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3 years ago

Sin5A/SinA-cos5A/cosA=4cos2A

Mathematics

1 answer:

irina1246 [14]3 years ago

5 0

Answer:

See Explanation

Step-by-step explanation:

$\frac{ \sin5A}{\sin A} - \frac{ \cos5A}{\cos A} = 4\cos2A \\ \\ LHS = \frac{ \sin5A}{\sin A} - \frac{ \cos5A}{\cos A} \\ \\ = \frac{ \sin5A \:\cos A - \cos5A \: \sin A}{\sin A \:\cos A } \\ \\ = \frac{ \sin(5A -A )}{\sin A \:\cos A} \\ \\ = \frac{ \sin 4A}{\sin A \:\cos A} \\ \\ = \frac{ 2\sin 2A \: \cos 2A}{\sin A \:\cos A} \\ \\ = \frac{ 2 \times 2\sin A \: \cos A \: \cos 2A}{\sin A \:\cos A} \\ \\ = \frac{ 4\sin A \: \cos A \: \cos 2A}{\sin A \:\cos A} \\ \\ =4\cos 2A \\ \\ = RHS \\ \\ thus \\ \\ \frac{ \sin5A}{\sin A} - \frac{ \cos5A}{\cos A} = 4\cos2A \\ \\ hence \: proved$

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Arjun and Jessica each improved their yards by planting daylilies and shrubs. They bought their

Anvisha [2.4K]

Hi there! Let me know if you have questions about my answer:

One shrub is $11.

One daylily is $4.

Step-by-step explanation:

To find the cost of each item, write a system of equations, one equation for what each person bought, and solve for each variable.

<u>Define your variables.</u>

let 'd' be the cost of one daylily

let 'r' be the cost of one shrub

<u>Create a system using the variables and information from the question.</u>

Write an equation for what Arjun bought:

5d + 7r = 97 5 daylilies, 7 shrubs, totaling $97

Write an equation for what Jessica bought:

2d + 11r = 129 2 daylilies, 11 shrubs, totaling $129

<u>Solve the system.</u>

I will solve the system algebraically, using the substitution method. Isolate one variable in one of the equations.

I will isolate 'd' in Jessica's equation:

$2d + 11r = 129$ Start with Jessica's equation

$\frac{2d + 11r}{2} = \frac{129}{2}$ Divide everything in the equation by 2

$d + \frac{11r}{2} = \frac{129}{2}$ Simplify

$d = \frac{129}{2} - \frac{11r}{2}$ Isolate 'd' by subtracting $\frac{11r}{2}$ from both sides.

Now you have an expression for 'd'.

Substitute Arjun's equation with the expression for 'd'. Solve for 'r' to find the cost of one shrub.

$5d + 7r = 97$ Start with Arjun's equation

$5(\frac{129}{2} - \frac{11r}{2}) + 7r = 97$ Substitute 'd' for $d = \frac{129}{2} - \frac{11r}{2}$

$\frac{5*129}{2} - \frac{5*11r}{2} + 7r = 97$ Distribute the 5

$\frac{645}{2} - \frac{55r}{2} + 7r = 97$ Simplify the numerators

$\frac{645}{2} - \frac{55r}{2} + \frac{14r}{2} = 97$ Change 7r to a fraction over 2

$\frac{645}{2} - \frac{41r}{2} = 97$ Combine like terms, the terms with 'r'

$\frac{645-41r}{2} = 97$ Simplify

$645-41r = 194$ Multiply both sides by 2

$-41r = 194-645$ Subtract 645 from both sides

$-41r = -451$ Divide both sides by –41

$r = 11$ Solved for cost of one shrub

Substitute 'r' for 11 using either Arjun's or Jessica's equation. Then, isolate 'd' to solve for the cost of one daylily.

I will use Arjun's equation.

$5d + 7r = 97$ Start with Arjun's equation

$5d + 7(11) = 97$ Substitute 'r' for r = 11

$5d + 77 = 97$ Simplify. Subtract 77 from both sides.

$5d = 20$ Divide both sides by 5.

$d = 4$ Solved for the cost of one daylily

I hope this helped! Check out a similar problem about solving systems here to learn more:

brainly.com/question/11103098

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What is the range of the following relation?<br> {(100, 52), (805, -46), (945, 52), (-54, -46)}

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R:{-46, 52}. You cannot repeat any numbers and the order is from least to greatest.

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Timmy estimated he would spend $9 at the candy store. He went a little over-budget and spent $12. What was the percent error?

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<h2>Answer :</h2>

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$\boxed{ \mathrm{ \% \: error = \dfrac{error}{assumed \: value} \times 100}}$

$\mathrm{ \% \: error =\dfrac{3}{9} ×100}$

$\mathrm{ \% \: error = \dfrac{1}{3} ×100}$

$\mathrm{ \% \: error = 33.33 \%}$

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A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is la

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The exponential function which represented by the values in the table is $f(x)=4(\frac{1}{2})^{x}$ ⇒ 3rd answer

Step-by-step explanation:

The form of the exponential function is $f(x)=a(b)^{x}$ , where

a is the initial value (when x = 0)
b is the growth/decay factor
If k > 1, then it is a growth factor
If 0 < k < 1, then it is a decay factor

The table:

→ x : f(x)

→ -2 : 16

→ -1 : 8

→ 0 : 4

→ 1 : 2

→ 2 : 1

∵ $f(x)=a(b)^{x}$

- To find the exponential function substitute the value of x and f(x)

by some values from the table to find a and b, at first use the

point (0 , 4) to find the value of a

∵ x = 0 and f(x) = 4

∴ $4=a(b)^{0}$

- Remember that any number to the power of zero equal 1

except the zero

∵ $b^{0}=1$

∴ 4 = a(1)

∴ a = 4

Substitute the value of a in the equation

∴ $f(x)=4(b)^{x}$

- Chose any other point fro the table to find b, lets take (1 , 2)

∵ x = 1 and f(x) = 2

∴ $2=4(b)^{1}$

∴ 2 = 4 b

- Divide both sides by 4

∴ $b=\frac{2}{4}=\frac{1}{2}$

- Substitute the value of b in the equation

∴ $f(x)=4(\frac{1}{2})^{x}$

The exponential function which represented by the values in the table is $f(x)=4(\frac{1}{2})^{x}$

Learn more:

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Rudiy27

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Sin5A/SinA-cos5A/cosA=4cos2A​

Sin5A/SinA-cos5A/cosA=4cos2A