The sum of two consecutive integers is -207

2. Find the general relation of the equation cos3A+cos5A=0

mars1129 [50]

<h2>Answer:</h2>

$A=\frac{\pi}{8}+\frac{n\pi}{4}or\ A=\frac{\pi}{2}+n\pi$

<h2>Step-by-step explanation:</h2>

<h3>Find angles</h3>

$cos3A+cos5A=0$

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<h3>Transform the expression using the sum-to-product formula</h3>

$2cos(\frac{3A+5A}{2})cos(\frac{3A-5A}{2})=0$

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<h3>Combine like terms</h3>

$2cos(\frac{8A}{2})cos(\frac{3A-5A}{2})=0\\\\ 2cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

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<h3>Divide both sides of the equation by the coefficient of variable</h3>

$cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

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<h3>Apply zero product property that at least one factor is zero</h3>

$cos(\frac{8A}{2})=0\ or\ cos(\frac{-2A}{2})=0$

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<h3>Cross out the common factor</h3>

$cos\ 4A=0$

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<h3>Solve the trigonometric equation to find a particular solution</h3>

$4A=\frac{\pi}{2}or\ 4A=\frac{3\pi}{2}$

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<h3>Solve the trigonometric equation to find a general solution</h3>

$4A=\frac{\pi}{2}+2n\pi \ or\\ \\ 4A=\frac{3 \pi}{2}+2n \pi\\ \\A=\frac{\pi}{8}+\frac{n \pi}{4\\}$

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<h3>Reduce the fraction</h3>

$cos(-A)=0$

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<h3>Simplify the expression using the symmetry of trigonometric function</h3>

$cosA=0$

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<h3>Solve the trigonometric equation to find a particular solution</h3>

$A=\frac{\pi }{2}\ or\ A=\frac{3 \pi}{2}$

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<h3>Solve the trigonometric equation to find a general solution</h3>

$A=\frac{\pi}{2}+2n\pi\ or\ A=\frac{3\pi}{2}+2n\pi,n\in\ Z$

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<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{2}+n\pi$

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<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{8}+\frac{n\pi}{4}\ or\ A=\frac{\pi}{2}+n\pi ,n\in Z$

<em>I hope this helps you</em>

5 0

2 years ago

Hannah Ortega is considering expanding her business. She plans to hire a salesperson to cover trade shows. Because of compensati

mariarad [96]

Answer:

a) Total Cost for EzRecords = $13000

Cost per unit of EzRecords = $162.50

Total Cost for ProOffice = $10000

cost per unit of ProOffice = $200.00

b) Total Cost for EzRecords = $25000

Cost per unit of EzRecords = $125.00

Total Cost for ProOffice = $17500

cost per unit of ProOffice = $175.00

Step-by-step explanation:

a) Total Cost = Fixed Cost + Variable Cost

Fixed Cost = $7500

Variable Cost = cost of making a unit of output × number of units produced.

Variable Cost of EzRecords products = $100 × 80 = $8000

Variable Cost of proOffice products = $150 × 50 = $7500

Fixed Cost for EzRecords = (20/30) × 7500 = $5000

Fixed Cost for ProOffice = (10/30) × 7500 = $2500

Variable cost for EzRecords = $8000

Variable cost for ProOffice = $7500

Total cost for EzRecords = Fixed Cost + Variable Cost = $5000 + $8000 = $13000

Total Cost for ProOffice = $2500 + $7500 = $10000

Cost per unit for EzRecords = (total cost of production)/(total units produced) = 13000/(80) = $162.50

Cost per unit of ProOffice = 10000/50 = $200.00

b) Total Cost = Fixed Cost + Variable Cost

Fixed Cost = $7500

Variable Cost = cost of making a unit of output × number of units produced.

Variable Cost of EzRecords products = $100 × 200 = $20000

Variable Cost of proOffice products = $150 × 100 = $15000

Fixed Cost for EzRecords = (20/30) × 7500 = $5000

Fixed Cost for ProOffice = (10/30) × 7500 = $2500

Variable cost for EzRecords = $20000

Variable cost for ProOffice = $15000

Total cost for EzRecords = Fixed Cost + Variable Cost = $5000 + $20000 = $25000

Total Cost for ProOffice = $2500 + $15000 = $17500

Cost per unit for EzRecords = (total cost of production)/(total units produced) = 25000/(200) = $125.00

Cost per unit of ProOffice = 17500/100 = $175.00

8 0

3 years ago

Amy purchased a house for $551,000 and obtained a mortgage for $519,000 she purchased 3 discount points and 2 origination points

Olegator [25]

Discount points are normally a type of prepaid interests that lowers the interest on subsequent payments for mortgage borrowers pay.

Each of the points is given by:

1 point = 1% of the mortgage value.

Therefore,
Cost of discount points = 0.01*519,000*3 = $15,570
Cost of origination points = 0.01*519,000*2 = $10,380

In this regard, option B. is the correct answer on the cost of discount and origination points respectively.

4 0

4 years ago

What value of x makes this inequality true?<br> x+9 < 4x

wariber [46]

Answer:

X>3

Step-by-step explanation:

X+9<4X

x-x+9<4x-x

9<3x

3<x

6 0

3 years ago

{x|x is an odd counting number between 8 and 16} find n(a) for the sets of 3-6

Alex

Answer:

vsdddddddddddddddd

Step-by-step explanation:

888iiiiiiiiiiiiit3jjgfifhhh

7 0

3 years ago