(a+b)^3=? hhihiihihihihih

Recall the angle sum identity for cosine:

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==>   sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))

Then rewrite the equation as

sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0

1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0

1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0

sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0

-sin(5x) (sin(4x) + sin(2x)) = 0

sin(5x) (sin(4x) + sin(2x)) = 0

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Rewrite the equation again as

sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0

sin(5x) sin(2x) (2 cos(2x) + 1) = 0

sin(5x) = 0   or   sin(2x) = 0   or   2 cos(2x) + 1 = 0

sin(5x) = 0   or   sin(2x) = 0   or   cos(2x) = -1/2

sin(5x) = 0   ==>   5x = arcsin(0) + 2nπ   or   5x = arcsin(0) + π + 2nπ

… … … … …   ==>   5x = 2nπ   or   5x = (2n + 1)π

… … … … …   ==>   x = 2nπ/5   or   x = (2n + 1)π/5

sin(2x) = 0   ==>   2x = arcsin(0) + 2nπ   or   2x = arcsin(0) + π + 2nπ

… … … … …   ==>   2x = 2nπ   or   2x = (2n + 1)π

… … … … …   ==>   x = nπ   or   x = (2n + 1)π/2

cos(2x) = -1/2   ==>   2x = arccos(-1/2) + 2nπ   or   2x = -arccos(-1/2) + 2nπ

… … … … … …    ==>   2x = 2π/3 + 2nπ   or   2x = -2π/3 + 2nπ

… … … … … …    ==>   x = π/3 + nπ   or   x = -π/3 + nπ

(where n is any integer)

Answer:

The first three terms in the geometric sequence are 18, 24, 32.

Step-by-step explanation:

A number when added to [tex]x,y,z[/tex] that yields consecutive terms of a geometric sequence is an unknown number [tex]t\in \mathbb{Z}[/tex]

Given

[tex]x = 1, y = 7, z = 15[/tex]

We know

[tex]\alpha _1 = 1+t[/tex]

[tex]\alpha _2 = 7+t[/tex]

[tex]\alpha _3 = 15+t[/tex]

Recall that a geometric sequence is in the form

[tex]\boxed{a_n = a_1 \cdot r^{n-1}}[/tex]

Therefore, once  [tex]\alpha_1, \alpha_2, \alpha_1[/tex] are consecutive terms,

[tex]15+t = (1+t) r^{3-1} \implies 15+t = (1+t) r^2[/tex]

To find the ratio, for

[tex]\dots a_{k-1}, a_k, a_{k+1} \dots[/tex]

we know

[tex]\dfrac{a_k}{a_{k-1}} =\dfrac{a_k}{a_{k-1}} =r[/tex]

Therefore,

[tex]\dfrac{(7+t)}{(1+t)} =\dfrac{(15+t)}{(7+t)} \implies (7+t)^2 = (15+t)(1+t)[/tex]

[tex]\implies 49+14t+t^2=15+16t+t^2 \implies -2t=-34 \implies t=17[/tex]

The ratio is therefore

[tex]r=\dfrac{4}{3}[/tex]

Therefore, the first three terms in the geometric sequence are 18, 24, 32.

Answer:

fyi b's answer has imaginary numbers in it...

Imaginary: 1 +[tex]\frac{\sqrt{2i} }{2 }[/tex]    

Imaginary: 1 -  [tex]\frac{\sqrt{2i} }{2 }[/tex]  

Step-by-step explanation:

[tex]2x^{2} - 4x -3 = 0[/tex]

[tex]\sqrt{-4^{2} -4(2)(3)}[/tex] = [tex]\sqrt{-8}[/tex] ... the negative root will produce imaginary solutions

9514 1404 393

Answer:

  1a. -4, 3/4

  1b. 1-0.71i, 1+0.71i

Step-by-step explanation:

The directions tell you to use the quadratic formula. Factoring may get you the solution somewhat more easily, but does not comply with the directions.

