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kirill [66]
3 years ago
11

The illuminance of a surface varies inversely with the square of its distance from the light source.If the illuminance of a surf

ace is 120 lumens per square meter when its distance from a certain light source is 6 meters, by how many meters should the distance of the surface from the source be increased to reduce its illuminance to 30 lumens per square meter?
Mathematics
1 answer:
VashaNatasha [74]3 years ago
6 0

Answer:

Distance between the surface and source of light will be increased by 6 meters.

Step-by-step explanation:

The illuminance of a surface varies inversely with the square of ts distance from the light source.

Let illuminance of the surface = x lumens per square meter

and distance from a light source = y meter.

Now x ∝ \frac{1}{y^{2} }

Or x=\frac{k}{y^{2} } [k = proportionality constant]

Now we will find the value of k.

k = xy²

k = 120×(6)²

k = 4320

We have to calculate the distance of the source if illuminance of the surface is 30 lumens per square meter.

30=\frac{4320}{y^{2}}

y² = \frac{4320}{30}

y² = 144

y = √144 = 12 meters

So the source of the light will be shifted away from the surface = 12 - 6 = 6 meters.

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17/20 equals t plus -13/20 solve for t
docker41 [41]

The value of t is 3/2 or 1.5

<u>Step-by-step explanation</u>:

The given expression is 17/20 equals t plus -13/20.

<u>Changing it into an equation form :</u>

⇒ t + (-13/20) = 17/20

Keeping t alone on one side and constant terms to the another side,

t = (17/20) + (13/20)

Since the denominators are same, it is easy to simplify those fractions.

⇒ t = (17+13)/20

⇒ t = 30/20

⇒ t = 3/2

⇒ t = 1.5

The solution is t= 3/2 or t= 1.5

8 0
3 years ago
How do I find and round the principal square root of 8​
irga5000 [103]

Answer: The square root of 8 is expressed as √8 in the radical form and as (8)½ or (8)0.5 in the exponent form. The square root of 8 rounded up to 8 decimal places is 2.82842712. It is the positive solution of the equation x2 = 8.

Step-by-step explanation:

6 0
3 years ago
50 POINTS!
Hoochie [10]

Answer:

Solution given:

AB=3units

<B=45°

<C=63°

DF=3units

<E=63°

<F=45°

for congruence opposite corresponding angle or side should be equal

so

∆ABCis congruent to ∆DFE by A.A.S axiom

Similarly

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∆BAC=~ ∆FDE

you got it.third one.

7 0
3 years ago
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jan, mya, and Sara ran a total of 64 miles last week. jan and mya ran the same number of miles. Sara ran 8 less miles than mya.
Debora [2.8K]
So,

We'll just use A to represent both Jan and Mya's miles, since they ran the same number.

We have the equations:
1. Jan (J) = Mya (M)
2. Sara (S) = M - 8
3. 2A + S = 64
J = M
S = M - 8

We'll just use A to represent both J and M.

S = M - 8

We'll use Elimination by Substitution.
2A + A - 8 = 64

Collect Like Terms
3A - 8 = 64

Add 8 to both sides
3A = 72

Divide both sides by 3
A = 24

Since
A = J
and
A = M
and
J = M
then
J = 24
M = 24

Substitute
S = 24 - 8
S = 16

Check
24 + 24 + 16 = 64
64 = 64 This checks.

So,
J = 24
M = 24
S = 16
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