago

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In parallelogram QRST QS RT Is QRST a rectangle ?

fomenos

Answer:

The correct option is A.

Step-by-step explanation:

It is given that the QRST is a parallelogram and the diagonals QS and RT are congruent.

According to the property of parallelogram if the length of diagonals are same, then the parallelogram is rectangle. We can also prove it.

Let QRST be an parallelogram and QS=RT.

In triangles QRT and RQS.

$RT=QS$ (Diagonals)

$QR=QR$ (Common side)

$QT=RS$ (Opposite sides of the parallelogram are same)

So by SSS rule of congruence, triangle QRT and triangle RQS are congruent.

By CPCT,

$\angle R=\angle Q$

Since the sum of two consecutive angles of a parallelogram is 180 degree.

$\angle R+\angle Q=180$

$2\angle R=180$

$\angle R=90$

Therefore the measure of angle R and angle Q are 90 degree.

Similarly in triangle QST and RTS,

$RT=QS$ (Diagonals)

$ST=ST$ (Common side)

$QT=RS$ (Opposite sides of the parallelogram are same)

So by SSS rule of congruence, triangle QST and RTS are congruent.

By CPCT,

$\angle S=\angle T$

Since the sum of two consecutive angles of a parallelogram is 180 degree.

Therefore the measure of angle S and angle T are 90 degree.

Since the measure of all interior angles of QRST are 90 degree, therefore the parallelogram QRST is a rectangle.

6 0

3 years ago

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