All categories

4 years ago

Find the common ratio for the series 64, 48, 36, 27, ... *

Mathematics

1 answer:

andreyandreev [35.5K]4 years ago

5 0

Answer:

Common ratio = 3/4

Step-by-step explanation:

The nth term of a geometric progression is given by

an = a1 . rn - 1

Where;

an = the nth term

a1 = the first term

r = common ratio

n = the number of terms in the series

Common ratio, r = the ratio of the second term to the first term

= a2 : a1

Given from the series,

a2 = 48

a1 = 64

Common ratio, r = 48 : 64

= 48/64 = 3/4

You might be interested in

U - 5.3 = 3.99 gxmdksgsjdkd

Rina8888 [55]

Answer:

Assuming you want to find u, u = 9.29

Step-by-step explanation:

u - 5.3 = 3.99

Add 5.3 to both sides.

u = 3.99 + 5.3

u = 9.29

5 0

4 years ago

Find the projection of the vector A = î - 2ġ + k on the vector B = 4 i - 4ſ + 7k. 15. Given the vectors A = 2 i +3 ſ +6k and B =

Gwar [14]

Answer:

Part 1)

Projection of vector A on vector B equals 19 units

Part 2)

Projection of vector B' on vector A' equals 35 units

Step-by-step explanation:

For 2 vectors A and B the projection of A on B is given by the vector dot product of vector A and B

Given

$\overrightarrow{v_{a}}=\widehat{i}-2\widehat{j}+\widehat{k}$

Similarly vector B is written as

$\overrightarrow{v_{b}}=4\widehat{i}-4\widehat{j}+7\widehat{k}$

Thus the vector dot product of the 2 vectors is obtained as

$\overrightarrow{v_{a}}\cdot \overrightarrow{v_{b}}=(\widehat{i}-2\widehat{j}+\widehat{k})\cdot (4\widehat{i}-4\widehat{j}+7\widehat{k})\\\\\overrightarrow{v_{a}}\cdot \overrightarrow{v_{b}}=1\cdot 4+2\cdot 4+1\cdot 7=19$

Part 2)

Given vector A' as

$\overrightarrow{v_{a'}}=2\widehat{i}+3\widehat{j}+6\widehat{k}$

Similarly vector B' is written as

$\overrightarrow{v_{b'}}=\widehat{i}+5\widehat{j}+3\widehat{k}$

Thus the vector dot product of the 2 vectors is obtained as

$\overrightarrow{v_{b'}}\cdot \overrightarrow{v_{a'}}=(\widehat{i}+5\widehat{j}+3\widehat{k})\cdot (2\widehat{i}+3\widehat{j}+6\widehat{k})\\\\\overrightarrow{v_{a'}}\cdot \overrightarrow{v_{b'}}=1\cdot 2+5\cdot 3+3\cdot 6=35$

7 0

4 years ago

Assume that it costs Apple approximately E(x) 25,600 + 100x + 0.012 dollars to manufacture x 32GB iPods in a day. (a) The averag

uranmaximum [27]

Answer:

(a) $C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)x=1600, Minimum Average Cost Per iPod=$132

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

Step-by-step explanation:

Given that it costs Apple approximately $ C(x) to manufacture x 32GB iPods in a day, where:

$C(x)=25,600+100x+0.01x^2$

(a)The average cost per iPod when they manufacture x iPods in a day is given by:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}$

The average cost per iPod is therefore:

$C'(x)=\dfrac{x^2-2560000}{x^2}$

(b)To minimize average cost of x iPods per day, we set the average cost per iPod=0 and solve for x.

$C'(x)=\dfrac{x^2-2560000}{x^2}=0\\x^2-2560000=0\\x^2=2560000\\x=\sqrt{2560000}=1600$

The resulting minimum average cost (at x=1600) is given as:

$Cost \:Per \:iPod=\dfrac{C(x)}{x} =\dfrac{25,600+100x+0.01x^2}{x}\\\dfrac{25,600+100(1600)+0.01(1600)^2}{1600}\\=\$132$

<u>Second derivative test</u>

(c)The answer above is a critical point for the average cost function. To show it is a minimum, we calculate the second derivative of the average cost function.

$C''(x)=\dfrac{5120000}{x^3}$

At the critical point, x=1600

$C''(1600)=\dfrac{5120000}{1600^3}=0.00125$

The result, C''(1600) is positive, which means that the average cost is Concave up at the critical point, and the critical point is a minimum.

3 0

3 years ago

What is the inverse of the function H(x)=3/4x+12

Mrac [35]

Answer:

$h^{-1}$ (x) = $\frac{4x-48}{3}$

Step-by-step explanation:

let y = h(x) and rearrange making x the subject, that is

y = $\frac{3}{4}$ x + 12 ( multiply through by 4 to clear the fraction )

4y = 3x + 48 ( subtract 48 from both sides )

4y - 48 = 3x ( divide both sides by 3 )

$\frac{4y-48}{3}$ = x

Change y back into terms of x, thus

$h^{-1}$ (x) = $\frac{4x-48}{3}$

3 0

4 years ago

A boat goes 32 miles downstream in two hours. The return trip againts the current takes sixteen hours. Find the rate of the boat

zepelin [54]

Answer: the rate of the boat in calm water is 9 mph and the rate of the current is 7 mph

Step-by-step explanation:

Let x represent the rate of the boat in calm water.

Let y represent the rate of the current.

A boat goes 32 miles downstream in two hours. Assuming that it travelled in the direction of the current, its total speed would be

x + y mph

Distance = speed × time

Distance covered downstream is

32 = 2(x + y)

16 = x + y - - - - - - - - - - - -1

The return trip against the current takes sixteen hours.

Its total speed would be x - y mph

Distance = speed × time

Distance covered on return trip is

32 = 16(x - y)

2 = x - y - - - - - - - - - - - -2

Adding equation 1 and equation 2, it becomes

18 = 2x

x = 18/2 = 9 mph

Substituting x = 9 into equation 1, it becomes

16 = 9 + y

y = 16 - 9 = 7 mph

3 0

3 years ago