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2 years ago

Please help in maths

Mathematics

1 answer:

Readme [11.4K]2 years ago

7 0

The equivalent expressions of 22c + 33d are (a), (c) and (e)

<h3>How to determine the equivalent expressions?</h3>

The expression is given as:

22c + 33d

Factor out 11 from the expression

11(2c + 3d)

Multiply by 1

1 * 11(2c + 3d)

Express 1 as -1 * -1

-1 * -1 * 11(2c + 3d)

Evaluate the product

(-11) * (-2c - 3d)

Also, we have:

22c + 33d

Multiply by 1

(22c + 33d) * 1

Express 1 as 3/3

(22c + 33d) * 3/3

Evaluate the product

(66c + 99d) * 1/3

Hence, the equivalent expressions are (a), (c) and (e)

Read more about equivalent expressions at:

brainly.com/question/27911936

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The function f(x,y)=2x + 2y has an absolute maximum value and absolute minimum value subject to the constraint 9x^2 - 9xy + 9y^

deff fn [24]

Answer:

the minimum is located in x = -5/3 , y= -5/3

Step-by-step explanation:

for the function

f(x,y)=2x + 2y

we define the function g(x)=9x² - 9xy + 9y² - 25 ( for g(x)=0 we get the constrain)

then using Lagrange multipliers f(x) is maximum when

fx-λgx(x)=0 → 2 - λ (9*2x - 9*y)=0 →

fy-λgy(x)=0 → 2 - λ (9*2y - 9*x)=0

g(x) =0 → 9x² - 9xy + 9y² - 25 = 0

subtracting the second equation to the first we get:

2 - λ (9*2y - 9*x) - (2 - λ (9*2x - 9*y))=0

- 18*y + 9*x + 18*x - 9*y = 0

27*y = 27 x → x=y

thus

9x² - 9xy + 9y² - 25 = 0

9x² - 9x² + 9x² - 25 = 0

9x² = 25

x = ±5/3

thus

y = ±5/3

for x=5/3 and y=5/3 → f(x)= 20/3 (maximum) , while for x = -5/3 , y= -5/3 → f(x)= -20/3 (minimum)

finally evaluating the function in the boundary , we know because of the symmetry of f and g with respect to x and y that the maximum and minimum are located in x=y

thus the minimum is located in x = -5/3 , y= -5/3

4 0

4 years ago

Consider the system of equations:

vodka [1.7K]

Answer:

(x, y) = (5, 1)

Step-by-step explanation:

To <em>eliminate</em> x, you can double the second equation and subtract the first.

... 2(x +4y) -(2x -3y) = 2(9) -(7)

...11y = 11 . . . . . simplify

... y = 1 . . . . . . divide by 11

Using the second equation to find x, we have ...

... x + 4·1 = 9

... x = 5 . . . . . subtract 4

_____

<u>Check</u>

2·5 -3·1 = 10 -3 = 7 . . . . agrees with the first equation

(Since we used the second equation to find x, we know it will check.)

5 0

4 years ago

Read 2 more answers

Identify the values of the variables. Give your answers in the simplest radical form.

Lena [83]

Answer/Step-by-step explanation:

✔️Find k:

Reference angle = 60°

Hypotenuse = k

Opposite = 9

Therefore, using trigonometric ratio, we have:

$sin(60) = \frac{9}{k}$

Multiply both sides by k

$k*sin(60) = 9$

Divide both sides by sin(60)

$k = \frac{9}{sin(60)}$

$k = \frac{9}{\frac{\sqrt{3}}{2}}$

$k = 9*\frac{2}{\sqrt{3}}$

$k = \frac{18}{\sqrt{3}}$

Rationalize

$k = \frac{18*\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$k = \frac{18\sqrt{3}}{3}$

$k = 6\sqrt{3}$

✔️Find f:

Reference angle = 60°

Opposite = 9

Adjacent = f

Therefore, using trigonometric ratio, we have:

$tan(60) = \frac{9}{f}$

Multiply both sides by f

$f*tan(60) = 9$

Divide both sides by tan(60)

$f = \frac{9}{tan(60)}$

$k = \frac{9}{\sqrt{3}}$

Rationalize

$k = \frac{9*\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$k = \frac{9\sqrt{3}}{3}$

$k = 3\sqrt{3}$

8 0

3 years ago

A cone has a diameter of 4 cm and a height that is 6 times the diameter. Using 3.14 for pi, which of the following can be used t

Triss [41]

Answer:

1/3(3.14)2^2(24)

Step-by-step explanation:

The volume of a cone is given by the formula;

1/3πr³

Considering the radius is 2 cm and the height is 24 cm (4 times the diameter).

Therefore;

Volume = 1/2(3.14)2²(24)

This can be used to calculate the volume.

3 0

3 years ago

Mr. Fernandez uses 7 boards that are 4 feet long and 6 inches wide to make on bookshelf. If he buys lumber in lengths of 8 feet

True [87]

Bookshelf =7boards each
Lumber=4 boards each
He wants to make 5 bookshelves total
5x7=35
So he needs 35 boards
And each lumber makes 4 boards
So what number times 4 is equal to or more than 35?

9times 4 is 36

So he needs 9 pieces of lumber to make 5 bookshelves.

Good luck with your work! Brainliest would be appreciated :)

3 0

3 years ago