The quadratic formula tells you ...

  [tex]\text{The solution to }ax^2+bx+c=0\text{ is given by }\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

__

1a. a=4, b=13, c=-12

  [tex]x=\dfrac{-13\pm\sqrt{13^2-4(4)(-12)}}{2(4)}=\dfrac{-13\pm\sqrt{361}}{8}=\dfrac{-13\pm19}{8}\\\\x=\left\{-4,\dfrac{3}{4}\right\}[/tex]

__

1b. After adding 3 to both sides, a=2, b=-4, c=3

  [tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(2)(3)}}{2(2)}=\dfrac{4\pm\sqrt{-8}}{4}=1\pm\dfrac{\sqrt{2}}{2}i\\\\x=\left\{1-\dfrac{\sqrt{2}}{2}i,1+\dfrac{\sqrt{2}}{2}i\right\}\approx\{1-0.71i,1+0.71i\}[/tex]

Answer:

2.56

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(3.5 - 1.5)² + (4.3 - 2.7)²

√(2)² + (1.6)²

√(4) + (2.56)

√6.56

= 2.56

Answer:

no,  

(

1

,

0

)

is not an ordered pair of the function  

f

(

x

)

=

1

+

x

.

Step-by-step explanation:

Ordered pairs are usually written in the form  

(

x

,

y

)

by tradition.

so usingthe function,

f

(

x

)

=

1

+

x

we can rewrite it as,

y

=

1

+

x

any pair of x and y that satisfy this equation are solutions to the equation.

so subbing in  

(

1

,

0

)

,

0

=

1

+

(

1

)

0

=

2

which is not true so the point does not make the function true.

It might be easier to see graphically,

graph{1+x [-10, 10, -5, 5]}

any combination of x and y on this line make the equation true and as such are an ordered pair of the function.

Answer:

Step-by-step explanation:

Answer:

x = π/4.

Step-by-step explanation:

3sin(2x) = 2sin(2x) + 1

3sin(2x) - 2sin(2x) = 1

1sin(2x) = 1

sin(2x) = 1

When a variable n = π/2, sin(π/2) = 1 [refer to the unit circle].

2x = π/2

x = π/4.

Hope this helps!

Answer:

Point has co-ordinates, (0, 5)

Step-by-step explanation:

If they cut y-axis, then x = 0

[tex]2y - x = 10 \\ 2y - 0 = 10 \\ 2y = 10 \\ y = 5[/tex]

Answer:

a

Step-by-step explanation:

g(1)=5

f(g(1))=f(5)

f(5)=2

Answer:

Step-by-step explanation:

y = ½(x-4)² + 13

y = ½(x² - 8x + 16) + 13

y = ½x² - 4x + 21

Answer:

Plese explain your answer properly

Step-by-step explanation:

Answer:what is the answer

Step-by-step explanation:

since the two triangles are congruent..

AB=ED

AC=FD(side opposite to the right angle)

FD=AC

•°•FD=13m

Answer:

167.64 cm

Step-by-step explanation:

I dont kno how to work it out

Answer:

27

Step-by-step explanation:

x-y

We are subtracting and we want the smallest number

We want the smallest number for x and the largest number for y

The smallest number for x is 71

The largest number for y is 44

71-44

27

Answer:

N = 1000

Step-by-step explanation:

The population growth of species per capita of any geographical can be computed by using the formula:

[tex]\dfrac{dN}{dT}=rN (1 - \dfrac{N}{K})[/tex]

here;

N = population chance

T = time taken

K = carrying capacity

r = the constant exponential growth rate

From the given equation, we can posit that the value of r will be the greatest at the time the value of dN is highest:

As such, when the population chance = 1000

[tex]\dfrac{dN}{dT}=0.17 * 1000 (1 - \dfrac{1000}{10000})[/tex]

[tex]\dfrac{dN}{dT}=0.17 * 1000 (0.9)[/tex]

