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Roman55 [17]
3 years ago
7

Simplify the given expression below:

Mathematics
2 answers:
Zina [86]3 years ago
4 0
The answer will be C. OR 3. 11−<span>13<span>i</span></span>
WINSTONCH [101]3 years ago
4 0

Answer:

The correct option is 3.

Step-by-step explanation:

The given expression is

(7-3i)\cdot(2-i)

We need to find the simplified form of given expression.

Using distributive property, the given expression can be written as

7\cdot(2-i)-3i\cdot(2-i)

7(2)+7(-i)-3i(2)-3i(-i)

On further simplification we get

14-7i-6i+3i^2

14-13i+3(-1)               [\because i^2=-1]

14-13i-3

On combining like terms we get

(14-3)-13i

11-13i

The simplified form of given expression is 11-13i. Therefore the correct option is 3.

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There is 6/8 of a cake leftover after a birthday party. How many 1/4 pieces can be made out of the leftover cake?
ikadub [295]

3/4 because if you make it smaller you would get that

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There are 2.54 cm in 1 inch. they are 100 cm in 1 m, to the nearest meter, how many meters are in 474 inches
zlopas [31]

Multiply total meters by 100 to get total centimeters:

6 meters x 100 = 600 centimeters.

Now divide total centimeters by 2.554 to get total inches:

600 centimeters / 2.54 = 236.22 inches.

Rounded to the nearest inch = 236 inches.

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I REALLY NEED HELP WITH THIS
gtnhenbr [62]

Answer:

x=24

Step-by-step explanation:

6 0
2 years ago
Help please calculus
VLD [36.1K]

Let x, y, and z denote the side lengths of the box, with the bottom face having dimensions x-by-y and z is the height. Naturally this means each of x, y, and z must be greater than 0.

The box has a fixed volume of 252 cm³, so

xyz = 252

The surface area of the box is

2xy + 2xz + 2yz

and we're told that the material cost for each face is different. The total cost of the material needed to make the box is given by

C (x, y, z) = ($5/cm²) xy + ($2/cm²) xy + 2 ($3/cm²) (xz + yz)

or, omitting units and simplifying,

C (x, y, z) = 7xy + 6 (x + y) z

In the volume constraint, solve for any one variable; I'll do z.

z = 252/(xy)

Substitute this into the cost function:

C (x, y, 252/(xy)) = 7xy + 1512 (x + y)/(xy)

Since this is now a function of 2 variables, I'll rewrite this as

C* (x, y) = 7xy + 1512 (1/y + 1/x)

Compute the partial derivatives of C and find the critical points:

∂C/∂x = 7y - 1512/x² = 0   ⇒   x² y = 216

∂C/∂y = 7x - 1512/y² = 0   ⇒   x y² = 216

It follows that

x² y = x y²   ⇒   x = y

Just like before, we can think about C* as yet another function but only of 1 variable,

C** (x) = 7x² + 3024/x

Now find the critical points of C** :

dC**/dx = 14x - 3024/x² = 0   ⇒   x = 6

All of this tells us that C (x, y, z) has a critical point when x = y = 6 and z = 252/6² = 7. So the box that costs the least has dimensions 6 × 6 × 7 cm, which gives the box a surface area of 240 cm² and a total cost of $756.

6 0
2 years ago
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