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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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Combine like terms in the expression below:<br> 9x + 4.05xy + 15y + 30y - 11x + 9.46
aev [14]

Answer: 4.05 x y  − 2 x  +  45 y  +  9.46

Step-by-step explanation:

9x + 4.05xy + 15y + 30y - 11x + 9.46

4.05xy + 9x - 11x  + 15y+ 30y+ 9.46

4.05 x y  − 2 x  +  45 y  +  9.46

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2 years ago
The volume v of a gas kept at constant temperature varies inversely with the pressure p. If the pressure is 24 pounds per square
daser333 [38]

Answer:

V=12\ ft^{3}

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form y*x=k or y=k/x

In this problem

P*V=k

step 1

Find the value of K

For P=24\ psi ,V=15\ ft^{3}

substitute

24*15=k

k=360

the equation is P*V=360

step 2

For P=30\ psi ,V=\ ft^{3}

substitute in the equation

(30)*V=360

V=360/30=12\ ft^{3}

5 0
3 years ago
How do you determine if a relation is quadratic by calculation differences, analyzing a graph, examining the degree in an equati
Kryger [21]

1) We can determine by the table of values whether a function is a quadratic one by considering this example:

x | y 1st difference 2nd difference

0 0 3 -0 = 3 7-3 = 4

1 3 10 -3 = 7 11 -7 = 4

2 10 21 -10 =11 15 -11 = 4

3 21 36-21 = 15 19-5 = 4

4 36 55-36= 19

5 55

2) Let's subtract the values of y this way:

3 -0 = 3

10 -3 = 7

21 -10 = 11

36 -21 = 15

55 -36 = 19

Now let's subtract the differences we've just found:

7 -3 = 4

11-7 = 4

15-11 = 4

19-15 = 4

So, if the "second difference" is constant (same result) then it means we have a quadratic function just by analyzing the table.

3) Hence, we can determine if this is a quadratic relation calculating the second difference of the y-values if the second difference yields the same value. The graph must be a parabola and the highest coefficient must be 2

4 0
9 months ago
3. Points Q, R, and S are the midpoints of the sides of triangle LMN. LM = 16, QR = 6, and QS = 10. Find the length of LN. The d
ss7ja [257]
Qr=1/2 mn = ms
mn=2 ms=12
ln^2=lm^2+mn^2 using phythagoras rule
ln^2=400
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5 0
3 years ago
A new theater is being built for the city ballet. The balcony has 200 seats. The floor has 10 rows with x seats in each row. The
Andreyy89

Answer:

B

Step-by-step explanation:

Because I got it right

6 0
2 years ago
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