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Olin [163]
3 years ago
7

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto

R, where the sides of S are parallel to the u- and v- axes. (Let u play the role of r and v the role of θ. Enter your answers as a comma-separated list of equations.) R lies between the circles x2 + y2 = 1 and x2 + y2 = 7 in the first quadrant
Mathematics
1 answer:
ruslelena [56]3 years ago
6 0
X(u, v) = (2(v - c) / (d - c) + 1)cos(pi * (u - a) / (2b - 2a))
y(u, v) = (2(v - c) / (d - c) + 1)sin(pi * (u - a) / (2b - 2a))

As v ranges from c to d, 2(v - c) / (d - c) + 1 will range from 1 to 3, which is the perfect range for the radius. As u ranges from a to b, pi * (u - a) / (2b - 2a) will range from 0 to pi/2, which is the perfect range for the angle. So, this maps the rectangle to R.
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Write the converse of the following statement:
Shkiper50 [21]

Answer:

Option 4 (If it is fall, then the trees have no leaves).

Step-by-step explanation:

Conditional Statements are the statements which involve "if" and "then". It contains two sets of statements in it. The statement after the word "if" is the hypothesis, and the statement after the word "then" is the conclusion. Conditional statements are written in the form "If A, then B"; where A is the hypothesis, and B is the conclusion. The converse of a conditional statement is the opposite of the original statement: hypothesis and conclusion replace each other. So the converse of the above statement will be "If B, then A".

In this case, A=The trees have no leaves and B=It is fall. Therefore, the converse will be:

If it is fall, then the tress have no leaves. Option 4 is the right answer!!!

5 0
3 years ago
Solve x4 – 17x2 + 16 = 0.<br> Let u =<br> Select all of the zeroes of the function. i i
Soloha48 [4]

Solve \ x^4 - 17x^2 + 16 = 0

To solve this equation , we need to write it in quadratic form

ax^2+bx+c=0

To get the equation in quadratic form we replace x^2 with u

x^2 = u

x^4 - 17x^2 + 16 = 0 can be written as

(x^2)^2 - 17x^2 + 16 = 0, Replace u for x^2

So equation becomes

u^2 - 17u + 16 = 0

Now we factor the left hand side

-16  and -1  are the two factors whose product is +16  and sum is -17

(u-16) (u-1) = 0

u -16 = 0  so u=16

u-1 =0  so u=1

WE assume u = x^2, Now we replace u with x^2

u = 16 so \ it \ becomes \ x^2 =16

Now take square root on both sides , x= +4  and x=-4

u = 1 so \ it \ becomes \ x^2 =1

Now take square root on both sides , x= +1  and x=-1

So zeros of the function are -4, -1, 1, 4


8 0
3 years ago
Read 2 more answers
A certain company's main source of income is a mobile app. The company's annual profit (in millions of dollars) as a function of
liberstina [14]

Answer:

x = $3, or x = $11


Step-by-step explanation:

The equation given is P(x)=-2(x-3)(x-11)

where

  • P(x) is the profit, and
  • x is the app price

<u>We want app prices (x's) when profit (P(x)) is 0, so plugging in into the equation:</u>

P(x)=-2(x-3)(x-11)\\0=-2(x-3)(x-11)\\0=(x-3)(x-11)

<em>It means (x-3) = 0  OR  (x-11) = 0</em>

So, x = 3, or 11

7 0
3 years ago
Read 2 more answers
6m-2 = m+13 how do i solve it
kakasveta [241]
First move the terms to get
6m-m=13+2
Then collect the like terms and calculate the sum, 5m=15
Divide both sides by 5
And you get m=3
4 0
3 years ago
There are 7 people in a room. Each person shakes hands once. How many handshakes will there be?
DiKsa [7]

7 people so first one shakes hand with the remaining people. that is 6

The 2nd person also shakes hand with 6 persons but we have already counted his handshake with first person. so we have to add 6-1 = 5 shakes for 2nd person

like wise 3rd person shakes hand with the remaining 6-2 = 4 people

4th person with 6-3=3 people

5th person with 6-4= 2 persons

6th person with 6-5=1 person

and 7th one with no one because already he has shaken his hand with everyone.

since these people shake their hands with others only once we just have to add the obtained values

6+5 +4+3+2+1= 21

totally 21 handshakes will be there in that room

7 0
3 years ago
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