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raketka [301]
3 years ago
10

13. In the triangle below, the sides have length x + 3, 3x - 1. and 4x. Determine the range of possible

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
7 0

Answer:

Hence as long as x > 2/3, we can form a triangle from the three given sides.

Step-by-step explanation:

Given:

Length of 3 sides of triangle are x+3, 4x,3x-1

Solution:

From the length of the 2nd side 4x, we know that x > 0

Let this be 1 st statement.

Now from the triangle inequality we can say that;

x + 3 + 4x > 3x -1\\5x+3>3x-1\\5x-3x>-1-3\\2x>-2\\x>-1

No new information from this because of the 1st statement above.

Also,  

4x + 3x - 1 > x +3\\7x-1>x+3\\7x-x>3+1\\6x>4\\x>\frac{4}{6}\\\\x>\frac{2}{3}

Lastly,

x+3 +3x - 1 > 4x\\4x-2>4x\\4x-4x>2\\0>2

and again no new information is obtained from this inequality.

Hence as long as x > 2/3, we can form a triangle from the three given sides.

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Work out the volume of the solid shape<br><br> Give your answers in terms of pi please
kirill [66]

*The complete question is in the picture attached below.

Answer:

756πcm³

Step-by-step Explanation:

The volume of the solid shape = volume of cone + volume of the hemisphere.

==> 270πcm³ + ½(4/3*π*r³)

To calculate the volume of the hemisphere, we need to get the radius of the hemisphere = the radius of the cone.

Since volume of cone = 270πcm³, we can find r using the formula for the volume of cone.

==> Volume of cone = ⅓πr²h

⅓*π*r²*10 = 270π

⅓*10*r²(π) = 270 (π)

10/3 * r² = 270

r² = 270 * ³/10

r² = 81

r = √81

r = 9 cm

Thus, volume of hemisphere = ½(4/3*π*r³)

==> Volume of hemisphere = ½(⁴/3 * π * 9³)

= ½(972π)

Volume of hemisphere = 486πcm³

Volume of the solid shape

= volume of cone + volume of the hemisphere.

==> 270πcm³ + 486πcm³

= 756πcm³

3 0
3 years ago
What is the factorization of 84
Vladimir79 [104]

Answer:

2×2×3×7

Step-by-step explanation:

84 is even, so divisible by 2. 84 = 2×42

42 is even, so divisible by 2. 82 = 2×2×21

21 has a sum of digits of 3, so is divisible by 3. 84 = 2×2×3×7

4 0
3 years ago
If I have a triangular prism with the length of 9mm, the base of 6.6 mm, and the height 4 mm or 5.2 mm. What would be the surfac
Lelu [443]

The surface area of triangular prism is 117.12 mm²

<u>Explanation:</u>

Base side, a = 9 mm

Base side, b = 6.6 mm

Base side, c = 5.2 mm

Height, h = 4 mm

Total surface area = ?

We know,

Surface area, A = 2 Ab ( a+b+c) h

Ab = √s(s-a) (s-b) (s-c)

s = a+b+c/2

Solving for A

A = ah + b h + ch + 1/2 √ -a⁴ + 2(ab)² + 2(ac)² - b⁴ + 2 (b c)² - c⁴

A = 9.4 + 6.6 X 4 + 5.2 X 4 + 1//2 √ -9⁴ + 2(9 X 6.6)² + 2(9 X 5.2)² - (6.6)⁴ + 2 (6.6 X 5.2)² - (5.2)⁴

A = 117.12 mm²

Therefore, the surface area of triangular prism is 117.12 mm²

4 0
3 years ago
Im confused right now. What equasion is represented by the area model? Format as 2x2
algol [13]

40x30=120x5=600x6=3600

Awnser:3600

8 0
3 years ago
What is the solution to the inequality?<br><br><br><br> -3x+2&lt;29−3x+2&lt;29
Dvinal [7]

Answer:  x>-9

Step-by-step explanation:

5 0
2 years ago
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