Directions Solve the following problems
31-35. The length that a spring will stretch varies directly as the force applied to the spring!
a force of 1016 will stretch oring by 2 inches, what force will stretch the same spring
by 3 inches?
36-40. The time to complete a project varies inversely with the numbers of employees. If 3
people can complete the project in 7 days, how long will it take 5 people?
Designing Vector
41-45. Suppose a varies inversely as the square ol w and that a = 18 when w= 8. Find the
value of a when w = 3
46 50. Letp be directly proportional to q and inversely proportional to the square ofr.
Ifp 3 when = 8 and r = 4, find p when a = 9 and re 6.
51-55 a varies jointly as x and y. II 2 = 36 whenx = 2 and y = 3, find a whenx=1 and y = 1/2
56-60). The illumination / from a light source varies inversely as the square of the distanced
from the light source. If the illumination! = 20 foot candles when d = 4 feet, find the
Illumination at distance of 8 feet.
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Answer:
31-35.
GIVEN:
SOLUTION:
In direct variation,the general form is:
Let us substitute our given and find the constant of variation.
Now,we have our new x value,which is 3 inches.Let us input it into our equation,and find the force required.
36-40.
GIVEN:
SOLUTION:
The general form for an inverse variation is:
Let us substitute our initial values and solve for constant of variation.
Then,input the new values and solve for y.
41-45.
GIVEN:
SOLUTION:
Inverse Variation has a general form.
However,since we have a different variables and have a squared expression,our new form is:
Now,substitute the given and find k.
Solve for a when w=3.
46-50.
GIVEN:
SOLUTION:
The form of a combined variation is:
Since we have different variables and exponents,let us revise the equations.
Let us calculate the constant of variation.
Let us now calculate the value of p with new values.
51-55.
GIVEN:
EQUATION:
The general form of joint variation is:
Let us find now the constant of variation.
Now,let us find the new value of a.
56-60.
GIVEN:
EQUATION:
The general form of inverse variation is:
Let us find k.
Now,let us find l when d=8 ft.
Answer:
59.0769230764 or 59.08 in approx
Step-by-step explanation:
40cm divided by 65kg then multiply by 96 is equal to 59.0769230764
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