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2 years ago

Find the x if the sequence 3, x, 4x/3 is (a)arithmetic and (b)geometric

Mathematics

1 answer:

jolli1 [7]2 years ago

6 0

(a) When the sequence is arithmetic, sequential terms have a common difference.

... x - 3 = (4x/3) - x . . . . differences of sequential terms are equal

... (2/3)x = 3 . . . . . . . add 3-(1/3)x

... x = 9/2 . . . . . . . . . multiply by 3/2

(The arithmetic sequence is 3, 4.5, 6. The common difference is 3/2.)

(b) When the sequence is geometric, sequential terms have a common ratio.

... x/3 = (4x/3)/x . . . . . ratios of sequential terms are equal

... x^2 = 4x . . . . . multiply by 3x

... x = 4 . . . . . . . . divide by x. (the "solution" x=0 is extraneous)

(The geometric sequence is 3, 4, 16/3. The common ratio is 4/3.)

You might be interested in

You pack sandwiches for a mountain hike with your friends. Each sandwich takes 222 slices of bread, and each hiker eats one sand

Goryan [66]

Answer:

This question contains some errors; the correct question is:

You pack sandwiches for a mountain hike with your friends. Each sandwich takes 2 slices of bread, and each hiker eats one sandwich. How many slices of bread are used for n hikers? Write your answer as an expression.

The answer is:

(2n) slices of bread for n hikers

Step-by-step explanation:

According to the question, sandwiches packed for a mountain hike with friends is made of two (2) slices of bread.

Each hiker gets one sandwich

This, n hikers will get n× 1 sandwich

= (n) sandwiches.

If 1 sandwich contains 2 slices of bread, then (n) sandwiches for n hikers will contain:

(2 × n) slices of bread

That is, (2n) slices of bread.

The expression is (2n).

4 0

2 years ago

Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar pe

telo118 [61]

With the choices you gave, the answer to this question is the first statement, "2 loaves of bread and 4 batches of muffins''. I arrived with the answer through multiplying the amount of flour and sugar required for each loaf of bread and batch of muffins.

4 0

2 years ago

A cardboard box without a lid is to have a volume of 16,384 cm3. Find the dimensions that minimize the amount of cardboard used.

Reika [66]

Answer:

The dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

Step-by-step explanation:

Volume of the cardboard = 16,384 $cm^{3}$

The function that represents the area of the cardboard without a lid is given by

$f (x,y,z) = xy + 2xz + 2yz$ ------ (1)

Volume of the cardboard with sides x, y & z is

$xyz = 16384$

$z = \frac{16384}{xy}$

Put this value of z in equation (1) we get

$f (x,y,z) = xy + 2x(\frac{16384}{xy} ) + 2y(\frac{16384}{xy} )$

$f (x,y,z) = xy + \frac{32768}{y} + 2y(\frac{32768}{x} )$

Differentiate above equation with respect to x & y we get

$f_{x} = y - \frac{32768}{x^{2} }$

$f_{y} = x - \frac{32768}{y^{2} }$

Take $f_{x} = 0 \ and \ f_{y} = 0$

$y - \frac{32768}{x^{2} } = 0$

$y = 32768 \ x^{-2}$ ------ (2)

$x - \frac{32768}{y^{2} } = 0$

$x = 32768 \ y^{-2}$ ------- (3)

By solving equation (2) & (3) we get

$x^{3} = 32768$

x = 31 cm

From equation 2

$y = 32768 \ x^{-2}$

y = 32768 ( $31^{-2}$ )

y = 34 cm

$z = \frac{16384}{xy}$

$z = \frac{16384}{(34)(31)}$

Z = 15.54 cm

Thus the dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

6 0

2 years ago

The system on the left can be reduced to: t + u = 9 9t – 9u = –9 Solving the system t= , u=

LenaWriter [7]

We have that
<span>t + u = 9 --------> t=9-u-----------> equation 1
9t – 9u = –9----------> equation 2
</span>
I substitute 1 in 2
9*[9-u]-9u=-9
81-9u-9u=-9
18u=81+9
18u=90
u=90/18---------> u=5
t=9-u------> t=9-5----> t=4

the answer is
u=5
t=4

5 0

2 years ago

Read 2 more answers

Suppose a research paper states that the distribution of the daily sea-ice advance/retreat from each sensor is similar and is ap

strojnjashka [21]

Answer:

The value of the parameter is λ is 0.03692

Step-by-step explanation:

Consider the provided function.

$f(x) = 0.5\lambda e^{-\lambda |x|}$ for −∞ < x < ∞.

It is given that standard deviation is given as 38.3 km.

Now we need to calculate the value of parameter λ.

The general formula for the probability density function of the double exponential distribution is: $f(x)=\frac{e^{-|\frac{x-\mu}{\beta}|}}{2\beta}$

Where μ is the location parameter and β is the scale parameter.

Compare the provided equation with the above formula we get.

$\lambda=\frac{1}{\beta}$ and μ = 0.

Standard deviation = √2β

$S.D=\sqrt{2} \beta\\\beta=\frac{38.3}{\sqrt{2}}\\\beta=27.08219$

Now substitute the value of β in $\lambda=\frac{1}{\beta}$ .

$\lambda=\frac{1}{27.08219}=0.03692$

Hence, the value of the parameter is λ is 0.03692

7 0

2 years ago