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2 years ago

Find the value of x^2+1/x^2 if x-1/x=root 3.

Mathematics

1 answer:

daser333 [38]2 years ago

8 0

Observe that

$\left(x-\frac{1}{x}\right)^2 = x^2 + \frac{1}{x^2} - 2$

but since $\x-\frac{1}{x} = \sqrt{3}$ , we can rewrite it as

$(\sqrt{3})^2 = x^2+\frac{1}{x^2}-2 \iff x^2+\frac{1}{x^2} = 3+2 = 5$

So, the answer is $5$

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What is the descending order of the integers 0, -2,3,-1,2,-3,1 ?

shepuryov [24]

Answer:

3,2,1,0,-1,-2,-3

Step-by-step explanation:

5 0

2 years ago

A pet survey found that the ratio of dogs to cats is 2/5. Write and solve a proportion that shows the number of dogs

Irina18 [472]

So,

The ratio of dogs to cats:
$\frac{2}{5}$

The other proportion:
$\frac{x}{140}$

$\frac{2}{5} = \frac{x}{140}$

5 times 28 is 140.

Multiply the fraction by the appropriate form of 1
$\frac{2}{5} * \frac{28}{28} = \frac{56}{140}$

There are 56 dogs when the number of cats is 140.

7 0

2 years ago

A bank sampled its customers to determine the proportion of customers who use their debit card at least once each month. A sampl

Zinaida [17]

Answer:

(0.084,0.396)

Step-by-step explanation:

The 99% confidence interval for the proportion of customers who use debit card monthly can be constructed as

$p-z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} }$

$p=\frac{x}{n}$

$p=\frac{12}{50}$

$p=0.24$

$q=1-p=1-0.24=0.76$

$\frac{\alpha }{2} =\frac{\0.01 }{2}=0.005$

$p-z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} }$

$0.24-z_{0.005} \sqrt{\frac{0.24*0.76}{50} }$

$0.24-2.58(0.0604)$

$0.24-0.155832$

By rounding to three decimal places we get,

$0.084$

The 99% confidence interval for the proportion of customers who use debit card monthly is (0.084,0.396).

3 0

2 years ago

Solve for x. 7(1x - 3) = 4(x + 5)

alexandr1967 [171]

Answer:

x = 41/3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Step-by-step explanation:

Step 1: Define equation

7(1x - 3) = 4(x + 5)

Step 2: Solve for x

Simplify: 7(x - 3) = 4(x + 5)
Distribute: 7x - 21 = 4x + 20
Subtract 4x on both sides: 3x - 21 = 20
Add 21 on both sides: 3x = 41
Divide 3 on both sides: x = 41/3

Step 3: Check

Plug in x to verify it's a solution.

Substitute: 7(1(41/3) - 3) = 4(41/3 + 5)
Multiply: 7(41/3 - 3) = 4(41/3 + 5)
Subtract/Add: 7(32/3) = 4(56/3)
Multiply: 224/3 = 224/3

Here, we see that 224/3 is indeed equivalent to 224/3. ∴ x = 41/3 is a solution to the equation.

And we have our final answer!

6 0

2 years ago

What is the maximum of the sinusoidal function?

Alex17521 [72]

Answer:

The maximum of y = sin x is 1. The amplitude of a sinusoidal function is one-half of the positive difference between the maximum and minimum values of a function.

Step-by-step explanation:

4 0

2 years ago