given that the energy E,varies directly as the resistance R,as the square of the distance D, obtain an equation connecting E,R and D.E=32/25 when R=8 and D=5 calculate the value of R when E=16 and D=5

E = kRD^2

So,
(32/25)=(8*5^2)k
E = 4/625 RD^2
Now use your values to find the desired R.

E =kRD^2. So(32/25)=(8*√5)K crossmultiply =32 /25=8k/25. 800=200k. Divide both sides by 200. 800/200=200/200k. K=4. Calculate value of R when E=16,d=3,k=4. 16×4×R/√3.cross multiply. 4r=16×9. 4r=144. Divide both sides by 4. 4r/4=144/4. R=35

Oh, you want me to dust off my math skills? Alright, here we go!

According to the given information, we have the following relationship: E ∝ R × D^2

To find an equation connecting E, R, and D, we'll introduce a constant k. So it becomes: E = k × R × D^2

Now let's use the given values E = 32/25, R = 8, and D = 5 to solve for k:

32/25 = k × 8 × 5^2

Simplifying, we get:

k = (32/25) / (8 × 25) = 1/50

So now we have our equation: E = (1/50) × R × D^2

To find the value of R when E = 16 and D = 5, we'll substitute those values into our equation:

16 = (1/50) × R × 5^2

Solving for R:

16 = 1/50 × R × 25

16 = R/2

Multiplying both sides by 2:

32 = R

Thus, the value of R when E = 16 and D = 5 is 32.

We are given that the energy E varies directly as the resistance R and as the square of the distance D. Let's denote the constant of variation as k.

Step 1: Setting up the equation
We can set up an equation relating E, R, and D using the given information:

E = k * R * D^2

Step 2: Finding the value of k
To find the value of k, we can substitute the values E = 32/25, R = 8, and D = 5 into the equation:

32/25 = k * 8 * 5^2
32/25 = k * 8 * 25
32/25 = 200k

Let's simplify the equation by multiplying both sides by 25/32:

1 = 5k

Therefore, k = 1/5.

Step 3: Calculating the value of R when E = 16 and D = 5
Now that we have the value of k, we can use it to find the value of R when E = 16 and D = 5:

16 = (1/5) * R * 5^2
16 = (1/5) * R * 25
16 = 5R
R = 16/5
R = 3.2

Therefore, when E = 16 and D = 5, the value of R is 3.2.

To obtain an equation that connects the energy (E), resistance (R), and the square of the distance (D), we use the concept of direct variation.

The given relationship states that the energy (E) varies directly as the resistance (R) and as the square of the distance (D). Mathematically, it can be represented as:

E = k * R * D^2

where k is the constant of variation.

To find the value of k, we can use the given values E = 32/25, R = 8, and D = 5:

32/25 = k * 8 * 5^2
32/25 = k * 8 * 25
32/25 = 200k

To solve for k, we divide both sides of the equation by 200:

k = (32/25) / 200
k = 32 / (25 * 200)
k = 32 / 5000
k = 0.0064

Now that we have the value of k, we can use the equation to calculate the value of R when E = 16 and D = 5:

16 = 0.0064 * R * 5^2
16 = 0.0064 * R * 25
16 = 0.16R

To solve for R, we divide both sides of the equation by 0.16:

R = 16 / 0.16
R = 100

Therefore, when E = 16 and D = 5, the value of R is 100.