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3 years ago

Simplify ( 1/2A + 1/2B )^2

Mathematics

2 answers:

ANTONII [103]3 years ago

5 0

A^2 ab b^2
___+ ___+ ___
4 2 4

this is your answer

zysi [14]3 years ago

4 0

Notice that both A and B are multiplied by (1/2).

Thus, the given expression can be re-written as [(1/2)(A+B)]^2.

Square the (1/2) and the (A+B) separately, and then multiply together the resulting squares:

(1/4)(A^2 + 2AB + B^2)

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During the mayoral election,two debates were held between the candidates. The first debate lasted 1 2/3 hours.The second one was

butalik [34]

Answer:

2nd debate was 3 hours long.

Step-by-step explanation:

We have been given that during the mayoral election,two debates were held between the candidates. The first debate lasted 1 2/3 hours. The second one was 1 4/5 times as long as the first one.

Let us find the estimate of time spent on 2nd debate.

1 2/3 hours would be approximately 2 hours. 1 4/5 times would be equal to 2 times.

$2*2=4$

Therefore, the estimated time is less 4 hours.

To find the time spent on 2nd debate, we will multiply 1 2/3 by 1 4/5.

First of all, we will convert mixed fractions into improper fractions as:

$1\frac{2}{3}=\frac{5}{3}$

$1\frac{4}{5}=\frac{9}{5}$

Now, we will multiply both fractions as:

$\frac{5}{3}\times \frac{9}{5}$

$\frac{1}{3}\times \frac{9}{1}$

$\frac{9}{3}\Rightarrow 3$

Therefore, the 2nd debate was 3 hours long.

5 0

3 years ago

А<br> D<br> 11x+8<br> 950<br> B<br> с<br> Find the value of X

Ivenika [448]

Answer:

write your question properly...

4 0

2 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

3 years ago

Please please help me!!!!

uysha [10]

Sure with what? what subject?

7 0

3 years ago

Help ASAP, i don't understand this.

Inessa [10]

The given polynomial expressed as partial fraction is 5x^3 + 9/x

<h3>Polynomial function and partial fractions</h3>

Polynomial function are function that have a leading degree of 3. Given the expression below;

f(x) = (5x^4+9)/x

Applying partial fraction

Since the part fraction means separating the fraction into two parts, hence;

f(x) = 5x^4/x + 9/x

Simplify

Since there is value of x at both numerator and denominator, it will cancel out to have

f(x) = 5x^3 + 9/x

From the result, we can see that p(x) = 5x^3 and k = 9

Hence the given polynomial expressed as partial fraction is 5x^3 + 9/x

Learn more on polynomial here: brainly.com/question/2833285

#SPJ1

8 0

2 years ago