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nick has designed a diamond-shaped kite as shown below. the measures of some sides of the kite are marked in the figure. find the value of x. (justify)

show your work.

The value of x is approximately 3.5 inches.

Step-by-step explanation:

Given:

Side OC = 5 in

Side DC = 7 in

side OP = x

We need to find the value of x.

Solution:

Now In Δ COD;

m∠COD = 90°⇒(Given in the figure)

So by using Pythagoras theorem we get;

Substituting the values we get;

Now Squaring on both sides we get;

Now

Sin D =

So, Sin D =  ⇒ equation 1

Now In Δ DPO;

m∠DPO = 90°⇒(Given in the figure)

Also Now

Sin D =

So, Sin D =  ⇒ equation 2

Hence we can Left hand side of equation 1 and equation 2 are same;

So we can say that Right hand side will be equal too.

Hence equation can be framed as;

Hence, The value of x is approximately 3.5 inches.

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step-by-step explanation:

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.