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2 years ago

Find the volume of the figure above.

Mathematics

1 answer:

leonid [27]2 years ago

7 0

Answer:

234

Step-by-step explanation:

Base can be divided on 2 rectangles : 4*4.5 and 9*(9 - 4.5).

Area base = 4*4.5 + 9*(9 - 4.5)

height prism = 4

Volume prism = Area base* height prism = [4*4.5 + 9*(9 - 4.5)] *4 = 234 cm³

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A box has a volume of 192 cubic inches, a length that is twice as long as its width, and a height that is 2 inches greater than

ruslelena [56]

Answer:

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

Step-by-step explanation:

Cuboid : A cuboid is a three dimension shape. The length ,breadth and height of a cuboid are not same.

A cuboid has 6 faces.
A cuboid contains 8 vertices.
A cuboid contains 12 edges .
The total surface area of a cuboid is

= 2(length×breadth+breadth×height+length×height) square units

The dimension of a cuboid is written as length×breadth×height.

The volume is( length×breadth×height) cubic units

Given that the volume of the box is 192 cubic inches.

Let x inches be the width of the cuboid.

Since the length is twice as long as its width.

Then length = 2x inches

Again height is 2 inches longer than width.

Then height = (x+2) inches.

Therefore the volume of the cuboid is

$=[x\times 2x\times (x+2)]$ cubic inches

$=[2x^2(x+2)]$ cubic inches

$=(2x^3+4x^2)$ cubic inches

According to the problem,

$2x^3+4x^2=192$

$\Rightarrow 2x^3+4x^2-192=0$

$\Rightarrow 2(x^3+2x^2-96)=0$

$\Rightarrow (x^3+2x^2-96)=0$

$\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0$

$\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0$

$\Rightarrow (x-4)(x^2+6x+24)=0$

Therefore x=4

Since the all zeros of x²+6x+24 =0 is negative.

Therefore breadth = 4 inches

length=(2×4) inches=8 inches

and height = (4+2)inches = 6 inches.

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

8 0

3 years ago

PQR is a right angled triangle calculate the size of angle marked x

romanna [79]

Answer:

$\displaystyle x \approx 37.4^\circ$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Trigonometry

[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] cosθ = adjacent over hypotenuse

Step-by-step explanation:

Step 1: Define

Angle θ = x

Adjacent Leg = 5.8

Hypotenuse = 7.3

Step 2: Solve for x

Substitute in variables [Cosine]: $\displaystyle cosx^\circ = \frac{5.8}{7.3}$
[Fraction] Divide: $\displaystyle cosx^\circ = 0.794521$
[Equality Property] Trig inverse: $\displaystyle x^\circ = cos^{-1}(0.794521)$
Evaluate trig inverse: $\displaystyle x = 37.39^\circ$
Round: $\displaystyle x \approx 37.4^\circ$

8 0

2 years ago

Identify the solution set of the given inequality using the given replacement set.

scoundrel [369]

Another user previously answered this same question and had a good rating, his answer was as follows:

"{-9; -6.5; -5.2}"

Which I suppose would be answer D.
- Hope it helps.

3 0

3 years ago

Divide the polynomial (x^2 + 3x + 5) by 2x + 1

umka21 [38]

Answer:

50888888888888888888+++++

7 0

3 years ago

A researcher at the Centers for Disease Control and Prevention is studying the growth of a certain bacteria. He starts his exper

SpyIntel [72]

The population of the bacteria after 7 hours is 230 bacteria.

An exponential function is given by:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the population of bacteria after x hours.

Given that he starts his experiment with 200 bacteria, hence

a = 200

The bacteria grow at a rate of 2% per hour, hence:

b = 100% + 2% = 1.02

The exponential equation becomes:

y = 200(1.02)ˣ

After 7 hours:

y = 200(1.02)⁷ = 230

The population of the bacteria after 7 hours is 230 bacteria.

Find out more at: brainly.com/question/12490064

6 0

2 years ago