Question

A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (1, 2). (a) Write the length L of the hypotenuse as a function of x. (b) Use a graphing utility to approximate x graphically such that the length of the hypotenuse is a minimum. (c) Find the vertices of the triangle such that its area is a minimum.

y
4
(0, у)
(1, 2)
2
1
(х, 0)
1
2 3
4
3.
Expand
Transcribed Image Text

y 4 (0, у) (1, 2) 2 1 (х, 0) 1 2 3 4 3.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Other

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: See attached

A: Click to see the answer

Q: See attached

A: Click to see the answer

Q: \sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{p}}

A: Click to see the answer

Q: Factor using the formula for the sum or difference of two cubes. x3 - 27

A: DIFFERENCE of CUBES:    a3 - b3 = (a - b)(a2 + ab + b2)

Q: In Example 6 in this section, we were given f(x) = 3x2 + 2x + 11 and found f '(x) = 6x + 2.

A: Differentiating with respect to x, we get

Q: Find the upper and lower sums for the region bounded by the graph of the function and the x-axis on ...

A: Click to see the answer

Q: Use a graph of $y-1 / x$ to show that if $s_{n}$ is the $n$ th partial sum of the harmonic series, t...

A: Click to see the answer

Q: Find the length of the parabolic cable in Exercise 65.

A: Click to see the answer

Q: Consider a wire 4 ft long cut into two pieces. One piece forms a circle with radius r and the other ...

A: Click to see the answer

Q: Find f by solving the initial-value problem. f'(x)=6/(x)1/2 , f(1)=19

A: Click to see the answer

Q: Construct the augmented matrix

A: We first write the given equations in standard form

Q: The measures of two angles in standard position are given. Determine whether the angles are cotermin...

A: Click to see the answer

Q: Find an angle between 0degree and 360degree that is coterminal with the given angle. 400°

A: Coterminal Angles : These are the angles which share the same initial side and terminal sides. To fi...

Q: Find the function f given that the slope of the tangent line at any point  (x, f(x)) is f '(x) and t...

A: Click to see the answer

Q: Evaluate: 1. x Arcsec x dx

A: Click to see the answer

Q: Evaluate the function g(x) = x2 + 2x + 3 at the given values of the independent variable a. g(-1) b....

A: Click to see the answer

Q: Convert r = 2 sin θ to an equation in rectangular coordinates. Please do not have any square roots i...

A: We will use the formulas

Q: If f '(3) = 0 and f"(3) < 0, then what must be true?

A: f '(3) = 0 and f"(3) < 0

Q: Calculus Question

A: Click to see the answer

Q: Calculus Question

A: Click to see the answer

Q: Without using any tech, put these radians in increasing order  sin(1), sin(2), sin(3), sin(4)  Show ...

A: Click to see the answer

Q: Please help with Worksheet 15.7 #1. Thanks!

A: Click to see the answer

Q: Find the length of the polar curve r=eª1ª, for 0s0s25. Must work the integral out by hand and show a...

A: Click to see the answer

Q: Consider the following. z = x3 +  x2 1 − x − 4x2 Let u(x) = x2 and v(x) = 1 − x − 4x2.

A: Click to see the answer

Q: The marginal cost function for the manufacture of wireless headphones is given by C'(x) = 45 − x/90...

A: Click to see the answer

Q: Use the Root Test to determine whether the series is convergent or divergent. n = 4 Identify a, 6(1+...

A: Given: compare given series with . Therefore,

Q: \sum_{n=1}^{\infty} \frac{4+3^{n}}{2^{n}}

A: Click to see the answer

Q: Suppose that a series $\sum a_{n}$ has positive terms and its partial sums $s_{n}$ satisfy the inequ...

A: Click to see the answer

Q: y′′ + 2y′ − 8y = 2e-2x − e−x , y(0) = 1, y′ (0) = 0.

A: Click to see the answer

Q: A cubic function is a polynomial of degree 3; that is, it hasthe form f(x)  =ax3 + bx2 +cx + d , whe...

A: For finding the critical numbers, at first we find the derivative of function and then set it equal ...

Q: An airplane is flying at an elevation of 5150 ft, directly above a straight highway. Two motorists a...

A: Click to see the answer

Q: \sum_{n=1}^{=} \frac{\sin 4 n}{4^{n}}

A: Click to see the answer

Q: Use Gauss-Jordan elimination to solve system of equations 6x+9y=9 7x+3y=33

A: Given: System of equations 6x+9y=9 7x+3y=33  

Q: True or false: y = x2 - 1 defines y as a function of x._______

A: Click to see the answer

Q: In Exercises 37–40, find the center, foci, vertices, and eccentricity of the hyperbola, and sketch i...

A: Click to see the answer

Q: Antiderivative of  (4+(x)1/2)/(4-(x)1/2)

A: Click to see the answer

Q: Please help with 15.7 #2. Thank you!

A: The equation of tetrahedron with intercepts (a,0,0), (0,b,0) and (0,0,c) is given by: Given tetrahe...

Q: The ordered pair (2, 5) satisfies 3y - 2x = -4. Determine whether the statement is true or false. If...

A: Click to see the answer

Q: the Pollowing D-E Solve +4Cy -1)x %3D

A: Click to see the answer

Q: 1 11 1 Compute SS S 16xyzw dx dw dz dy. 0 0 0 0

A: Click to see the answer

Q: Find the indefinite integral ∫ 1( 4 + 4x2 + x4)dx

A: Click to see the answer