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3 years ago

!!Plz urgent help!!

Mathematics

1 answer:

Firdavs [7]3 years ago

3 0

Answer:

890 beads can be fitted in the triangular prism.

Step-by-step explanation:

If we can fill the spherical beads completely in the triangular prism,

Volume of the triangular prism = Volume of the spherical beads

Volume of triangular prism = Area of the triangular base × Height

From the picture attached,

Area of the triangular base = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(AB)(BC)$

By applying Pythagoras theorem in the given triangle,

AC² = AB² + BC²

(13)² = 5² + BC²

169 = 25 + BC²

BC² = 144

BC = 12

Area of the triangular base = $\frac{1}{2}(5)(12)$

= 30 cm²

Height of the triangular prism = 18 cm

Volume of the triangular prism = 30 × 18

= 540 cm³

Volume of one spherical bead = $\frac{4}{3}\pi r^{3}$

= $\frac{4}{3}\pi (0.525)^{3}$

= 0.606 cm³

Let there are 'n' beads in the triangular prism,

Volume of 'n' beads = Volume of the prism

540 = 0.606n

n = 890.90

n ≈ 890

Therefore, 890 beads can be fitted in the triangular prism.

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Line A passes through the points (-5, 1) and (5, 11).

11111nata11111 [884]

Line A: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{11 - 1}{5 - (-5)} = \frac{10}{5 + 5} = \frac{10}{10} = 1$
y - y₁ = m(x - x₁)
y - 1 = 1(x - (-5))
y - 1 = 1(x + 5)
y - 1 = 1(x) + 1(5)
y - 1 = x + 5
   + 1    + 1
   y = x + 6

Line B: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{20 - (-1)}{-3 - 4} = \frac{20 + 1}{-7} = \frac{21}{-7} = -3$
   y - y₁ = m(x - x₁)
y - (-1) = -3(x - 4)
   y + 1 = -3(x) + 3(4)
   y + 1 = -3x + 12
   - 1 - 1
   y = -3x + 11

y = x + 6
y = -3x + 11

   x + 6 = -3x + 11
+ 3x     + 3x
   4x + 6 = 11
       - 6   - 6
   4x = 5
      4   4
       x = 1¹/₄
   y = x + 6
   y = 1¹/₄ + 6
   y = 7¹/₄
     (x, y) = (1¹/₄, 7¹/₄)

The answer is B.

4 0

4 years ago

Kakakkaiaia919q8q89amamz..z.zjsiaiaiwu:<br><br>É URGENTE

Alexus [3.1K]

Oh that’s really cool

8 0

3 years ago

Sam and Harry are family. Sam is currently is three times Harry's age. Sam's age is also 10 more than twice Henry's age. What ar

kramer

Answer:

<em>Sam is 30 years old, and Harry is 10 years old.</em>

Step-by-step explanation: