Mathematics, 21.06.2019 14:20, alissalhenry

If sin θ=24/25 and 0 less than or equal to θ less than or equal to π/2, find the exact value of tan 2θ. answers; a) -527/336 b) -336/527 c)7/24 d) 24/7

Answers: 3

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Answers

The correct answer was given: Alysssssssssssa

Option B. $tan(2\theta)= -\frac{336}{527}$

Step-by-step explanation:

we know that

$tan(2\theta)= \frac{sin(2\theta)}{cos(2\theta)}$

$sin(2\theta)=2(sin(\theta))(cos(\theta))$

$cos(2\theta)=cos^{2}(\theta)-sin^{2}(\theta)$

$cos^{2}(\theta)+sin^{2}(\theta)=1$

we have

$sin(\theta)=\frac{24}{25}$

step 1

Find the value of cosine of angle theta

$cos^{2}(\theta)+sin^{2}(\theta)=1$

$cos^{2}(\theta)+(\frac{24}{25})^=1$

$cos^{2}(\theta)=1-\frac{576}{625}$

$cos^{2}(\theta)=\frac{49}{625}$

$cos(\theta)=\frac{7}{25}$

The value of cosine of angle theta is positive, because angle theta lie on the I Quadrant

step 2

Find $sin(2\theta)$

$sin(2\theta)=2(sin(\theta))(cos(\theta))$

we have

$sin(\theta)=\frac{24}{25}$

$cos(\theta)=\frac{7}{25}$

substitute

$sin(2\theta)=2(\frac{24}{25})(\frac{7}{25})$

$sin(2\theta)=\frac{336}{625}$

step 3

Find $cos(2\theta)$

$cos(2\theta)=cos^{2}(\theta)-sin^{2}(\theta)$

we have

$sin(\theta)=\frac{24}{25}$

$cos(\theta)=\frac{7}{25}$

substitute

$cos(2\theta)=(\frac{7}{25})^{2}-(\frac{24}{25})^{2}$

$cos(2\theta)=(\frac{49}{625})-(\frac{576}{625})$

$cos(2\theta)=-\frac{527}{625}$

step 4

Find the value of $tan(2\theta)$

$tan(2\theta)= \frac{sin(2\theta)}{cos(2\theta)}$

we have

$sin(2\theta)=\frac{336}{625}$

$cos(2\theta)=-\frac{527}{625}$

substitute

$tan(2\theta)= -\frac{336}{527}$

The correct answer was given: hannahdrumsey

8.723175703x 10 to the -3 power

The correct answer was given: sherthornton67pebyd0

Basic EPS 3.95

Basic EPS Dilutive 3.337

Explanation:

Calculation for the basic and diluted EPS for the current year

First step is to find the convertible securities outstanding for the current year from 1 to 5

1. Numerator effect=6,000

(6%*100,000)

Denominator effect=15,000

[(100,000/10)*1.5]

ME=6000/15,000=.402.

2. Premium=5,000

[(105%-100%)*100,000]

Yearly Amortization= 500

5,000/10 years

Yearly Payment= 8,000

(8%*100,000)

Numerator effect= 8,000-500

= 7,500 * (100%-34%)= 4,950

Denominator effect= 100,000/1,000

= 100*90 per share= 9000

ME= 4,950/9,000

ME=.553.13 percent

3. Discount=900

[(100%-97%)*30,000]

Yearly Amortization=180

(900/5years)

Yearly Payment=3,900

Numerator effect= 3,900+180

=4,080*(100%-34%)

= 2,692.8

Denominator effect= 900

ME=2693/900

ME= 2.994.7 percent

4. Discount=3,000

(60,000/20)

Yearly Amortization=375

(3,000/ 8years )

Yearly Payment= 4,200

Numerator effect= 4,200+375

Numerator effect= 4,575*(100%-34%)

= 3,019.5

Denominator effect= 1,200

ME= 3020/1200= 2.525

5. Numerator effect= 55,000*(100%-34%)

= 36,300

(11%*500,000=55,000)

Denominator effect= 10,000

ME=36300/10000= 3.63

Second step is to calculate the basic and diluted EPS

Calcualtion for BASIC EPS

Net income = 500,000- (100,000*.06=6000)

Net income= 494,000

Average Outstanding=125,000

Using this formula

Basic EPS=Net income/Average Outstanding

Let plug in the formula

Basic EPS:494,000/125,000

Basic EPS=3.95

Therefore the Basic EPS will be 3.95

Calculation for BASIC EPS DILUTIVE

Dilutive=494,000+6,000+4,950+2,693+3,020/125,000+2,000+15,000+9,000+900+1200

Basic EPS Dilutive=510,663/153,000

Basic EPS Dilutive=3.337

Therefore Basic EPS Dilutive will be 3.337

The correct answer was given: Brain

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

e2020 got it right

The correct answer was given: Brain

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

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If sin θ=24/25 and 0 less than or equal to θ less than or equal to π/2, find the exact value of tan 2θ. answers; a) -527/336 b) -336/527 c)7/24 d) 24/7

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