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valkas [14]
3 years ago
6

An oblique rectangular prism with a square base has a volume of 539 cubic units. The edges of the prism measure 7 by 7 by 14 uni

ts. How many units longer is the slanted edge length of the prism, 14, compared to its perpendicular height?
Physics
2 answers:
Gala2k [10]3 years ago
8 0

Answer:

3 units

Solution:

V=539 cubic units

Square base, with edge a=7 units

Slanted edge length: s=14 units

V=Ab h

Ab=49 square units

539 cubic units = (49 square units) h

h= 11 units

s-h=14 units-11 units

s-h=3 units

Karo-lina-s [1.5K]3 years ago
5 0

Answer:

3 units

Explanation :

Volume of an oblique rectangular prism with a square base = A×B×h

Where h = perpendicular height

From the question, Volume of an oblique rectangular prism with a square base = 539 cubic units

We were asked from the question to find how many units longer the slanted edge length of the prism, 14 is compared to its perpendicular height.

The first step is : Find the perpendicular height

Edges A = 7 units

Edges B = 7 units

Perpendicular height ?

Hence,

539 = 7 × 7 × h

539 = 49h

h = 539 ÷ 49

h = 11 units

Therefore, perpendicular height of the prism = 11 units

To find how many units longer, we would subtract the perpendicular height of the prism from the slanted edge length of the prism

= 14 units - 11 units

= 3 units .

Therefore the slanted edge length of the prism , 14, is 3 units longer compared to its perpendicular height.

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3 years ago
A vertical spring withk= 245N/m oscillates with an amplitude of 19.2cm when 0.457kg hangs from it. The mass posses through the e
Makovka662 [10]

Answer:

 y = -19.2 sin (23.15t) cm

Explanation:

The spring mass system is an oscillatory movement that is described by the equation

      y = yo cos (wt + φ)

Let's look for the terms of this equation the amplitude I

     y₀ = 19.2 cm

Angular velocity is

     w = √ (k / m)

     w = √ (245 / 0.457

     w = 23.15 rad / s

The φ phase is determined for the initial condition   t = 0 s ,  the velocity is negative v (0) = -vo

The speed of the equation is obtained by the derivative with respect to time

     v = dy / dt

     v = - y₀ w sin (wt + φ)

For t = 0

     -vo = -yo w sin φ

The angular and linear velocity are related v = w r

      v₀ = w r₀

      v₀ = v₀ sinφ

      sinφ = 1

      φ = sin⁻¹ 1

      φ = π / 4    rad

Let's build the equation

      y = 19.2 cos (23.15 t + π/ 4)

Let's use the trigonometric ratio π/ 4 = 90º

      Cos (a +90) = cos a cos90 - sin a sin sin 90 = 0 - sin a

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8 0
3 years ago
A certain quantity of a liquid has a volume of 10cm at 20°C. Calculate its volume at 50°C, if it’s cubic expansivity is 10^(-3)
Pavel [41]

Answer:

10.3 cm³

Explanation:

From the question given above, the following data were obtained:

Original volume (V₁) = 10 cm³

Initial temperature (θ₁) = 20 °C

Final temperature (θ₂) = 50 °C

Cubic expansivity (γ) = 10¯³ K¯¹

Final volume (V₂) =?

γ = V₂ – V₁ / V₁(θ₂ – θ₁)

10¯³ = V₂ – 10 / 10( 50 – 20)

10¯³ = V₂ – 10 / 10(30)

10¯³ = V₂ – 10 / 300

Cross multiply

10¯³ × 300 = V₂ – 10

0.3 = V₂ – 10

Collect like terms

0.3 + 10 = V₂

10.3 = V₂

V₂ = 10.3 cm³

Thus, the volume at 50 °C is 10.3 cm³

6 0
2 years ago
What is the full form of work?​
Pepsi [2]

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7 0
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