What is the image of the point (3, 2) after a rotation of 90° counterclockwise about the origin?​

Let y = √x, so the limit can be rewritten as

[tex]\displaystyle \lim_{y\to\infty}\left(\frac{\sqrt{y^6+y^2}}{y^2+3} - \frac{\sqrt{y^4+1}}{y+4}\right)[/tex]

Now,

[tex]\sqrt{y^6+y^2} = \sqrt{y^2\left(y^4+1\right)} = y\sqrt{y^4+1}[/tex]

so we can rewrite the limit further as

[tex]\displaystyle \lim_{y\to\infty}\left(\frac{y}{y^2+3} - \frac1{y+4}\right)\sqrt{y^4+1}[/tex]

Combine the rational terms:

[tex]\dfrac y{y^2+3} - \dfrac1{y+4} = \dfrac{y(y+4)-(y^2+3)}{(y^2+3)(y+4)} = \dfrac{4y-3}{(y^2+3)(y+4)}[/tex]

Then in the limit, we get

[tex]\displaystyle \lim_{y\to\infty}\frac{(4y-3)\sqrt{y^4+1}}{(y^2+3)(y+4)} = \lim_{y\to\infty}\frac{(4y^3-3y^2)\sqrt{1+\dfrac1{y^4}}}{y^3+4y^2+3y+12} \\\\ = \lim_{y\to\infty}\frac{\left(4-\dfrac3y\right)\sqrt{1+\dfrac1{y^4}}}{1+\dfrac4y+\dfrac3{y^2}+\dfrac{12}{y^3}} = \boxed{4}[/tex]

Answer:

2

Step-by-step explanation:

|-6+8|

Add/subtract the numbers: -6 + 8 = 2

= |2|

Apply the absolute value rule: |a| = a, a ≥ 0

= 2

Answer:c

Step-by-step explanation:

Answer:

  -25, 25

Step-by-step explanation:

Since the numbers have the same absolute value and the sum of their absolute values is 50, they both must have an absolute value of 50/2 = 25.

Unique numbers with the same absolute value will have opposite signs.

The numbers are -25 and 25.

Answer:

Cylinder has a formula

π×r²×h

so of it is open

π×r²×h - π×r²

Answer:

pls give brainiest

Step-by-step explanation:

A=2πr×h(r+h)

Answer: 2x2−3x−8

Step-by-step explanation:

Answer:

The equation would be 8h= 128

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

When you divide both sides by 8, you end up with:

16

Answer:

6

Step-by-step explanations:

The remainder is what is left over after dividing whatever from d. So if you add one to d, then the remainder would increase from 5 to 6.

Hope this helps.

Answer:

B. There are two distinct rational solutions

Step-by-step explanation:

x^2 -1 = 24

Add 1 to each side

x^2 -1+1 = 24+1

x^2 = 25

Take the square root of each side

sqrt(x^2) = ±sqrt(25)

x = ±5

Answer:

B.

Step-by-step explanation:

x^2 - 1 = 24

x^2 = 25

Taking the square root of both sides:

x = -5, 5.

2 distinct rational solutions.

Answer:

C

Step-by-step explanation:

They all have and addition and subtraction pattern in each cube, thank me later - PrObLeM OcCuReD

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the amount invested at 3%. Then (x -500) is the amount invested at 2%, and 4x is the amount invested at 4%. The total interest income is ...

  0.02(x -500) + 0.03x + 0.04(4x) = 179

  0.21x -10 = 179 . . . . . simplify

  0.21x = 189 . . . . . . . . add 10

  x = 900 . . . . . . . . . . . divide by 0.21

  x -500 = 400

  4x = 3600

$400 is invested at 2%; $900 is invested at 3%, $3600 is invested at 4%.

Answer:

b) (_6,198,) 1112334dccfsshh

Answer:

(a) 40

(b) 15% per week, to the nearest percent.

Step-by-step explanation:

Given:

old production,

P(w) = 230(1.1^w)

(a) At week 0, w=0, so

P(0) = 230(1.1^0) = 230

Difference (old - new) = 230-190 = 40

(b) about 15% per week

(c) from the 4th week on

approximate growth rate of new factory

N(w) = 190(R^w)

we know

w=0, N(0) = 190

w=7, N(7) = 505

so R=(505/190)^(1/7) = 1.1499 = 1.15 approx.

(c)

The old production tabulated:

w P(w) New

0 230 190

1 253 220

2 278 252

3 306 290

4 337 337

5 370 380

6 407 440

7 448 505

So we see that at the end of the 4th week, the two productions match, and new factory begins to exceed old production.

Answer:

The next three terms are 1.8, 2.0, and 2.2.

Step-by-step explanation: We can subtract a number of the sequence minus the number right before that number. For example, 1-0.8=0.2 and 1.4-1.2=0.2. So, we have to add 0.2 from 1.6 to find the next term which is 1.8, then add 1.8+0.2 to get 2 as the number after that, then add 2+0.2=2.2 to get the final number. Som your answer is 1.8,2.0,2.2. Hope this helped.

Answer: 17

Step-by-step explanation:

Using Pemdas, simplify the exponents, and then solve the multiplication and division inside the parentheses before subtracting. 10-9 = 1 so 1*7 =7

10 +7 is 17.

also i hope this helps and i hope this is not a test...

Hi there! Hopefully this helps!

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Answer: 14.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

First we calculate 3 to the power of 2 and get 9.

|

\/

9 + 9 - [tex]\frac{8}{2}[/tex] = 14.

Now we add 9 + 9 to get 18.

18 - [tex]\frac{8}{2}[/tex] = 14.

Then, we divide 8 by 2 to get 4.

18 - 4 = 14.

Then we subtract 4 from 18 to get.....You guessed it, 14!

