1. The sum of the squares of two numbers is 74 and the difference of their squares is 24.
a) What system of equations models this situation?
b) What are the two numbers?

2. For what value of b will the line y= -2x+b be tangent to the parabola y=3x^2+4x-1?

1. 👍
2. 👎
3. 👁
1. (x+y)(x-y) = 24
x^2+y^2 = 74

you want some place where the tangent to the parabola has slope = -2

6x+4 = -2
x = -1
so, y=-2
The tangent line at (-1,-2) is
y+2 = -2(x+1)
y = -2x-4
b = -4

see

http://www.wolframalpha.com/input/?i=plot+y%3D3x^2%2B4x-1%2C+y+%3D+-2x-4

1. 👍
2. 👎

## Similar Questions

1.Tasha believes that she can rewrite the difference 120-36 as a product of the GCF of the two numbers and another difference.Is she correct?Explain your answer. 2.Explain how to find the GCF of three numbers 3.Xiao's teacher

2. ### math

The sum of two numbers is 10.The sum of their squares is 52.Find the numbers.

3. ### MATH

A four by four grid of unit squares contains squares of various sizes (1 by 1 through 4 by 4), each of which are formed entirely from squares in the grid. In each of the 16 unit squares, write the number of squares that contain

4. ### Math

Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the

1. ### Calculus

Find two numbers whose sum is 10 for which the sum of their squares is a minimum.

2. ### Algebra

The difference of the cubes of two consecutive odd positive integers is 400 more than the sum of their squares. Find the sum of the two integers.

3. ### Math

1. If the product of 5 and the sum of 10 and a certain number is equal to 15, what is the number? 2. The sum of two consecutive counting numbers divided by their positive difference is 9. Find the larger numbers.

4. ### Math

Minimizing Sum: Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.

1. ### calculus

Find two numbers whose product is 16 and whose sum of squares is minimum

2. ### maths

the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers

3. ### Math

The sum of the squares of three consecutive whole numbers is 77. Form a quadratic equation and hence solve it to determine the numbers. (Hint: let the three consecutive numbers be x, x+1 and x+2)

4. ### Math

the sum of two numbers is 30. the difference of their squares is 180. find the two numbers by elimination method