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3 years ago

Which formula gives the x-coordinates of the maximum values for y = cos(x)?

1 answer:

8 0

You must remember that the periodicity of the function cos(x) is 2Pi. Also you should know that the maximum value of cos(x) is obtained when x = 0. So, the values of x for which cos(x) is maximum is x =0, 2Pi, 4 Pi, 6 Pi. <span>So, x = Pi * k, with k = 0, 2, 4, 6, ... An equivalent formula is x = 2Pi * n, with n = 0, 1, 2, 3, ..</span>

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Find the midpoint between (-1+9i) and B=(5-3i)

sdas [7]

Answer:

2 + 3i, midpoint is (2,3)

Step-by-step explanation:

we need to find the midpoint between (-1+9i) and B=(5-3i)

To find the midpoint of two points (a+bi) and (c+di) in a complex plane,

we apply formula

$\frac{a+c}{2} + \frac{b+d}{2} i$

A = (-1+9i) and B=(5-3i)

Midpoint for AB is

$\frac{-1+5}{2} + \frac{9+(-3)}{2}i$

$\frac{4}{2} + \frac{6}{2}i$

2 + 3i , so midpoint is (2,3)

8 0

3 years ago

Read 2 more answers

What is the 2nd term of the linear sequence below? 5 , 8 , 11 , 14 , 17 , . . .

julia-pushkina [17]

Answer:

2nd term is 8.

nth term is 3n + 2.

Step-by-step explanation:

nth term = 5 + 3(n - 1)

= 3n + 2

5 0

3 years ago

1. Write a rule that will take the triangle to a congruent triangle. Write your rule as (x,y)

olga nikolaevna [1]

Transforming a shape involves changing the size and/or the location of the shape.

The rule that will take the triangle to a congruent triangle is $(x,y) \to (x,-y)$
The rule that will take the triangle to a figure that is similar is $(x,y) \to (0.5x,0.5y)$ .
The rule that will take the triangle to a figure that is not similar or congruent is $(x,y) \to (0.5x,2y)$ .

<h3>Rigid transformation</h3>

When a shape is transformed by a rigid transformation, then the image of the shape will be congruent to the original shape.

An example of a rigid transformation is a reflection over the x-axis; and the rule is:

$(x,y) \to (x,-y)$

So, a rule that will take the triangle to a congruent triangle is $(x,y) \to (x,-y)$

<h3>Nonrigid transformation</h3>

When a shape is transformed by a nonrigid transformation, then the image of the shape will not be congruent to the original shape, however the original shape and the transformed shape would be similar

An example of a nonrigid transformation is a dilation by a scale factor od 0.5; and the rule is:

$(x,y) \to (0.5x,0.5y)$

So, a rule that will take the triangle to a figure that is similar is $(x,y) \to (0.5x,0.5y)$

However, if the x and y coordinates of the shape are dilated by different scale factors, then the resulting shape would neither be similar nor be congruent to the original shape.

A rule that will take the triangle to a figure that is not similar or congruent is $(x,y) \to (0.5x,2y)$ .

Read more about transformation at:

brainly.com/question/4289712

6 0

3 years ago

Find the average value of f over region

yan [13]

The area of D is given by:

$\int\limits \int\limits {1} \, dA = \int\limits_0^7 \int\limits_0^{x^2} {1} \, dydx \\ \\ = \int\limits^7_0 {x^2} \, dx =\left. \frac{x^3}{3} \right|_0^7= \frac{343}{3}$

The average value of f over D is given by:

$\frac{1}{ \frac{343}{3} } \int\limits^7_0 \int\limits^{x^2}_0 {4x\sin(y)} \, dydx = -\frac{3}{343} \int\limits^7_0 {4x\cos(x^2)} \, dx \\ \\ =-\frac{3}{343} \int\limits^{49}_0 {2\cos(t)} \, dt=-\frac{6}{343} \left[\sin(t)\right]_0^{49} \, dt=-\frac{6}{343}\sin49$

3 0

3 years ago

NO LINKS!! Please help me with this problem

Anastaziya [24]

Answer:

y²/324 -x²/36 = 1

Step-by-step explanation:

Where (0, ±b) are the ends of the transverse axis and y = ±(b/a)x describes the asymptotes, the equation of the hyperbola can be written as ...

y²/b² -x²/a² = 1

<h3>Application</h3>

Here, we have transverse axis endpoints of (0, ±18) and asymptotes of y = ±3x, so we can conclude ...

b = 18

b/a = 3 ⇒ a = 18/3 = 6

The equation of the hyperbola in standard form is ...

y²/324 -x²/36 = 1

7 0

2 years ago