Tutor profile: Manisha P.
Subject: SAT II Mathematics Level 1
If 8x + 4 = k ( (2x + 1) / 2), then what is the value of k?
Step 1 : Copy the above equation. 8x + 4 = k ( (2x + 1) / 2) Step 2 : Bring the denominator of the right hand side to the left hand side to reduce the complexity of the equation. 2( 8x + 4 ) = k ( 2x + 1 ) which is 16x + 8 = k ( 2x + 1 ) Step 3 : Collect the x terms together to solve for k. k = 16x / 2x = 16 / 2 = 8 Step 4 : Check if k=8 is correct but substituting back in the equation. 8 ( 2x +1 ) = 16x +8 Since it matches, our final answer for k is 8.
Integrate dy = 10xˆ(- 3) dx.
To integrate the above question, we have to follow the following steps. Step 1 : Copy the above equation and insert an integral symbol in front of both the sides of the equation. ∫dy = ∫ (10xˆ(- 3)) dx Step 2 : Integrate on the left hand side first. y = ∫ (10xˆ(- 3)) dx Step 3 : Integrate on the right hand side now. y = 10xˆ(- 3+1) / (- 3+1) Step 4 : Simplify the previous step. y = 10xˆ(- 2) / (- 2) Step 5 : This is your final answer. y = - 5xˆ(- 2) or y = - 5 / (xˆ2)
Is a market supply curve more or less elastic in the long run? Support your answer with reasoning.
A market supply curve is more elastic in the long run than in the short run. As time passes, the elasticity of a good increases. So, a supply curve in the long run will be more elastic than a supply curve in the short run because producers will have more time to change inputs (variable factors) , which increases the elasticity of supply.
needs and Manisha will reply soon.