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3 years ago

6

Express cos 5x in terms of sine multiples of x

1 answer:

Nataly_w [17]3 years ago

8 0

<span>cos x = [ e^(ix) - e^(-ix) ] / 2i along with [ A - B ]^5 =

( A^5 - B^5) - 5 AB ( A^3 - B^3) + 10 A²B² (A - B )...A = e^(ix) , B = e^(-ix)

[ cos x ] ^5 = (1/32i) { [ e^(5ix) - e^(-5x) ] - 5 [ ( e^(3ix) - e^(-3ix) ] + 10 [ e^(ix) - e^(-ix) ] }

= ( 1 / 16 ) { cos 5x - 5 cos 3x + 10 cos x }.....much faster</span>

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Quadrilateral RSTU has vertices R(1,3), S(4,1), T(1,-3) and U(-2,-1). Is it true or false that this is a rectangle because the d

Alex777 [14]

Given vertices ofQuadrilateral RSTU as R(1,3), S(4,1), T(1,-3) and U(-2,-1).

We need to check if diagonals are congruent.

The coordinates of verticales diagonal RT are R(1,3) and T(1,-3).

The coordinates of verticales diagonal SU are S(4,1), and U(-2,-1),

By applying distance formula:

$\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

RT = $=\sqrt{\left(1-1\right)^2+\left(-3-3\right)^2}$ = $\sqrt{36}$

RT = 6

SU $=\sqrt{\left(-2-4\right)^2+\left(-1-1\right)^2}$ .

$=2\sqrt{10}$ .

Diagonal RT is not congruent to Diagonal SU.

Therefore, Quadrilateral RSTU is not a rectangle because the diagonals are not congruent.

So, it is False.

6 0

3 years ago

Consider the following hypothesis test H0 p 20 Ha p 20 A sample of 400 provided a sample proportion p 175 a Compute the value of

Bogdan [553]

Answer:

a) -1.25

b) 0.2112

c) -1.96

Step-by-step explanation:

Data provided in the question:

Sample size, n = 400

H0 : p = 20

$\bar{p}$ = 175

Now,

a) The test statistic is given as:

Z = $\frac{(\bar{p}-p)}{\sqrt{\frac{p(1-p)}{n}}}$

on substituting the respective values, we get

Z = $\frac{(0.175-0.2)}{\sqrt{\frac{0.2\times0.8}{400}}}$

= -1.25

b) The p-value = 2 × P(Z <-1.25)

Now from the standard normal table

P(Z <-1.25) = 10.56% = 0.1056

Thus,

p-value = 2 × 1056 = 0.2112

c) for a = 0.05,

the critical value is $Z_{\frac{a}{2}}=Z_{\frac{0.05}{2}}$ i.e $Z_{0.025}$

Now from standard normal table

$Z_{0.025}$ = -1.96

3 0

3 years ago

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harkovskaia [24]

Answer:

D

Step-by-step explanation:

1:55 is lower that 125 minutes

7 0

3 years ago

What value of x makes this equation true. X/3 - 3 = X/9 + 3

OLga [1]

27, you need to simplify both sides of the equation to get x on one side.

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3 years ago

2x²-5x-6=0 What are the values for a,b,c of the equation in standard form?

zlopas [31]

Answer:

Standard form: 2x²-5x+12=0

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Step-by-step explanation:

2(x+3)²-5x=6

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2x²+18-5x-6=0

2x²-5x+18-6=0

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8 0

1 year ago