[tex]\dfrac{dN}{dT}= 153[/tex]

At N = 5000;

[tex]\dfrac{dN}{dT}= 85[/tex]

At N= 8000;

[tex]\dfrac{dN}{dT}= 34[/tex]

At N = 10000

[tex]\dfrac{dN}{dT}= 0[/tex]

Answer:

5,20,80,320

Step-by-step explanation:

a1 = 5

an = 4 an-1

Let n = 2

a2 = 4 * a1 = 4*5 = 20

Let n = 3

a3 = 4 * a2 = 4*20 = 80

Let n = 4

a4 = 4 * a3 = 4*80 = 320

Answer:

False

Step-by-step explanation:

Answer:

0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive test

Event B: Person has diabetes.

Probability of a positive test:

0.95 out of 0.1(person has diabetes).

0.007 out of 1 - 0.1 = 0.9(person does not has diabetes). So

[tex]P(A) = 0.95*0.1 + 0.007*0.9 = 0.1013[/tex]

Probability of a positive test and having diabetes:

0.95 out of 0.1. So

[tex]P(A \cap B) = 0.95*0.1 = 0.095[/tex]

What is the probability that a randomly selected person has diabetes, given that his test is positive?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.095}{0.1013} = 0.9378[/tex]

0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.

Answer:

x=30.5

Step-by-step explanation:

Using midsegment 's theorea:

[tex]2=\dfrac{RG}{RS} =\dfrac{RH}{RQ} =\dfrac{GH}{SQ} \\\\4x-65=2x-4\\\\2x=61\\\\x=\dfrac{61}{2} \\\\x=30.5\\[/tex]

Answer:

totally 16 numbers can be formed

It is hard and the condition of repeat of number should be clear if you have formula ( it is obvious to have) you can use that.

Answer:

A. 4000 meters because

1 km = 1000 meters

and 4 km = 1000 × 4 = 4000

............

Answer:

-15

Step-by-step explanation:

Let a = 2 and c = -7.

[tex]c-4a\\(-7)-4(2)\\-7-8\\-15[/tex]

we know that the value of a is 2 and c is -7

Expression-

c-4a

= (-7)-4×2

= (-7)-8

= -15

Answer:

‼️D) To the right‼️

Explanation

There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.

Answer:

i dont no the ans

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, we add them all up.

98+70+52+87+46+120+72+41 = 586

Now, we divide 586 by the number of things there are. 586 / 8 = 73.25.

The mean of the swear words condition is 73.25.

Answer:

The number of hits would follow a binomial distribution with [tex]n =10,\!000[/tex] and [tex]p \approx 4.59 \times 10^{-6}[/tex].

The probability of finding [tex]0[/tex] hits is approximately [tex]0.955[/tex] (or equivalently, approximately [tex]95.5\%[/tex].)

The mean of the number of hits is approximately [tex]0.0459[/tex]. The variance of the number of hits is approximately [tex]0.0459\![/tex] (not the same number as the mean.)

Step-by-step explanation:

There are [tex](26 + 10)^{6} \approx 2.18 \times 10^{9}[/tex] possible passwords in this set. (Approximately two billion possible passwords.)

Each one of the [tex]10^{9}[/tex] randomly-selected passwords would have an approximately [tex]\displaystyle \frac{10,\!000}{2.18 \times 10^{9}}[/tex] chance of matching one of the users' password.

Denote that probability as [tex]p[/tex]:

[tex]p := \displaystyle \frac{10,\!000}{2.18 \times 10^{9}} \approx 4.59 \times 10^{-6}[/tex].

For any one of the [tex]10^{9}[/tex] randomly-selected passwords, let [tex]1[/tex] denote a hit and [tex]0[/tex] denote no hits. Using that notation, whether a selected password hits would follow a bernoulli distribution with [tex]p \approx 4.59 \times 10^{-6}[/tex] as the likelihood of success.

