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3 years ago

Multiply or divide as indicated a^5/a^3

Mathematics

2 answers:

Korolek [52]3 years ago

8 0

Answer:

The answer is $a^{2}$ .

Step-by-step explanation:

$\frac{a^{5} }{a^{3} }$

when we divide exponents that have the same base, we subtract the powers and keep the base same.

So, this given fraction will become:

$a^{5-3}$

=> $a^{2}$

Or in more simpler terms we can write this off as:

$\frac{a*a*a*a*a}{a*a*a}$

So, we are left with $a*a=a^{2}$

Alex73 [517]3 years ago

5 0

When you divide you subtract exponents....so a^2

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Question in picture please answer!

lesantik [10]

The bottom one

Basically the question is what graph shows a number below or equal to -1

6 0

3 years ago

An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out squares of equal size from the fou

Burka [1]

Answer:

Maximum volume of the box will be 7.41 cubic feet.

Step-by-step explanation:

Open box has been made from a metal sheet measuring 3 ft and 8 ft.

Let four square pieces were removed from the four corners with one side measurement x ft.

Volume of the open box = Length × width × height

Length of the box = (3 - 2x) ft

Width of the box = (8 - 2x) ft

Height of the box = x ft

Volume of the box = (3 - 2x)(8 - 2x)x

V = (24 - 6x - 16x + 4x²)x

V = 24x - 22x² + 4x³

Now we take the derivative of V with respect to x and equate the derivative to zero,

$\frac{d}{dx}(V)=\frac{d}{dx}(24x - 22x^{2}+4x^{3})$

V' = 24 - 44x + 12x²

V' = 0

12x² - 44x + 24 = 0

3x² - 11x + 6 = 0

3x² - 9x - 2x + 6 = 0

3x(x - 3) - 2(x - 3) = 0

(3x - 2)(x - 3) = 0

(3x - 2) = 0

and (x - 3) = 0

Therefore, x = 3, $\frac{2}{3}$

For x = 0.67

Length of the box = (3 - 2x) = 3 - 1.34

= 1.66 ft

Width of the box = (8 - 2x) = 8 - 1.34

= 6.66 ft

Volume of the box = 0.67 × 1.66 × 6.66

V = 7.41 cubic feet.

Similarly, for x = 3,

Length of the box = (3 - 2\times 3) = -3

which is negative but the length of the box can not be negative.

Therefore, maximum volume of the box will be 7.41 cubic feet.

6 0

3 years ago

Please help me solve this LCM

hodyreva [135]

Note that

$x^2 - y^2 = (x - y) (x + y)$

and

$x^2 + 2xy + y^2 = (x + y)^2$

Then their LCM is $\boxed{x + y}$ .

7 0

2 years ago

Are two equilateral triangles always similar

sukhopar [10]

Yes because all equilateral triangles have equal angles and side lengths so they are all similar. hope i helped -J

4 0

3 years ago

Given f(x) = log(x+1), x >-1 and g(x) = x^2 + 2x, XER find (f•g)(1)

worty [1.4K]

Answer:

Like terms, functions may be combined by addition, subtraction, multiplication or division.

Example 1. Given f ( x ) = 2x + 1 and g ( x ) = x2

+ 2x – 1 find ( f + g ) ( x ) and

( f + g ) ( 2 )

Solution

Step 1. Find ( f + g ) ( x )

Since ( f + g ) ( x ) = f ( x ) + g ( x ) then;

( f + g ) ( x ) = ( 2x + 1 ) + (x2

+ 2x – 1 )

= 2x + 1 + x2

+ 2x – 1

= x

+ 4x

Step 2. Find ( f + g ) ( 2 )

To find the solution for ( f + g ) ( 2 ), evaluate the solution above for 2.

Since ( f + g ) ( x ) = x2

+ 4x then;

( f + g ) ( 2 ) = 22

+ 4(2)

= 4 + 8

= 12

Example 2. Given f ( x ) = 2x – 5 and g ( x ) = 1 – x find ( f – g ) ( x ) and ( f – g ) ( 2 ).

Solution

Step 1. Find ( f – g ) ( x ).

( f – g ) ( x ) = f ( x ) – g ( x )

= ( 2x – 5 ) – ( 1 – x )

= 2x – 5 – 1 + x

= 3x – 6

Step 2. Find ( f – g ) ( 2 ).

( f – g ) ( x ) = 3x – 6

( f – g ) ( 2 ) = 3 (2) – 6

= 6 – 6

= 0

Example 3. Given f ( x ) = x2

+ 1 and g ( x ) = x – 4 , find ( f g ) ( x ) and ( f g ) ( 3 ).

Solution

Step 1. Solve for ( f g ) ( x ).

Since ( f g ) ( x ) = f ( x ) * g ( x ) , then

= (x2

+ 1 ) ( x – 4 )

= x

– 4 x2

+ x – 4 .

Step 2. Find ( f g ) ( 3 ).

Since ( f g ) ( x ) = x3

– 4 x2

+ x – 4, then

( f g ) ( 3 ) = (3)3

– 4 (3)2

+ (3) – 4

= 27 – 36 + 3 – 4

= -10

Example 4. Given f ( x ) = x + 1 and g ( x ) = x – 1 , find ( x ) and ( 3 ). f

⎛ ⎞ ⎜

⎝ ⎠

⎛ ⎞ ⎜

⎝ ⎠ ⎟ ⎟

Solution

Step 1. Solve for ( x ). f

⎛

⎜

⎝ ⎠

⎞

⎟

Since ( x ) = , then ( )

( )

f x

g x

⎛

⎜

⎝ ⎠

⎞

⎟

= ; x ≠ 1 1

−

Step 2 Find . ( ) 3 f

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

Since = , then 1

− ( ) f x

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

3 1

− ( ) 3 f

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

= 2

Step-by-step explanation:

did this Help?

3 0

3 years ago