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zhannawk [14.2K]
3 years ago
12

If a = 4 - √15, find a^4 +1\a^4

Mathematics
1 answer:
Luden [163]3 years ago
7 0

Answer:

(\frac{-3+\sqrt{15} }{4-\sqrt{15} })^{2}  -4\\

Step-by-step explanation:

a=4-\sqrt{15}

a^{4} +\frac{1}{a^{4} }\\=a^{2^{2} } +\frac{1}{a^{2^{2} } }\\\\=(x^{2} +\frac{1}{a^{2} } )^{2} -2a^{2} \frac{1}{a^{2} } \\=(a +\frac{1}{a } )^{2} -2a \frac{1}{a}-2\\=(4-\sqrt{15} +\frac{1}{4-\sqrt{15} }) ^{2} -4\\\=(\frac{16-15-4+\sqrt{15} }{4-\sqrt{15} })^{2}  -4\\=(\frac{-3+\sqrt{15} }{4-\sqrt{15} })^{2}  -4\\

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Because Charles David Keeling and his new colleagues began measuring CO2 in 1958, we now have an excellent record of how CO2 con
Alecsey [184]

Answer:

1. 516 ppm; 2. 561 ppm

Step-by-step explanation:

1. CO₂ increase at old rate

Time = 2100 - 2010 = 90 years

Increase in CO₂ = 90 yr × (1.4 ppm/1 yr) = 126 ppm

CO₂ in 2010 = 390 + 126 = 516 ppm

At the old rate, the CO₂ concentration in 2100 will be 516 ppm.

2. CO₂ increase at new rate

Time = 2100 - 2010 = 90 years

Increase in CO₂ = 90 yr × (1.9 ppm/1 yr) = 171 ppm

CO₂ in 2010 = 390 + 171 = 561 ppm

At the new rate, the CO₂ concentration in 2100 will be 561 ppm.

6 0
2 years ago
Given y = a(x - h)^2 + k, p = <br> A. a <br> B. 4a <br> C. 1/4a
Flauer [41]

9514 1404 393

Answer:

  C.  1/(4a)

Step-by-step explanation:

We assume you're comparing the vertex form ...

  y = a(x -h)^2 +k

to the form used to write the equation in terms of the focal distance p.

  y = 1/(4p)(x -h)^2 +k

That comparison tells you ...

  a = 1/(4p)

  p = 1/(4a) . . . . . . multiply by p/a; matches choice C

__

<em>Additional comment</em>

When using plain text to write a rational expression, parentheses are needed around any denominator that has is more than a single constant or variable. The order of operations requires 1/4a to be interpreted as (1/4)a. The value of p is 1/(4a).

When rational expressions are typeset, the fraction bar serves as a grouping symbol identifying the entire denominator:

  p=\dfrac{1}{4a}

8 0
2 years ago
Solve the inequality 6x - 2(x + 1) &gt; 0
castortr0y [4]
The answer would be 2 > 0.
4 0
3 years ago
Givenf(x)=6(8−x)+5.<br> (a) What does the notation f (−2) mean? (b) What is the value of f (−2) ?
Nonamiya [84]

Answer:

b. 65

a. The notation f(-2) means that we want to evaluate the value of the equation when x = -2

Step-by-step explanation:

A. The notation f(-2) means that we want to evaluate the value of the equation when x = -2

B. We will simply substitute the value of 2 for x

f(x) = 6(8-x) + 5

f(-2) = 6(8 - (-2)) + 5

f(-2) = 6(8 + 2) + 5

f(-2) = 6(10) + 5 = 60 + 5 = 65

5 0
3 years ago
In circle O, RT and SU are diameters.
nataly862011 [7]

In circle O, RT and SU are diameters. mArc R V = mArc V U = 64°. Thus, option C is correct.

Given that:

mArc R V = mArc V U,

Angle S O R = 13 x degrees

Angle T O U = 15 x - 8 degrees

<h3>How to calculate the angle TOU ?</h3>

∠SOR = ∠TOU  (Vertically opposite angles are equal).

Therefore:

13 x = 15x - 8

Subtracting 13x from both sides

13x - 13x = 15x - 8 - 13x

0 = 15x - 13x - 8

2x - 8 = 0

Adding 8 to both sides:

2x - 8 + 8 = 0 + 8

2x = 8

2x/2 = 8/2  

x = 4

∠SOR = 13x

= 13(4)

= 52°

∠TOU = 15x - 8

= 15(4) - 8

= 60 - 8

= 52°

Let a = mArc R V = mArc V U

Therefore:

mArc R V + mArc V U + ∠TOU = 180 (sum of angles on a straight line)

Substituting:

a + a + 52 = 180

2a = 180-52

2a = 128

a = 128/2

a= 64°

mArc R V = mArc V U = 64°

In circle O, RT and SU are diameters. mArc R V = mArc V U = 64°. Thus, option C is correct.

Learn more about angles here:

brainly.com/question/2882938

#SPJ1

6 0
1 year ago
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