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 ∝ 
Or 
[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.
y² = 
y² = 144
y = √144 = 12 meters
So the source of the light will be shifted away from the surface = 12 - 6 = 6 meters.
Answer:
-5
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
Answer:
32 and 58
Step-by-step explanation:
Let's set up equations.
The sum of two numbers (x and y) is 90: x + y = 90
The larger number (y) is 6 less than twice the smaller number (x): y = 2x - 6
We have our system of equations:
x + y = 90
y = 2x - 6
Let's use substitution.
Substitute y = 2x - 6 into the first equation.
x + y = 90
x + (2x - 6) = 90
Combine like terms.
x + 2x - 6 = 90
3x - 6 = 90
Add 6 to both sides to isolate x.
3x = 96
Divide both sides by 3 to further isolate x.
x = 32
Now that we know x, let's find y.
Plug in x = 32 into one of our original equations.
y = 2x - 6
y = 2(32) - 6
Multiply.
y = 64 - 6
y = 58
Now we have x = 32, y = 58.
Check your answer by plugging these values into one of our original equations.
x + y = 90
32 + 58 = 90
Add.
90 = 90
Your solution is correct.
Hope this helps!
Answer:
5 + (-3/2√2) = irrational number
5 - (-3/2√2) = irrational number since we have √2
Step by step explanation
Here the given two numbers are 5 and -3/√8.
Here we can rewrite √8 = √2√4
Which is 2√2.
So √8 = 2√2, where √2 is an irrational number.
-3/√8 = -3 / 2√2 = =3/ 2√2 is an irrational number.
When you add, subtract, multiply and divide a whole number (5) with an irrational number (-3/2√2) is always an irrational number.
Therefore, when you do the operations with 5 and -2/2√2 always result in irrational number.
Hope you will understand the concept.
Thank you.
