Joan is H cm tall. Gill is 3 cm shorter than Joan. Write down Gill's height in terms of H

How do you determine the domain of a function ?

Sunny_sXe [5.5K]

Answer:

Let y = f(x) be a function with an independent variable x and a dependent variable y.

If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that

chosen x-value is said to belong to the domain of f. If there is a requirement that a y-value produced by a function

must be a real number, the following conditions are commonly checked:

1. Denominators cannot equal 0.

2. Radicands (expressions under a radical symbol) of even roots (square roots, etc)

cannot have a negative value.

3. Logarithms can only be taken of positive values.

4. In word problems physical or other real-life restrictions might be imposed, e.g. time is

nonnegative, number of items is a nonnegative integer, etc.

8 0

2 years ago

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Ted is making a bread recipe that uses three 1/4 cups of flour and a muffin recipe that uses 2 3/4 cups of flour eggs. How much

wlad13 [49]

Amount of flour used in bread recipe = $3 \frac{1}{4}$ cups

Amount of flour used in muffin recipe = $2 \frac{3}{4}$ cups

We have to determine how much more flour is in the recipe.

Since, more amount of flour is used in bread recipe than in muffin recipe.

Total amount of more flour = $3 \frac{1}{4} - 2 \frac{3}{4}$

= $\frac{13}{4} - \frac{11}{4}$

= $\frac{2}{4}$

= $\frac{1}{2}$

Therefore, $\frac{1}{2}$ more cup of flour is used in bread recipe than in muffin recipe.

Now, we will determine the total amount of flour used in both recipe.

Total amount of flour used in bread and muffin recipe

= $3 \frac{1}{4} + 2 \frac{3}{4}$

= $\frac{13}{4} + \frac{11}{4}$

= $\frac{24}{4}$

= 6 cups

Therefore, total 6 cups of flour are used in both the recipes.

3 0

3 years ago

I have 120 cm of framing material to make a picture frame, which will be most pleasing to the eye if its height is 2/3 of its wi

Ilia_Sergeevich [38]

The formula for perimeter is:

P = 2 h + 2 w

where P is perimeter = 120 cm, h is height, w is width

we are also given that: h = (2/3) w, therefore:

P = 2 (2/3) w + 2 w = 120

(4/3) w + 2 w = 120

w = 36 cm

Therefore l is:

l = (2/3) w = 24 cm

Hence the dimension should be 24cm by 36 cm

6 0

3 years ago

Multiply 5x107 * 3x105

djverab [1.8K]

Answer:

the first on 5×107=535 the second one 3×105=315

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3 years ago

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Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x

nevsk [136]

For given f(x, y) the extremum: (12, 24) which is the minimum.

For given question,

We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108

We use the constraint to build the constraint function,

g(x, y) = 3x + 3y

We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:

$f_x=8x$

$f_y=4y$

$g_x=3$

$g_y=3$

Setting up the Lagrange multiplier equations:

$f_x=\lambda g_x$

⇒ 8x = 3λ .....................(1)

$f_y=\lambda g_y$

⇒ 4y = 3λ ......................(2)

constraint: 3x + 3y = 108 .......................(3)

Taking (1) / (2), (assuming λ ≠ 0)

⇒ 8x/4y = 1

⇒ 2x = y

Substitute this value of y in equation (3),

⇒ 3x + 3y = 108

⇒ 3x + 3(2x) = 108

⇒ 3x + 6x = 108

⇒ 9x = 108

⇒ x = 12

⇒ y = 2 × 12

⇒ y = 24

So, the saddle point (critical point) is (12, 24)

Now we find the value of f(12, 24)

⇒ f(12, 24) = 4(12)² + 2(24)²

⇒ f(12, 24) = 576 + 1152

⇒ f(12, 24) = 1728 ................(1)

Consider point (18,18)

At this point the value of function f(x, y) is,

⇒ f(18, 18) = 4(18)² + 2(18)²

⇒ f(18, 18) = 1296 + 648

⇒ f(18, 18) = 1944 ..............(2)

From (1) and (2),

1728 < 1944

This means, given extremum (12, 24) is minimum.

Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.

Learn more about the extremum here:

brainly.com/question/17227640

#SPJ4

6 0

2 years ago