Identify the scale factor for the dilation below if ABCD is the preimage.

What are the vertical<br> asymptotes of y = cot x for<br> -Зп

RideAnS [48]

Nanakjanajisnanwj ajnwjwhwbjejs

4 0

1 year ago

Please help me with this

Tatiana [17]

<h2><u>Given</u> :</h2>

The given equations are :

$\longrightarrow15b + 10g = 8640 \: \: \: \: \: - (1)$

$\longrightarrow b + g = 708 \: \: \: \: \: \: - (2)$

Let's solve for g in equation (2) :

$\longrightarrow b + g = 708$

$\longrightarrow g = 708 - b \: \: \: \: \: - (3)$

now, let's plug value of g from equation (3) into equation (1) :

$\longrightarrow15b + 10g = 8640$

$\longrightarrow15b + 10(708 - b) = 8640$

$\longrightarrow15b - 10b + 7080 = 8640$

$\longrightarrow5b = 1560$

$\longrightarrow b = 312$

plugging value of b in equation (3) :

$\longrightarrow g = 708 - b$

$\longrightarrow g = 708 - 312$

$\longrightarrow g =39 6$

since " g " represents ground seats, number of ground seats :

=》396

And " b " represents balcony seat, therefore it is equal to :

=》312

$\mathrm{ ☠ \: TeeNForeveR \:☠ }$

4 0

3 years ago

The answer to this problem?

LenaWriter [7]

The simplified expression of $\sqrt{\frac{162x^9}{2x^{27}}}$ is $\frac{9}{x^9}$

<h3>How to simplify the expression?</h3>

The expression is given as:

$\sqrt{\frac{162x^9}{2x^{27}}}$

Divide 162 and 2 by 2

$\sqrt{\frac{81x^9}{x^{27}}}$

Take the square root of 81

$9\sqrt{\frac{x^9}{x^{27}}}$

Apply the quotient rule of indices

$9\sqrt{\frac{1}{x^{27-9}}}$

Evaluate the difference

$9\sqrt{\frac{1}{x^{18}}}$

Take the square root of x^18

$\frac{9}{x^9}$

Hence, the simplified expression of $\sqrt{\frac{162x^9}{2x^{27}}}$ is $\frac{9}{x^9}$

Read more about expressions at:

brainly.com/question/723406

#SPJ1

5 0

2 years ago

The logarithmic expression ln(√e/y^3) can be rewritten as

kvv77 [185]

Answer:

$\dfrac{1 - 6 \ln y}{2}$

Step-by-step explanation:

$\ln \dfrac{\sqrt{e}}{y^3} =$

$= \ln \dfrac{e^\frac{1}{2}}{y^3}$

$= \ln e^\frac{1}{2} - \ln y^3$

$= \dfrac{1}{2} \ln e - 3 \ln y$

$= \dfrac{1}{2} - 3 \ln y$

$= \dfrac{1 - 6 \ln y}{2}$

6 0

3 years ago

A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x,

tatiyna

Answer:

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3

7 0

4 years ago