What is the value of the expression MATH HELP

What is the name of the shape graphed by the function r^2=9 cos(2 theta)?

Lady bird [3.3K]

The name of the shape graphed by the function r ^ 2 = 9 cos (2 theta) is called the “lemniscate”. A lemniscate is a plane curve with a feature shape which consists of two loops that meet at a central point. The curve is also sometimes called as the lemniscate of Bernoulli.

Explanation:

The period of coskθ is 2π/k. In this case, k = 2 therefore the period is π.

r ^ 2 = 9 cos 2θ ≥0 → cos 2θ ≥0. So easily one period can be chosen as θ ∈ [0, π] wherein cos 2θ ≥0.

As cos(2(−θ)) = cos2θ, the graph is symmetrical about the initial line.

Also, as cos (2(pi-theta) = cos 2theta, the graph is symmetrical about the vertical θ = π/2

A Table for half period [0,π4/] is adequate for the shape in Quarter1

Use symmetry for the other three quarters:

(r, θ) : (0,3)(3/√√2,π/8)(3√2/2,π/6)(0,π/4)

5 0

3 years ago

What is the answer for number 2?

steposvetlana [31]

Answer:

7/3

Step-by-step explanation:

integral of equation is x^3/3-6x^2/2+5x/1

the answer will be

7^3/3-3*7^2+5*7-0= 343/3-147+35= 7/3

4 0

3 years ago

2x + 6 96 solve for x using an algebraic equation

levacccp [35]

Answer:

v

Step-by-step explanation:

4 0

3 years ago

4 1/4 = 16/blank + 1/4

Tomtit [17]

Answer:

The “blank” is 4

Step-by-step explanation:

4 1/4= 16/x+ 1/4

We want to get rid of the 1/4. So we subtract it from both sides and get

4= 16/x

We know that if we put 16 divided by 4, you get 4.

This gives you 4= 16/4.

This is your final answer.

5 0

3 years ago

Which system of equations has no solution?

Firlakuza [10]

The system of equation 5x+5y=10 and 2x+2y=4 has no solution.

The system of equation 3x-6y=4 and -4x+8y=7 has no solution.

Step-by-step explanation:

The set of equations "which cannot be solved for X and Y values is said to have no solution".

Now, let's try to solve the following sets of equations for x and y values to find which system of equation has no solution.

option 1:

divide the 1st equation by 5,

the equation becomes x+y=2

divide the 2nd equation by 2,

the equation becomes x+y=2

Both the equations are same, it cannot be solved and has no solution.

option 2:

look for the least coefficients of x and y to make multiplication easy

so, the coefficients of x are 3 and 4.

multiply equation1 by 4

the 1st eqn becomes 12x-24y=16

multiply euation2 by 3

the 2nd eqn becomes -12x+24y=21

Try to solve these two equation for x and y values.

since they cannot be solved to x and y values, it has No solution

Similarly the options 3 and 4 is to be solved to find either it has solution or not.

After solving option 3, the solution is x=0 and y=3

After solving option 4, the solution is x=4 and y=-1

7 0

3 years ago

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