The lateral area of a cone is 555 \pi cm^2 and the radius is 15.1 what is the slant height?

Explaining how to determine the symmetry of a polar graph based on the given equation r = 5 + 4 cos θ.

To determine the symmetry of the graph r = 5 + 4 cos θ, we can substitute (-θ) for θ in the equation and check if the resulting polar equation remains the same, indicating symmetry about the origin.

If replacing (-θ) gives us the same equation, the graph is symmetric about the y-axis. If replacing (π - θ) gives the same equation, then the graph is symmetric about the x-axis.

In this case, replacing (-θ) in r = 5 + 4 cos θ gives r = 5 + 4 cos(-θ), which simplifies to r = 5 + 4 cos θ, indicating symmetry about the y-axis.

Answer:

The number is 3 and the another number is 9

Step-by-step explanation:

Let

x-------> the number

y-----> another number

we know that

[tex]y=x+6[/tex] ----> equation A

[tex]\sqrt{y}=x[/tex] ----> equation B

Substitute equation A in equation B

[tex]\sqrt{x+6}=x[/tex]

squared both sides

[tex]x+6=x^{2} \\x^{2}-x-6=0[/tex]

Using a graphing tool

solve the quadratic equation

see the attached figure

The solution is  x=3

Find the value of y

[tex]y=x+6[/tex] -------> [tex]y=3+6=9[/tex]

Answer:

For this case the amplitude is given by:

A = (l-1l + 3) / 2

A = 4/2

A = 2

The middle line is given by:

y = 1

The period of the function is given by:

T = l x2 - x1 l

T = l 0 - 2pi l

T = l - 2pi l

T = 2pi

Answer:

Amplitude: 2; period: 2π; midline: y = 1

Step-by-step explanation:

Answer:

B. (x+4)(x+i)(x-i)

Step-by-step explanation:

Let [tex]P(x)=x^3-4x^2+x-4[/tex]

We can factor this polynomial by grouping:

[tex]P(x)=x^2(x-4)+1(x-4)[/tex]

We factor further to obtain:

[tex]P(x)=(x^2+1)(x-4)[/tex]

[tex]P(x)=(x^2-\sqrt{-1}^2)(x-4)[/tex]

We apply difference of two squares to get:

[tex]P(x)=(x-i)(x+i)(x-4)[/tex]

Answer:

(x+1)(x-1)(x+4)

Step-by-step explanation:

In the parallelogram QRST then measure of  ∠Q is 62 degrees.

A quadrilateral is a four-sided polygon, having four edges and four corners.

Given that  QRST is a parallelogram.

We have to find the measure of ∠Q.

Both pairs of opposite sides are parallel, quadrilateral QRST is a parallelogram.

∠Q= ∠S

4x+10=5x-3

We have to find the value of to find ∠Q measure.

10+3=5x-4x

13=x

Now let us plug in the value of x in ∠Q measure.

∠Q = 4x+10

Now plug in x value in ∠Q

∠Q = 4(13)+10

=52+10

=62 degrees

Hence, in the parallelogram QRST then measure of  ∠Q is 62 degrees.

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Answer:

a

Step-by-step explanation:

Answer:

Amplitude: 1; midline: y = 1

Step-by-step explanation:

From the graph we can conclude that it is a sine or cosine function. In their standard form, these functions are given by the following equations:

[tex]y(t)=Acos(\omega t +\phi)\\\\or\\\\y(t)=Asin(\omega t+ \phi)[/tex]

Where:

[tex]A=Amplitude=\frac{|A_m_i_n-A_m_a_x|}{2}\\\omega=Angular\hspace{3}frequency\\\phi=Initial \hspace{3}phase[/tex]

And:

[tex]A_m_a_x=Maximum\hspace{3}amplitude\\A_m_i_n=Minimum\hspace{3}amplitude[/tex]

On the other hand, we can define the midline of these kind of functions as the halfway between the maximum and minimum amplitude of the function, Therefore:

[tex]Midline=M_l=\frac{A_m_a_x+A_m_i_n}{2}[/tex]

From the graph you can see that the maximum value of the function(maximum amplitude) is 2 and the minimum value of the function (minimum amplitude) is 0, thus:

[tex]A=\frac{|A_m_i_n-A_m_a_x|}{2} =\frac{|0-2|}{2} =\frac{|-2|}{2} =\frac{2}{2} =1[/tex]

And:

[tex]M_l=\frac{A_m_a_x+A_m_i_n}{2}=\frac{2+0}{2} =\frac{2}{2} =1[/tex]

Answer:

It is D

Step-by-step explanation:

Distance walked = 85.088 feet

The distance Sina walked would be equal to the length of the diagonal of rectangle.

As every angle in a rectangle is 90 degree. So, we can apply Pythagoras theorem in right triangle formed by sides,

Base- 74 feet, Altitude-  42 feet and Hypotenuse- Diagonal

Base^2 + Altitude ^ 2 = Hypotenuse ^2

74^2 + 42 ^ 2 = Diagonal ^2

On solving,

Diagonal = 85.088 feet

To calculate the distance Sina walked diagonally across the basketball court, we utilize the Pythagorean theorem using the court's length and width. The calculation gives us a diagonal distance of approximately 85 feet.

To calculate the distance Sina walked across the rectangular basketball court diagonally, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Since the court is 74 feet long and 42 feet wide, these dimensions can be considered the two shorter sides of a right triangle, with the diagonal Sina walked being the hypotenuse.

The Pythagorean theorem formula is:

[tex]c^2 = a^2 + b^2[/tex]

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. Substituting the known values:

[tex]c^2 = 742 + 422\\c^2 = 5476 + 1764\\c^2 = 7240[/tex]

To find c, we take the square root of 7240:

c ≈ 85.09 feet

Therefore, Sina walked approximately 85 feet diagonally across the basketball court.

The balance in the account after 7 years will be approximately $2,747.70.

To calculate the balance in the account after 7 years with a principal of $2,400 earning 2% interest compounded annually, you can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future balance

P = the principal amount ($2,400)

r = the annual interest rate (2% or 0.02 as a decimal)

n = the number of times the interest is compounded per year (annually, so n = 1)

t = the number of years (7 years)

Plug these values into the formula:

A = 2400(1 + 0.02/1)^(1*7)

A = 2400(1 + 0.02)⁷

A = 2400(1.02)⁷

A = 2400(1.144877)

A ≈ $2,747.70

So, the balance in the account after 7 years will be approximately $2,747.70.

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Answer:

one because the distance stay the same and infinite because the are infinite positions that the radii could be in

Step-by-step explanation: