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3 years ago

Is -2(x+y)+9=1 a linear function

Mathematics

1 answer:

yuradex [85]3 years ago

4 0

Answer:

yes

Step-by-step explanation:

The variable terms each have integer powers, and the highest sum of powers in any term is 1. The function is linear.

_____

Its graph is a straight line, as you expect from a linear function.

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Use De Moivre's theorem to write the complex number in trigonometric form: (cos(3pi/5) + i sin (3pi/5))^3

docker41 [41]

By De Moivre's theorem,

$\left(\cos\dfrac{3\pi}5+i\sin\dfrac{3\pi}5\right)^3=\boxed{\cos\dfrac{9\pi}5+i\sin\dfrac{9\pi}5}$

We can stop here ...

# # #

... but we can also express these trig ratios in terms of square roots. Let $x=\dfrac\pi5$ and let $c=\cos x$ . Then recall that

$\cos5x=c^5-10c^3\sin^2x+5c\sin^4x$

$\cos5x=c^5-10c^3(1-c^2)+5c(1-2c^2+c^4)$

$\cos5x=16c^5-20c^3+5c$

On the left, $5x=\pi$ so that

$16c^5-20c^3+5c+1=(c+1)(4c^2-2c-1)^2=0$

Since $c=\cos\dfrac\pi5\neq1$ , we're left with

$4c^2-2c-1=0\implies c=\dfrac{1+\sqrt5}4$

because we know to expect $\cos x>0$ . Then from the Pythagorean identity, and knowing to expect $\sin x>0$ , we get

$\sin x=\sqrt{1-c^2}=\sqrt{\dfrac58-\dfrac{\sqrt5}8}$

Both $\cos$ and $\sin$ are $2\pi$ -periodic, so that

$\cos\dfrac{9\pi}5=\cos\left(\dfrac{9\pi}5-2\pi\right)=\cos\left(-\dfrac\pi5\right)=\cos\dfrac\pi5$

and

$\sin\dfrac{9\pi}5=\sin\left(-\dfrac\pi5\right)=-\sin\dfrac\pi5$

so that the answer we left in trigonometric form above is equal to

$\cos\dfrac\pi5-i\sin\dfrac\pi5=\boxed{\dfrac{1+\sqrt5}4+i\sqrt{\dfrac58+\dfrac{\sqrt5}8}}$

7 0

3 years ago

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 449 gram setting. It is

stealth61 [152]

Answer:

We accetp H₀

Step-by-step explanation:

Information:

Normal distribution

Population mean = μ₀ = 449

Population standard deviation σ unknown

Sample size n = 23 n < 30 we use t-student test

so n = 23 degree of fredom df = n - 1 df = 23- 1 df = 22

Sample mean μ = 448

Sample standard deviation s = 20

Significance level α = 0,05

1.-Hypothesis Test

Null hypothesis H₀ μ₀ = 449

Alternative hypothesis Hₐ μ₀ ≠ 449

Problem statement ask for determine decision rule for rejecting the null hypothesis. For rejecting the null hypothesis we have to get an statistic parameter wich implies that μ is bigger or smaller than μ₀

2.-Significance level α = 0,05 ; as we have a two tail test

α/2 = 0,025

Then from t - student table for df = 22 and 0,025 (two tail-test)

t(c) = ± 2.074

3.- Compute t(s)

t(s) = ( μ - μ₀ ) / s /√n

plugging in values

t(s) = (448 - 449) / 20 /√23 ⇒ t(s) = - 1*√23 /20

t(s) = - 0.2398

4.-Compare t(c) and t(s)

t(s) < t(c) - 0.2398 < - 2.074

Therefore t(s) in inside acceptance region. We accept H₀

7 0

4 years ago

There are 48⋅5^{6} cows spread across 32⋅5^{4} square miles of land. Find the average number of cows per square mile. Round your

stich3 [128]

Answer:

69.1

Step-by-step explanation:

8 0

3 years ago

Jenna is driving 400 miles to visit her grandmother. She manages to travel the fist 100 miles of her trip in two hours. If she c

Yakvenalex [24]

Answer:

8 hours total

Step-by-step explanation:

100=2

400=8

2 times 4 =8

4 0

3 years ago

Read 2 more answers

if you buy 8 chocolate bars at the sale price of .61 cents how many chocolate bars could you have purchased at the regular price

Dahasolnce [82]

If you can buy [email protected] you must have at least 8(61)=488 cents

We get 488/75 = 6.50666... So at 75 cents a pop, you can buy 6 and have some change left over.

Answer: 6

4 0

4 years ago