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FromTheMoon [43]
2 years ago
9

EASY- Han has to build the figure below, which will serve as a counterweight, for his robotics project. Find the VOLUME of the f

inished object assuming it is empty inside.

Mathematics
1 answer:
Ymorist [56]2 years ago
7 0

Given:

A combined figure of a triangular prism and a cuboid.

To find:

The volume of the finished object assuming it is empty inside.

Solution:

From the given figure it is clear that the dimensions of the cuboid are 6 cm, 8 cm and 5 cm.

So, the volume of the cuboid is:

V_1=length\times width\times height

V_1=6\times 8\times 5

V_1=240

The volume of the cuboid is 240 cubic cm.

The area of a triangle is:

Area=\dfrac{1}{2}\times base\times height

Thus, the base area of the triangular prism whose base is 8 cm and height 4 cm, is:

B=\dfrac{1}{2}\times 8\times 4

B=16

The volume of a triangular prism is:

V_2=Bh

Where, B is the base area and h is the height of the prism.

The base area of the triangular prism is 16 square cm and the height is 5 cm. So, the volume of a triangular prism is:

V_2=16(5)

V_2=80

Now, the volume of the given figure is:

V=V_1+V_2

V=240+80

V=320

Hence, the volume of the finished object is 320 cubic cm.

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If line segment AB represents ​25%, what is the length of a line segment that is​ 100%?
kicyunya [14]

If I am correctly understanding the question, I think the length of the line segment would be 4AB

Step-by-step explanation:

25% = 1/4

AB = 1/4

100% = 4/4

AB*4 = 4AB

Multiply AB by 4 to find the value that 100% would equal, resulting in 4AB.

6 0
3 years ago
How many square feet of outdoor carpet will we need for this hole?
Mamont248 [21]

Answer:

The area of the outdoor carpet = 60 - 6 - 6 = 48 ft²

Step-by-step explanation:

The picture below is what you are referring to .

The whole area of the shape forms a rectangle. A triangle and a  rectangle has been cut off from the whole carpet rectangle. The square ft or area of the carpet is the subtraction of the area of the rectangle and triangle cut off from the whole area of the rectangle .

Area of the rectangle = Lb

where

L = 12 ft

b =  5 ft

area = 12 × 5  = 60 ft²

The cut off triangle area

area = 1/2 × base × height

area = 1/2 × 4 × 3

area = 12/2 = 6 ft²

The cut off rectangle area

area = Lb

area = 3 × 2

area = 6 ft²

The area of the outdoor carpet = 60 - 6 - 6 = 48 ft²

7 0
3 years ago
AYUDAAA PORFAVOOOOOOR!!
galben [10]

Answer:

4

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What is the length of a diagonal of a cube with a side length of 10 cm? 200 cm 210cm 300 cm 320cm
Scilla [17]

Answer:

The length of the diagonal of the cube = √(3 × 10²) = √300 cm

Step-by-step explanation:

* Lets revise the properties of the cube

- It has six equal faces all of them are squares

- It has 12 vertices

- The diagonal of the cube is the line joining two vertices in opposite

 faces (look to the attached figure)

- To find the length of the diagonal do that:

# Find the diagonal of the base using Pythagoras theorem

∵ The length of the side of the cube is L

∵ The base is a square

∴ The length of the diagonal d = √(L² + L²) = √(2L²)

- Now use the diagonal of the base and a side of a side face to find the

 diagonal of the cube by Pythagoras theorem

∵ d = √(2L²)

∵ The length of the side of the square = L

∴ The length of the diagonal of the cube = √[d² + L²]

∵ d² = [√(2L²)]² = 2L² ⇒ power 2 canceled the square root

∴ The length of the diagonal of the cube = √[2L² + L²] = √(3L²)

* Now lets solve the problem

∵ The length of the side of the square = 10 cm

∴ The length of the diagonal of the cube = √(3 × 10²) = √300 cm

- Note: you can find the length of the diagonal of any cube using

 this rule Diagonal = √(3L²)

7 0
3 years ago
Read 2 more answers
Report Error Suppose $P(x)$ is a polynomial of smallest possible degree such that: $\bullet$ $P(x)$ has rational coefficients $\
motikmotik

Answer:

We want a polynomial of smallest degree with rational coefficients with zeros in \sqrt{7}, 1 - \sqrt{6} and -3. The last root gives us the factor (x+3). Hence, our polynomial is

P(x) =(x+3)q(x)

where q is a polynomial with rational coefficients and roots \sqrt{7} and 1 - \sqrt{6}. The root \sqrt{7} gives us a factor x-\sqrt{7}, but in order to obtain rational coefficients we must consider the factor x^2-7.

An analogue idea works with 1 - \sqrt{6}. For convenience write  x - 1 + \sqrt{6} = ( x - 1) + \sqrt{6}. This gives the factor (x-1)^2-6. Hence,

P(x) = (x+3)(x^2-7)((x-1)^2-6)=x^5+x^4-18x^3-22x^2+77x+105

Notice that P(-1)=24. So, in order to satisfy the last condition we divide by 3 the whole polynomial, without altering its roots. Finally, the wanted polynomial is

P(x) =(1/3)x^5+(1/3)x^4-6x^3-(22/3)x^2+(77/3)x+35

Step-by-step explanation:

We must have present that any polynomial it's determined by its roots up to a constant factor. But here we have irrational ones, in order to eliminate the irrational coefficients that a factor of the type x-\sqrt7 will introduce in the expression, we need to multiply by its conjugate x+\sqrt7. Hence, we will obtain x^2-7 that have rational coefficients. Finally, the last condition is given with the intention to fix the constant factor. Usually it is enough to evaluate in the point and obtain the necessary factor.

4 0
2 years ago
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