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3 years ago

Find the value of the expression

Mathematics

1 answer:

abruzzese [7]3 years ago

8 0

Answer:

Step-by-step explanation:

1) Lets rewrite the expression in expanded form to make is easier to understand:

(8*8)÷(2*2*2)

2) Simplify the interior of the parenthesis:

(64)÷(8)

3) Divide:

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9 unit percent change is 23, what is the 19th unit percent cahnge?

vichka [17]

Answer:

42.40705%

Step-by-step explanation:

(1 - (23/100)^(19/9) = 1 + r/100

0.57593 = 1 + r/100

r = 42.40705%

6 0

2 years ago

A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

$Width = 3 - 2x \\\\$

The length of the shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$

Volume of the box at x= 1.59:

$V = \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

Volume of the box at x= 0.53:

$V = \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3$

The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0

3 years ago

What is the side length of a cube with volume 343 in squared?

Thepotemich [5.8K]

Hi there!

The formula for a square is V = s^3. Using this formula, we can plug in the volume and solve for s.

WORK:
343 = s^3
s = 7

ANSWER:
The side length of a cube with volume 343 is 7 inches.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

6 0

3 years ago

The sum of two numbers is 21. the second number is six times the first number.

Tamiku [17]

Answer:

Therefore first number is 3 and second number is 18

Step-by-step explanation:

Sum of the two numbers is 21 and Second number is six times the first number

x+6x = 21

7x = 21

x = 21/7

x = 3

substitute x value in 6x to find second number,

= 6x

= 6*3

= 18

8 0

3 years ago

Solve.<br> –51/2 + 63/4 + (-41/4)

VladimirAG [237]

Answer:

-20

Step-by-step explanation:

cause i did the math hope this helped :D

7 0

3 years ago

Read 2 more answers