Calculus!! HELP!!

1) The sides of the triangle shown increase in such a way that (dz/dt=1) and (dx/dt=(3dy/dx))
At the instant when x = 12 and y = 5, what is the value of dx/dt?

2) Let f(x) = x^3 − 4.
Which of these is the equation for the normal line to this curve at the point (2,4).
A) y=1/2x-25/6
B) y=-1/12x+25/6
C) y= 12x-25/6
D) y=-12x-4
E) y= -12x-2

3) Which of the following could be the units for dy/dx if y is the surface area of a tumor and x is the radius of the tumor?

  1. 👍
  2. 👎
  3. 👁
  1. Prob. 1. Not sure...

    Prob. 2.
    The slope of the curve is df/dx = 3x^2.
    At (x,y) = (2,4), df/dx = 12.
    The normal line must have slope -1/12, which suggestscanswer b.

    Prob. 3.
    Area/Radius = meter^2/meter = meter
    (Or cm, whatever units your book specifies).

    1. 👍
    2. 👎
  2. 1) The sides of the triangle shown increase in such a way that (dz/dt=1) and (dx/dt=(3dy/dx))
    At the instant when x = 12 and y = 5, what is the value of dx/dt?
    =========================
    You do not say but I suspect this is a 5,12,13 right triangle. If I am guessing right about what you mean then

    and x=12, y = 5, z = 13
    x^2+y^2= z^2
    2xdx+2ydy = 2zdz
    dz= 1 dt
    dx/dt = 3 dy/dx

    24 dx +10 dy = 26 dz
    24 + 10dy/dx = 26 dz/dx
    24 + (10/3) dx/dt = 26 dt/dx
    =26/dx/dt
    (10/3)(dx/dt)^2+24 dx/dt -26 = 0

    I get dx/dt = .956 or -8.16

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    1. Find the length of the missing side of the right triangle (A triangle is shown to have a base of 15 cm and a height of 8 cm. The slope of it is unmarked A. 289 cm B. 17 cm *** C. 23 cm D. 4.79 cm 2. Find the length of the

  2. Math (please help!!)

    Which of the statements about the picture below is true? Choose 3. postimg(.)org/image/qb71bjkjh/f11870c4/ A. F is the circumcenter of the triangle

  3. GEOMETRY

    Which statement is contrapositive of the conditional: If a triangle is isosceles, then it has 2 congruent sides. 1. If a triangle does not have 2 congruent sides, then it is not isosceles. 2. If a triangle is isosceles, then it

  4. math

    1. What is the correct classification for the triangle shown below? A triangle has two angles measuring 68 degrees and 22 degrees. (1 point) acute, scalene acute, isosceles --- right, scalene obtuse, scalene 2. What is the value

  1. Algebra

    What is the value of b in the triangle shown below? The triangle they are showing is a right triangle...the length is 3b and the width is b...on the inside of the triangle it says 24in^2. A.–4 in B.4 in C.±4 in D.no solution

  2. Algebra

    Question 1 A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. A triangle ABC is shown. The base of

  3. Geometry

    The contrapositive of the following conditional statement: If a figure has four sides, then it is not a triangle. A.If a figure does not have four sides, then it is a triangle. B.If a figure is a triangle, then it does not have

  4. geometry

    If the sides of a triangle are in the ratio 3:4:5 and the perimeter of the triangle is 72 inches what are the lengths of the sides?

  1. C programming

    Pythagorean Triples. A right triangle can have sides that are all integers. The set of three integer values for the sides of a right triangle is called a Pythagorean triple. These three sides must satisfy the relationship that the

  2. Algebra 2

    Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Find the sum of a finite geometric series. The sides of an equilateral triangle measure 16 inches. The midpoints of the

  3. Geometry w. Data Analysis A

    Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. A triangle is shown with two sides that each measure 21. The angle between the two sides is 38 degrees. One of the other base

  4. geometry

    the sides of a triangle is 9,12,15cm..Find the sides of a similar triangle if the longest side is 20 cm

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