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3 years ago

Given (64y^2)+(4x^2)+128y+16x+64=0, transform the equation into the appropriate form

Mathematics

1 answer:

____ [38]3 years ago

6 0

Answer:

(8y+8)²+(4x²+16)=0

Step-by-step explanation:

Given:

(64y²)+(4x²)+128y+16x+64=0

Find:

Equation into the appropriate form

Computation:

(64y²)+(4x²)+128y+16x+64=0

(8y)²+(2x)²+128y+16x+64=0

(8y)²+(2x)²+2(8y)(8)+2(2x)(4) + 8²=0

(8y+8)²+(4x²+16)=0

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Please help show that the following are TRUE.

mafiozo [28]

Answer:

see below

Step-by-step explanation:

The formula for the sum of an infinite geometric series with first term a1 and common ratio r (where |r| < 1) is ...

sum = a1/(1 -r)

Applying this to the given series, we get ...

a. sum = 5/(1 -3/4) = 5/(1/4) = 20

b. sum = d/(1 -1/t) = d/((t-1)/t) = dt/(t-1)

_____

The derivation of the above formula is in most texts on sequences and series. In general, you write an expression for the difference of the sum (S) and the product r·S. You find all terms of the series cancel except the first and last, and the last goes to zero in the limit, because r^∞ → 0 for |r| < 1. Hence you get ...

S -rS = a1

S = a1/(1 -r)

7 0

3 years ago

A four year old is going to spin around with his arms stretched out 100 times. From past experience, his father knows it takes a

Sati [7]

Answer:

$P(X \geq0.55) \leq 0.22$

Step-by-step explanation:

Using central Limit Theorem (CLT), The sum of 100 random variables;

$Y=X_1+X_2+...+X_{100}$ is approximately normally distributed with

Y ~ N (100 × $\frac{1}{3^2}$ ) = N ( 50, $\frac{100}{9}$ )

The approximate probability that it will take this child over 55 seconds to complete spinning can be determined as follows;

N ( 50, $\frac{100}{9}$ )

$P(Y>55) =P(Z>\frac{55-50}{10/3})$

$P(Y>55) =P(Z>1.5)$

$P(Y>55) =\phi (-1.5)$

$P(Y>55) =0.0668$

Using Chebyshev's inequality:

$P(|X-\mu\geq K)\leq \frac{\sigma^2}{K^2}$

Let assume that X has a symmetric distribution:

Then:

$2P(X-\mu\geq K)\leq) \frac{\sigma^2}{K^2}$

$2P(X \geq \mu+K)\leq) \frac{\sigma^2}{K^2}$

$2P(X\geq0.5+0.05)\leq \frac{\frac{1}{\frac{3^2}{100} } }{0.05^2}$ where: ( $\sigma^2 = \frac{1}{3^2/100}$ )

$P(X \geq0.55) \leq 0.22$

6 0

3 years ago

Can someone please help me with this problem

LenKa [72]

Answer:

the piont was 10.15 away from the that is dead see yea

Step-by-step explanation:

5 0

3 years ago

The three angle bisectors of ΔABC intersect at point P. Point P is the

kvv77 [185]

Answer:

incenter

Step-by-step explanation:

The point of intersection of the three angle bisectors of a triangle is the incenter.

8 0

2 years ago

Read 2 more answers

The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% p

seropon [69]

We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.

<h3>How to use weighted averages to find the correct juice concentration</h3>

In this problem we have to use two kinds of juice with different concentrations. To get a certain concentration, we must adjust quantities of each kind and weighted averages offers a method that is easy to apply:

70 · 140 = 55 · x + 80 · (140 - x)

70 · 140 = 80 · 140 - 25 · x

25 · x = 10 · 140

x = 56

We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.

To learn more on weighted averages: brainly.com/question/28042295

#SPJ1

7 0

1 year ago