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Schach [20]
3 years ago
15

A man 6 feet tall walks at a rate of 6 feet per second away from a light that is 15 feet above the ground.

Physics
1 answer:
Tems11 [23]3 years ago
7 0

Answer:(a)10 ft/s

(b)4 ft/s

Explanation:

Given

height of light =15 feet

height of man=6 feet

\frac{\mathrm{d} x}{\mathrm{d} t}=6 ft/s

From diagram

\frac{15}{y}=\frac{6}{y-x}

5(y-x)=2y

3y=5x

differentiate both sides

3\times \frac{\mathrm{d} y}{\mathrm{d} t}=5\times \frac{\mathrm{d} x}{\mathrm{d} t}

Tip of shadow is moving at the rate of

\frac{\mathrm{d} y}{\mathrm{d} t}=\frac{5}{3}\times 6=10 ft/s

(b)rate at which length of his shadow  is changing

Length of shadow is y-x

differentiating w.r.t time

\frac{\mathrm{d} (y-x)}{\mathrm{d} t}=\frac{\mathrm{d} y}{\mathrm{d} t}-\frac{\mathrm{d} x}{\mathrm{d} t}

\frac{\mathrm{d} (y-x)}{\mathrm{d} t}=10-6=4 ft/s

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A hollow sphere of inner radius 8.82 cm and outer radius 9.91 cm floats half-submerged in a liquid of density 948.00 kg/m^3. (a)
kari74 [83]

Answer:

a) 0.568 kg

b) 474 kg/m³

Explanation:

Given:

Inner radius = 8.82 cm = 0.0882 m

Outer radius = 9.91 cm = 0.0991 m

Density of the liquid = 948.00 Kg/m³

a) The volume of the sphere = \frac{4\pi}{3}\times(0.0991^2-0.0882^2)

or

volume of sphere = 0.0012 m³

also, volume of half sphere = \frac{\textup{Total volume}}{\textup{2}}

or

volume of half sphere = \frac{\textup{0.0012}}{\textup{2}}

or

Volume of half sphere =0.0006 m³

Now, from the Archimedes principle

Mass of the sphere = Weight of the volume of object submerged

or

Mass of the sphere = 0.0006× 948.00 = 0.568 kg

b) Now, density =  \frac{\textup{Mass}}{\textup{Volume}}

or

Density = \frac{\textup{0.568}}{\textup{0.0012}}

or

Density = 474 kg/m³

8 0
2 years ago
In 1965, a group of students wore black arm bands to school in protest of American policies in Vietnam. Administrators banned th
Ede4ka [16]

Answer:

protected under students first amendment rights

Explanation:

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4 0
2 years ago
1. What are three appliances in your house that use a motor that turns electrical energy into mechanical energy?
AleksAgata [21]
A vacuum is an electrical motor and<span> which it  converts electrical energy into mechanical energy.

</span>
6 0
3 years ago
You want to move a heavy box with mass 30.0 across a carpeted floor. You pull hard on one of the edges of the box at an angle 30
ivolga24 [154]

Answer:

Explanation:

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3 years ago
Enzyme reaction and deactivation Lipase is being investigated as an additive to laundry detergent for removal of stains from fab
natita [175]

Answer:

t= 27.38 mins [this the time taken by the enzyme to hydrolyse 80% of the fat present]

Explanation:given values

Half life of lipase t_1/2 = 8 min x 60s/min = 480 s

Rate constant for first order reaction

k_d = 0.6932/480 = 1.44 x 10^-3 s-1

Initial fat concentration S_0 = 45 mol/m3 = 45 mmol/L

rate of hydrolysis Vm0 = 0.07 mmol/L/s

Conversion X = 0.80

Final concentration S = S_0(1-X) = 45 (1-0.80) = 9 mol/m3

K_m = 5mmol/L

time take is given by

t= -\frac{1}{K_d}ln[1-\frac{K_d}{V_m_0}(k_mln\frac{s_0}{s}+(s_0-s))]

all values are given and putting these value we get

t=1642.83 secs

which is equal to

t= 27.38 mins [this the time taken by the enzyme to hydrolyse 80% of the fat present]

5 0
2 years ago
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