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3 years ago

What is 4w to the power of -3 divided by 3 to the power of -2+ w to the power of 7 + x to the power of -2

Mathematics

1 answer:

Sindrei [870]3 years ago

3 0

Answer:

idk this stuff yet

Step-by-step explanation:

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The 5th term in a geometric sequence is 160. The 7th term is 40. What are possible values of the 6th term of the sequence?

omeli [17]

Answer:

C. The 6th term is positive/negative 80

Step-by-step explanation:

Given

Geometric Progression

$T_5 = 160$

$T_7 = 40$

Required

$T_6$

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;

To solve the common ratio;

Divide the 7th term by the 5th term; This gives

$\frac{T_7}{T_5} = \frac{40}{160}$

Divide the numerator and the denominator of the fraction by 40

$\frac{T_7}{T_5} = \frac{1}{4}$ ----- equation 1

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Where n is the nth term

So,

$T_7 = a r^{6}$

$T_5 = a r^{4}$

Substitute the above expression in equation 1

$\frac{T_7}{T_5} = \frac{1}{4}$ becomes

$\frac{ar^6}{ar^4} = \frac{1}{4}$

$r^2 = \frac{1}{4}$

Square root both sides

$r = \sqrt{\frac{1}{4}}$

r = ± $\frac{1}{2}$

Next, is to solve for the first term;

Using $T_5 = a r^{4}$

By substituting 160 for T5 and ± $\frac{1}{2}$ for r;

We get

$160 = a \frac{1}{2}^{4}$

$160 = a \frac{1}{16}$

Multiply through by 16

$16 * 160 = a \frac{1}{16} * 16$

$16 * 160 = a$

$2560 = a$

Now, we can easily solve for the 6th term

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Here, n = 6;

$T_6 = a r^{6-1}$

$T_6 = a r^5$

$T_6 = 2560 r^5$

r = ± $\frac{1}{2}$

So,

$T_6 = 2560( \frac{1}{2}^5)$ or $T_6 = 2560( \frac{-1}{2}^5)$

$T_6 = 2560( \frac{1}{32})$ or $T_6 = 2560( \frac{-1}{32})$

$T_6 = 80$ or $T_6 = -80$

$T_6 =$ ±80

Hence, the 6th term is positive/negative 80

8 0

3 years ago

-2.105 as a fraction?

Bezzdna [24]

The easiest way is if it doesn't need to be simplified. Multiply -2.105 by $\frac{1000}{1000}$ . You get the fraction $-\frac{2105}{1000}$ . While this is technically the answer, you can simplify this down to $\frac{421}{200}$ . Because 421 is a prime number, this can not be simplified any further. Therefore, the solution is $\frac{421}{200}$ .

$\frac{421}{200}$ .

6 0

3 years ago

a jet travels 410 miles in 5 hours. At this rate, how far could the jet fly in 14 hours? What is the rate of speed of the jet

Fudgin [204]

Answer:

Step-by-step explanation:

Rate X Time = distance

Therefore:

r (rate) X 5 (hours) = 600 (distance)

r = 600/5

r = 120 miles per hour

The rate of speed of the jet is 120 mph.

Then, to find out the distance flown in 13 hours:

120 (rate) X 13 (time) = d (distance)

120 X 13 = d

1560 = d

The distance flown in 13 hours is 1560 miles.

8 0

3 years ago

Please help me i need an answer

umka2103 [35]

3 / 5 = (x+1) / (y-2)
↓
↓ multiply by 5 / 3
↓
1 = 5 * (x+1) / 3 * (y-2)
↓
↓ move and simplify
↓
5x + 5 = 3y - 6
↓
↓ minus 5
↓
5x = 3y - 11
↓
↓ divide by 5
↓

Answer : x = (3y - 11) / 5

4 0

3 years ago

(-3<(x+2)<7) help pls

vampirchik [111]

3x - 2 = 7
3x = 7 + 2
3x = 9 (divide both sides by 3 to get x)
3x/3 = 9/3
x = 3

4 0

3 years ago