Math

you can draw a square inside another square by placing each vertex of the inner square on one side of the outer square. The large square in this diagram has side length 10 units

a) Determine the area of the inscribed square as a function of x ( X is from one corner of the large square to the vertex of the inner square - the shorter section of the side which has been divided by two by the inner square)
b)range for area function

* I know the answer for a is A(x) = 2x² - 20x + 100 ---Answer
and I know how to do it.
But how do you find b. Some one said that the value of X can only be from 0-5. Why is that?

  1. 👍 0
  2. 👎 0
  3. 👁 1,071
  1. b) let's look at
    A(x) = 2x^2 - 20x + 100
    This is an upwards parabola.
    I will assume you know how to find its vertex.
    In standard form you would get
    A(x) = 2(x-5)^2 + 50
    with vertex at (5,50)
    This means your smallest inner square has an area of 50 square units when x = 5, clearly at the midpoint of the original square.

    Look back at your diagram,
    it is obvious that the domain of our A(x) is
    0 < x < 10
    at x = 0, A(0) = 100
    (the inner square coincides with the outer square)
    at x = 5 , A(5) = 50 , our vertex (minimum)
    at x = 10, A(10) = 100, back to same inner as outer

    since range would be all the A(x)'s possible
    the range is

    50 < A(x) < 100

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    1. Rosa, Roberto, Andrea, and Inno find an estimate for square root 10. Who has proposed the best solution? (1 point) Rosa: "Use square root 9 and square root 25 to estimate." Roberto: "I will use square root 4 and square root 9."

  2. 7th grade math Ms. Sue please

    2. Shelly sews a blanket that has an area of 170 square feet. It has 30 square blocks, each the same size. What is the approximate length of each side of a block? (1 point) 1 foot 2 feet 3 feet 4 feet 3. Which of these numbers can

  3. Math ~CHECK MY ANSWER~

    1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers? a. Square root 120 , n , Square root 3

  4. Math

    Julie is digging a square area in her backyard for a vegetable garden. If the area is 52 square feet, what is the approximate length of one side of her garden? 6 square feet 7 square feet 8 square feet 9 square feet 7 square feet

  1. MATH please help

    A circle with radius 16 centimeters is inscribed in a square and it showes a circle inside a square and a dot inside the circle that shows 16 ft inbetween Which is the area of the shaded region A 804.25 square feet B 1024 square

  2. Math

    Four students work to find an estimate for square root 27. Who is closest to finding the true estimate? (1 point) Chelsey: "Use square root 16 and square root 25 to estimate." Carley: "I use square root 25 and square root 36."

  3. math

    Four students work to find an estimate for square root 37. Who is closest to finding the true estimate? (1 point) Rhonda: "Use square root 16 and square root 25 to estimate." Ricardo: it should be between square root 25 and square

  4. math

    Four students work to find an estimate for square root 54. Who is closest to finding the true estimate? (1 point) Rhonda: "Use square root 16 and square root 25 to estimate." Ricardo: "I use square root 25 and square root 36."

  1. math

    find the area of the shaded region in the figure assuming the quadrilateral inside the circle is a square. x^2+y^2=36 (the picture is of a square inside a circle on a coordinate plane)

  2. Math Help!

    Four students worked to find an estimate for square root 22. Who is closest to finding the true estimate? A. Tiffany: "Use square root 16 and square root 25 to estimate." B. Todd: "I use square root 9 and square root 16." C.

  3. math

    Please help I'm so confused!!!! 1. Which two square roots are used to estimate the square root of 5? a. square root of 1 and 2 b. square root of 2 and 4 c. square root 4 and 9 d. square root of 9 and 16 2.Which two square roots

  4. Geometry

    A square has the following vertices. Find the area of the square. (−7, −5), (−4, −2), (−4, −8), (−1, −5) 6√ square units 18√ square units 6 square units ** 18 square units check my work thx

You can view more similar questions or ask a new question.