Answer: 14

PEMDAS

P: Parentheses

E: Exponets

M: Multiplcaction

D: Divison

A: Addition

S: Subtraction

PEMDAS can also be known as Please Excuse My Dear Aunt Sally

P: [tex](9-8/2)[/tex]

E: [tex]3^2[/tex]

M: [tex]3*3[/tex]

D: [tex]8/2[/tex]

A: [tex]9+5[/tex]

S: [tex]9-8/2[/tex]

Multiply

E: [tex]3^2=3*3=9[/tex]

M: [tex]3*3=9[/tex]

Divide

D: [tex]8/2=4[/tex]

Subtract

S: [tex]9-4=5[/tex]

Add

A: [tex]9+5=14[/tex]

Answer: [tex]14[/tex]

The reason why we didn't use P to get our answer because it would of messed up the steps. So instead we separated it by dividing 8/2 in D and 9-4-5 for S.

Answer:

B, 10+ /10 units

Step-by-step explanation:

Answer:

x=(3e+2d)/(2g-ef)

Step-by-step explanation:

d=e(3+fx)/(2+gx)

or, 2d+2gx=3e+efx

or, 2gx-efx=3e+2d

or, x(2g-ef)=3e+2d

or, x=(3e+2d)/(2g-ef)

Answer:

x = (-2d + 3e) / (dg - fe)

Step-by-step explanation:

We solve it by using algebra.

1. Multiply each side by 2 + gx:

dgx + 2d = fxe + 3e

2. Subtract fxe on both sides:

dgx − fxe + 2d = 3e

3. Subtract 2d from both sides:

dgx − fxe = −2d + 3e

4. Factor out x:

x (dg − fe) = −2d + 3e

5. Divide dg - fe:

x = (-2d + 3e) / (dg - fe)

I hope this helped! :D

Answer:

6 meters and 3 meters are the dimensions of the vegetable patch.

Step-by-step explanation:

Keep in mind the formulas for perimeter and area of a rectangle are:

A - lw

P - 2 (l + w)

List the factors of 18:

1, 2, 3, 6, 9, 18

POSSIBLE DIMENSIONS of the vegetable patch:

1 meter and 18 meters

Area - 18 m^2

Perimeter - 38 meters

2 meters and 9 meters

Area - 18 m^2

Perimeter - 22 meters

3 meters and 6 meters

Area - 18 m^2

Perimeter - 18 meters

The rectangular vegetable patch with the dimensions 3 meters and 6 meters corresponds with the given area and perimeter of the vegetable patch mentioned. So that is your answer.

Hope this helps!

Answer:

Yes, you are correct.

Step-by-step explanation:

You are substituting the measure of angle x as the measure of angle a since they are congruent to each other.

Step-by-step explanation:

using the slope formula, we can see that the slope is 0

Answer:

Step-by-step explanation:

Hypotenuse = Length of  ladder = 10m

Distance between wall and end of the ladder at ground =   leg ²  = 2 m

Height of wall = x m

Use Pythagorean theorem

leg² +x² = 10²

2² + x² = 100

4 +x²    = 100

       x² = 100 -4

      x² = 96

      x = √96

       x  = 9.7979

      x = 9.798 m

Answer:

no

Step-by-step explanation:

5 books are $2.50, mean that 10 books should only be $4.00 not $4.50. Also making the 15 for $6.00 only $5.50. All because 5 books would be $2.50.

Answer:

(x-1)(x-2)(x-3)

Step-by-step explanation:

hy vọng nó giúp

Answer:that s math

Step-by-step explanation:

Answer:

the choices for answers are technically incorrect...

the "correct" answer is [tex]m^6n^4[/tex]

the answer that matches that (which is not simplified) is:

"A":    [tex]\frac{m^{7} n^{3} n}{m}[/tex]

Step-by-step explanation:

Answer:

[tex]\displaystyle z = 4\, \log_{10} \left(\frac{32}{5}\right)[/tex].

Step-by-step explanation:

Multiply both sides by [tex](1/5)[/tex] and simplify:

[tex]\displaystyle \frac{1}{5} \times 5\, (10)^{z/4} = \frac{1}{5} \times 32[/tex].

[tex]\displaystyle (10)^{z/4} = \frac{32}{5}[/tex].

Take the base-[tex]10[/tex] logarithm of both sides:

[tex]\displaystyle \log_{10}\left(10^{z/4}\right) = \log_{10} \left(\frac{32}{5}\right)[/tex].

[tex]\displaystyle \frac{z}{4} = \log_{10}\left(\frac{32}{5}\right)[/tex].

[tex]\displaystyle z = \log_{10}\left(\frac{32}{5}\right)[/tex].

Answer:

1,300 lb.

Step-by-step explanation:

V = 9 × 12 × 14.5 = 1566 ft³

1,566 × 0.83 = 1,299.78 ≈ 1,300 lb.

Answer:

-25 > -5(x+2.5)

-25 > -5x -12.5

x > 5/2

please click thanks and mark brainliest if you like :)

Answer:

x < 2.5

Step-by-step explanation:

-25>-5(x-12.5)

-25 > -5x -12.5

add 12.5 to both sides

-25+12.5 > -5x -12.5+12.5

-12.5> -5x

divide both sides by -5

(-12.5/-5)> -5x/-5

x>2.5

since we divided by a negative,the inequality sign will flip over

x<2.5

Answer:

x = 2

Step-by-step explanation:

3x - 5 = 1

Adding 5 to both sides gives us:

3x - 5 + 5 = 1 + 5

3x = 6

Dividing the equation by 3 gives us:

3x / 3 = 6 / 3

x = 2

Answer:

x = 2 Hfizfifsits96eotst9s