Sum these [tex]0[/tex]'s and [tex]1[/tex]'s over the set of the [tex]10^{9}[/tex] randomly-selected passwords, and the result would represent the total number of hits.

Assume that these [tex]10^{9}[/tex] randomly-selected passwords are sampled independently with repetition. Whether each selected password hits would be independent from one another.

Hence, the total number of hits would follow a binomial distribution with [tex]n = 10^{9}[/tex] trials (a billion trials) and [tex]p \approx 4.59 \times 10^{-6}[/tex] as the chance of success on any given trial.

The probability of getting no hit would be:

[tex](1 - p)^{n} \approx 7 \times 10^{-1996} \approx 0[/tex].

(Since [tex](1 - p)[/tex] is between [tex]0[/tex] and [tex]1[/tex], the value of [tex](1 - p)^{n}[/tex] would approach [tex]0\![/tex] as the value of [tex]n[/tex] approaches infinity.)

The mean of this binomial distribution would be:[tex]n\cdot p \approx (10^{9}) \times (4.59 \times 10^{-6}) \approx 0.0459[/tex].

The variance of this binomial distribution would be:

[tex]\begin{aligned}& n \cdot p \cdot (1 - p)\\ & \approx(10^{9}) \times (4.59 \times 10^{-6}) \times (1- 4.59 \times 10^{-6})\\ &\approx 4.59 \times 10^{-6}\end{aligned}[/tex].

Answer:

x+3

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

(x-3)(x-2)(x-4)

Step-by-step explanation:

x+4             x^2 -16

---------------÷ -------------

x^2 - 5x+6     x+3

Copy dot flip

x+4                x+3

--------------- * -------------

x^2 - 5x+6     x^2 -16

Factor

x+4                x+3

--------------- * -------------

(x-3)(x-2)     (x-4)(x+4)

Cancel like terms

1                   x+3

--------------- * -------------

(x-3)(x-2)     (x-4)1

x+3

---------------   x cannot equal 3,2,4 -4

(x-3)(x-2)(x-4)

Answer:

is y=x^2 a proportional relationship?

[tex]{ \sf{yes. \: constant \: of \: proportionality = 1}}[/tex]

is y=2+x a proportional relationship?

[tex]{ \sf{no. \: unless \: y \: is \: proportinal \: to \: (2 + x)}}[/tex]

is y=2/x a proportional relationship?

[tex]{ \sf{yes. \: where \: proportianality \: constant \: is \: 2}}[/tex]

is y=2x a proportional relationship?

[tex]{ \sf{yeah. \: constant \: is \: 2}}[/tex]

Step-by-step explanation:

X +1 + X + 2

X + X + 1 + 2

2x + 3

Therefore it's 2x + 3

Answer:

The change is of -1.3 percentage points.

Step-by-step explanation:

The humidity is currently 56% and falling at a rate of 4 percentage points per hour.

This means that after n hours the humidity is of:

[tex]H(n) = 56 - 4n[/tex]

Estimate the change in humidity over the next 20 minutes.

It currently is 56%.

20 minutes is 20/60 = 1/3 of an hours, so:

[tex]H(\frac{1}{3}) = 56 - 4\frac{1}{3} = 54.7[/tex]

Change:

54.7 - 56 = -1.3

The change is of -1.3 percentage points.

The change in humidity over the next 20 minutes falling at a rate of  4 percentage points per hour is -1.3.

The humidity is currently 56% and falling at a rate of 4 percentage points per hour.

The change is determined by the small about of humidity changes x to x+h, so the output of x+h is the value of f at x plus the approximate change in f, that is

[tex]\rm f(x+h) =f(x) + f'(x) \times h[/tex]

f(x)= 56%

20 minutes is 20/60 = 1/3 of an hours

So, The change in humidity is

[tex]f'(x) = 4 \times 1/3[/tex]

f'(x) = 1.3

Here, it is falling at the rate of 4% point per hour so we will take it as negative as -1.3.

Learn more about changes in humidity;

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