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2 years ago

Find the first four terms of the sequence given by the following. an= 4(2)^n-1 n=1, 2, 3...

Mathematics

1 answer:

mr_godi [17]2 years ago

4 0

Answer + Step-by-step explanation:

an= 4(2)ⁿ⁻¹

First term (n = 1) :

a1= 4(2)¹⁻¹ = 4(2)⁰ = 4×(1) = 4

Second term (n = 2) :

a2= 4(2)²⁻¹ = 4(2)¹ = 4×(2) = 8

Third term (n = 3) :

a3= 4(2)³⁻¹ = 4(2)² = 4×(4) = 16

Fourth term (n = 4) :

a4= 4(2)⁴⁻¹ = 4(2)³ = 4×(8) = 32

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Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minut

solmaris [256]

Answer:

6.11km/hr

Step-by-step explanation:

Let the speed that Kelli swims be represented by Y

Speed of the river = 5km/hr

Distance = Speed × Time

Kelli swam upstream for some distance in one hour

Swimming upstream takes a negative sign, hence:

1 hour ×( Y - 5) = Distance

Distance = Y - 5

She then swam downstream the same river for the same distance in only 6 minutes

Downstream takes a positive sign

Converting 6 minutes to hour =

60 minutes = 1 hour

6 minutes =

Cross Multiply

6/60 = 1/10 hour

Hence, Distance =

1/10 × (Y + 5)

= Y/10 + 1/2

Equating both equations we have:

Y - 5 = Y/10 + 1/2

Collect like terms

Y - Y/10 = 5 + 1/2

9Y/10 = 5 1/2

9Y/ 10 = 11/2

Cross Multiply

9Y × 2 = 10 × 11

18Y = 110

Y = 110/18

Y = 6.1111111111 km/hr

Therefore, Kelli's can swim as fast as 6.11km/hr still in the water.

4 0

2 years ago

Convert Зcis 180° to rectangular form. А. -3 в. -3i с. з D. Зі.

Sunny_sXe [5.5K]

Answer:

-3

Step-by-step explanation:

$3 cis(180^\circ)$ means $3(\cos(180^\circ)+i \sin(180^\circ))$

What is the $x$ -coordinate value that corresponds to $\theta=180^\circ$ . That value is -1.

What is the $y$ -coordinate value that corresponds to $\theta=180^\circ$ . That value is 0.

So this implies $\cos(180^\circ)=-1 \text{ and } \sin(180^\circ)=0$ .

$3 cis(180^\circ)$

$3(\cos(180^\circ)+i \sin(180^\circ))$

$3(-1+i (0))$

$3(-1+0)$

$3(-1)$

$-3$

5 0

3 years ago

The minute hand of a clock is 8 inches long and moves from 12 to 8 o’clock. How far does the tip of the minute hand move?

ryzh [129]

The minute hand is like an eight inch radius of a circle, whose circumference would equal 2 * PI * 8 = 50.265 inches. By moving to 8 o'clock, it travels 2/3 of the circumference or 50.265 * 2/3 = 33.510 inches

3 0

3 years ago

Read 2 more answers

(GIVING BRAINLIEST!!!!!!) Solve 1 ÷ 1/2 = ________ A) 2 B) 3 C) 4 D) 5

Tcecarenko [31]

Answer:

Step-by-step explanation:

Becuase 1 divide 1/2

You make the division sign a multiplication sign

1 time 1/2

get the recipricol of 1/2 wich is 2

1 times 2/1

is 2

5 0

3 years ago

2/3=x/6=9/y to find the value of y in this proportion you must divide 54 by

scZoUnD [109]

Answer:

You must divide $54$ by $4$

Step-by-step explanation:

we have

$\frac{2}{3}=\frac{x}{6}=\frac{9}{y}$

Step 1

Solve for x

$\frac{2}{3}=\frac{x}{6}$

$3x=6*2\\x=12/3\\x=4$

Step 2

Find the value of y

$\frac{x}{6}=\frac{9}{y}$

Substitute the value of x

$\frac{4}{6}=\frac{9}{y}$

$4y=9*6\\y=54/4\\y= 13.5$

therefore

You must divide $54$ by $4$

6 0

2 years ago

Read 2 more answers