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bija089 [108]
2 years ago
7

Over the interval [0,2pi), what are the solutions to cos(2x) = cos(x)? check all that apply​

Mathematics
1 answer:
kykrilka [37]2 years ago
6 0

\cos(2x)  =  \cos(x)

Solution (1)

2x = x + 2k\pi

2x - x = 2k\pi

x = 2k\pi

for k=0 / for k=1 / for k=-1

x=0 / x=2π / x=-2π

acc / acc / rej

solution (2)

2x =  - x  + 2k\pi

2x + x = 2k\pi

3x = 2k\pi

x =  \frac{2k\pi}{3}

for k=0 / for k=1 / for k=-1

x=0 / x=2π/3 / x=-2π/3

acc / acc / rej

Note that i'm trying values of K which make the answer belong to our interval;

So our solution which i will represent as a set is;

S € {0,2π/3,2π}

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Answer:

243 in^3

Step-by-step explanation:

Cut into 2 rectangles

First one would be ..

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second one would be

7 x 21 = 147

Add them together

147 + 96 = 243

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Owen's bedroom. has a perimeter of 46 feet. If the lengh of the bedroom is 11 feet. What is the width of the bedroom?
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Suppose . has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if o
V125BC [204]

The points are (0,0) Minimum and (1/6, 1/18) is the saddle point.

What is the saddle point?

  • A saddle point, also known as a minimax point, is a place on the surface of a function's graph where the slopes in orthogonal directions are all zero but the function does not have a local extremum.

To solve the question we have:

f(x,y) = xy(1-2x-6y)

Therefore, f(x,y) = xy-2x²y-6xy²

Finding the partial derivative of the above gives:

fₓ = y - 4xy-6y²

= x - 2x²-12xy

Therefore, when the above equations are set to 0 we get:

y - 4xy-6y² = 0.......(1)

x - 2x²-12xy  = 0......(2)

Dividing equations (1) and (2) by y and x respectively give:

1 - 4x - 6y = 0

1 - 2x - 12y = 0  

Solving gives:

x = 0.167 = 1/6

y = 0.056 = 1/18

When we place x in equation (1) we have:

y - 4(1/6)y-6y² = 0

y = 0 or y = 1/18

Similarly, x = 0 or 1/6

Therefore, the four critical points are:

(0,0) (1/6,1/18)

When x = 0 and y = 0

f(x,y) = 0 Hence this is a minimum

When x = 1/6 and y = 1/18

f (x,y) = 1/324 Which is a saddle point.

Therefore, the points are (0,0) Minimum, and (1/6, 1/18) is the saddle point.

Know more about saddle point here:

brainly.com/question/17465347

#SPJ4

The question you are looking for is here:

(1 point) The function f(x,y)=xy(1−2x−6y) has 4 critical points. List them and select the type of critical point. Points should be entered as ordered pairs and listed in increasing lexicographic order. By that, we mean that (x,y) comes before (z,w) if x

4 0
1 year ago
On March​ 1, 2018, Mandy Services issued a​ 3% long-term notes payable for​ $15,000. It is payable over a​ 3-year term in​ $5,00
lord [1]

Answer:

amount of total cash payment is $5450

Step-by-step explanation:

Given data

amount = $15000

principal = $5000

rate = 3% = 0.03

to find out

the amount of total cash payment

solution

we know according to question is Each yearly installment will include both principal repayment of​ $5,000 and interest payment for the preceding​ one-year period

so first we calculate interest i.e.

interest = rate × amount

interest = 0.03 × 15000

interest = 450

so interest is $450 for 1 year

now we calculate the amount of total cash payment i.e.

interest + principal

so the amount of total cash payment = 450 +5000 = 5450

amount of total cash payment is $5450

6 0
3 years ago
Read 2 more answers
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