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3 years ago

If a+1/a=3What is the answer? a⁵+1/a⁵

Mathematics

1 answer:

luda_lava [24]3 years ago

5 0

Answer:

123

Step-by-step explanation:

We can square and cube the equation, then multiply the results together.

(a + $\frac{1}{a}$ ) = 3 ← square both sides

a² + 2 + $\frac{1}{a^2}$ = 9 ( subtract 2 from both sides )

a² + $\frac{1}{a^2}$ = 7 → (1)

-----------------------

Now cube both sides

a³ + $\frac{1}{a^3}$ + 3(a + $\frac{1}{a}$ ) = 27

a³ + $\frac{1}{a^3}$ + 3(3) = 27

a³ + $\frac{1}{a^3}$ + 9 = 27 ( subtract 9 from both sides )

a³ + $\frac{1}{a^3}$ = 18 → (2)

------------------------------

Multiply (1) and (2)

(a² + $\frac{1}{a^2}$ )(a³ + $\frac{1}{a^3}$ ) = 7(18)

$a^{5}$ + ( $\frac{1}{a}$ + a) + $\frac{1}{a^5}$ = 126

$a^{5}$ + 3 + $\frac{1}{a^5}$ = 126 ( subtract 3 from both sides )

$a^{5}$ + $\frac{1}{a^5}$ = 123

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Simultaneous equations <br>3x + 2y= 13<br>x + 2y= -1

antoniya [11.8K]

Answer:

{x = 7 , y = -4

Step-by-step explanation:

Solve the following system:

{3 x + 2 y = 13 | (equation 1)

{x + 2 y = -1 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x + 2 y = 13 | (equation 1)

{0 x+(4 y)/3 = (-16)/3 | (equation 2)

Multiply equation 2 by 3/4:

{3 x + 2 y = 13 | (equation 1)

{0 x+y = -4 | (equation 2)

Subtract 2 × (equation 2) from equation 1:

{3 x+0 y = 21 | (equation 1)

{0 x+y = -4 | (equation 2)

Divide equation 1 by 3:

{x+0 y = 7 | (equation 1)

{0 x+y = -4 | (equation 2)

Collect results:

Answer: {x = 7 , y = -4

6 0

3 years ago

2. Vectors u and v are given by: u=5i-4j+ pk v=2i+tj-3k (a) Express p in terms of t when u and v are perpendicular.

Sindrei [870]

If u and v are perpendicular, then their dot product is zero:

$\vec u \cdot \vec v = (5\,\vec\imath-4\,\vec\jmath+p\,\vec k) \cdot (2\,\vec\imath+t\,\vec\jmath - 3\,\vec k) = 10 - 4t - 3p = 0$

Solve for p :

$10 - 4t - 3p = 0$

$3p = 10 - 4t$

$\boxed{p = \dfrac{10-4t}3}$

6 0

2 years ago

(1/2 + 3/2)² + (2/3 x 1/2)³

docker41 [41]

The result of the mathematical expression given as follows: (1/2 + 3/2)² + (2/3 x 1/2)³ is 5.59 or 5⅔.

<h3>How to calculate mathematical expressions?</h3>

According to this question, the following expression is given to solve: (1/2 + 3/2)² + (2/3 x 1/2)³

First, we solve the both parts as follows:

½ + 3/2 = 2
⅔ + ½ = 1..16

Next, we solve the exponential function as follows:

= (2)² + (1.16)³

= 4 + 1.59

= 5.59 or 5⅔

Therefore, the result of the mathematical expression given as follows: (1/2 + 3/2)² + (2/3 x 1/2)³ is 5.59 or 5⅔.

Learn more about mathematical expression at: brainly.com/question/1703934

#SPJ1

5 0

2 years ago

According to survey data, the distribution of arm spans for males is approximately Normal with a mean of 71.4 inches and a stan

Gekata [30.6K]

Answer:

a) 89.97% of men have arm spans between 66 and 76 inches.

b) The z-score for this person's arm span is 5.68. 0% of males have an arm span at least as long as this person

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of 71.4 inches and a standard deviation of 3.1 inches.

This means that $\mu = 71.4, \sigma = 3.1$

a. What percentage of men have arm spans between 66 and 76 inches?

The proportion is the pvalue of Z when X = 76 subtracted by the pvalue of Z when X = 66. The percentage is the proportion multiplied by 100.

X = 76

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{76 - 71.4}{3.1}$

$Z = 1.48$

$Z = 1.48$ has a pvalue of 0.9306

X = 66

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{66 - 71.4}{3.1}$

$Z = -1.74$

$Z = -1.74$ has a pvalue of 0.0409

0.9306 - 0.0409 = 0.8997

0.8997*100% = 89.97%

89.97% of men have arm spans between 66 and 76 inches.

b. A particular professional basketball player has an arm span of almost 89 inches. Find the z-score for this person's arm span. What percentage of males have an arm span at least as long as this person?

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{89 - 71.4}{3.1}$

$Z = 5.68$

The z-score for this person's arm span is 5.68.

Z = 5.68 has a pvalue of 1

1 - 1 = 0

0% of males have an arm span at least as long as this person

8 0

3 years ago

Why will i be a good role model essay <br>please i need help this is due tomorrow

WITCHER [35]

Answer:

Relate the points down below to yourself and give examples

Step-by-step explanation:

You show confidence and leadership

Being yourself/unique

You speak and interact kindly with everyone

You show respect and concern for others

You give advice to those who need it

You have humility and a willingness to admit mistakes.

You do good things outside of school

7 0

3 years ago

If a+1/a=3What is the answer? a⁵+1/a⁵​

If a+1/a=3What is the answer? a⁵+1/a⁵