If y varies directly as x^2 and y=20 when x=4, find y when x=7?
Y = kx^2 = 20. x = 4.
k*4^2 = 20.
16k = 20. k = 20/16 = 5/4.
Y = kx^2.
Y = (5/4)*7^2 = 61 1/4 = 61.25.
An investment of $63,000 was made by a business club. The investment was split into three parts and lasted one year. The first part of the investment earned 8% interest, the second 6% and the third 9%. Total interest from the investments was $4950. The interest from the investment was 4 times the interest from the second. Find totals of the three parts of the investment. What is the amount of the first part of the investment?
A hardware supplier manufactures three kinds of clamps, type A, B, and C. Production restrictions force it to make 20 more type C clamps than the total of the other types and twice as many as B clamps as type A clamps. The shop must produce 380 clamps per day. How many of each type are made per day? How many type A clamps are produced?
To solve this problem, we need to use the concept of direct variation. The relationship between two variables, y and x, is said to vary directly if their ratio remains constant. In this case, the relationship between y and x^2 is a direct variation.
Step 1: Write the direct variation equation
In direct variation, we can write the equation as:
y = k * x^2
Step 2: Find the constant of variation (k)
To find the constant of variation, we substitute the given values of y and x into the equation and solve for k.
y = k * x^2
20 = k * 4^2
20 = 16k
k = 20/16
k = 1.25
Step 3: Substitute the value of k into the equation
Now that we have the value of k, we can substitute it back into the direct variation equation.
y = 1.25 * x^2
Step 4: Using the equation to find y when x=7
Finally, substitute x = 7 into the equation and solve for y.
y = 1.25 * 7^2
y = 1.25 * 49
y = 61.25
Therefore, when x = 7, y will be equal to 61.25.
By following these steps, you can solve direct variation problems by finding the constant of variation and substituting the given values to find the unknown variable.