A closed box is in the shape of a rectangular solid with dimensions x, y, and zin inches. Suppose that each dimension is changing at the rate of -0.1 in/min. Find the rate of change of the total surface area of the box when x = 4 in, y = 2 in, and z = 5 in. Round to the nearest tenth if necessary. Provide your answer below: dA dt in/min

Q: Carry out three steps of the Bisection Method for f(x) = 4 - 5 as follows: (a) Show that f(x) has a…

A: Please see the below picture for detailed solution.

Q: The median home price in the United States over the period January 2010-January 2015 can be…

A: Given:- The median home price in the united states pt=4.5t2-15t+180

Q: If h (2) = 5 and h'(2) = -4, find d /h(x) dx h(x)) x = 2

A: we use quotient rule here

Q: Find an equation of the tangent plane to the surface at the given point. y (1, 9, 9) f(x, y) = −9x +…

A:

Q: Question Determine the absolute error when using the trapezoidal rule to find (2x³+4x) dx using 4…

A:

Q: Find f'(x). f(x) = 9x-8 4x+9

A:

Q: Question Determine the absolute error when using the trapezoidal rule to find ²(2x³ + 4x) dx using 4…

A:

Q: Question Determine the absolute error when using the trapezoidal rule to find ²(2x³+4x) dx using 4…

A: Given   ∫022x3+4xdx

Q: Find the general solution in the form y = yc + yp. y'' + 4y' + 5y = e-2tcos(t)

A:

Q: Find the exact value of the given expression. tan(cos-¹(²)) 2 3 4

A:

Q: Use any method to evaluate the integral. S 243 dw w²√√81-w² 243 dw w²√√81-w² W (Type an exact…

A: Given data:- ∫243w281-w2 dw

Q: 4. Use linearization to give an estimate for 264.

A:

Q: Differentiate (logarithmically) dy/dx, if y = ln(cos x)/2x^cot(3x)

A: given  y = ln(cosx)/2x^cot(3x)  dydx= ddx(ln(cosx)/2x^cot(3x)dydx ={ 2xcot(3x)ddx(ln(cosx) -…

Q: Consider the surface F(x,y,z)=x^9z^8+sin(y^4z^8)-4=0 Find the following partial derivatives dz/dx…

A:

Q: what is an improper integral?

A:

Q: The equation for the tangent line to the curve x² + y = 4 when x = 6 is y = i X + i

A: To find the equation of tangent line for the given curve.

Q: Find sin(), cos(4), and tan 2 cos(x) 180° < x < 270° sin (4) - COS cos (4) = tan (*) = = 24 25' from…

A: given cosx=-2425by half angle formula sinx2=±1-cos(x)2given that 180&lt;x&lt;270so 90&lt;x2&lt;135…

Q: 2. A fertilizer producer finds that it can sell its product at a price of p = 300 - 0.1x dollars per…

A:

Q: #8) Find the derivative of the function. y = sech(6x²)

A:

Q: Consider the function f(x)=4x2 −48x+3 on the interval [2,10]. Evaluate this function at the…

A: Topic = Functions

Q: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where…

A:

Q: Find the minimum and the maximum of the function f(x, y) = x² + xy + y on the set: D = {(x, y): 0 ≤…

A:

Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: To find indefinite integral.

Q: Suppose that y varies inversely with x, and y=6 when x=3. Write an inverse variation equation that…

A:

Q: 1. The additive inverse of -10 = 2. Let DC R. xois an point of D, if each E-neighborhood K. (xo) of…

A:

Q: If sin x 3 5' (without finding x) sin(2x) cos(2x) tan (2x) = = = x in quadrant I, then find

A:

Q: 3. Find a particular solution Y(t) of y" — 2y" — y' + 2y = e²t

A:

Q: Evaluate the integral. +∞ S 3 x 2xe dx

A:

Q: Use integration by parts to evaluate the integral. [5. 5x ln(2x) dx

A:

Q: Rewrite sin (+7) in terms of sin x and cos x. Simplify your answer. Enclose arguments of functions…

A: We use ⇒sinA+B=sinAcosB+cosAsinB

Q: Use the graphs for f(x) and g(x) to evaluate the expressions below. Write your answer as a whole…

A:

Q: Express the integrand as a sum of partial fractions and evaluate the integral. √6x² + 2x +7 dx 3 X…

A:

Q: Find the local maxima and minima for the function ƒ(x) = |x² + 4x − 5|. If there is more than one…

A: We have given function  fx=x2+4x-5 fx=x2+5x-x-5 fx=xx+5-1x+5 fx=x+5x-1 Range of the function is…

Q: Write the equation in its equivalent logarithmic form. 8³=512 What is the equivalent logarithmic…

A: See this solution in below.

Q: Differentiate the following function. 3 y=xaex dy CX

A: We know, d/dx(xn)=nx(n-1), for any real number n  And d/dx(ex)=ex

Q: Question 1 i) ii) iii) iv) Find the derivative of the following function using the first principle:…

A: i) f(t)=3t2+2t+1 Using the first principle: f'(t)=limh→0f(t+h_)-f(t)h…

Q: 7. Start from the given graph of y = log5 (x), then sketch the graph of the following function. f(x)…

A:

Q: Subject: Differential Equations Yoon Se-Ri is baking a cake for Captain Ri Jeong-Hyeok in a kitchen…

A: Concept: We have given the room temperature 76.81°F Cake temperature is given 420°F  also after…

Q: What is an upper bound for the error in 25 approximating (5x² + 3) dx using the trapezoidal rule…

A: We need to find the upper bound of the error

Q: 2. Match each logarithmic function with its graph. I II ++ (a) f(x) = log₂ (x) (b) f(x) = -log₂ (-x)…

A: We have given equation and graph to match From given graphs graph I :   (a)  fx=-log2x graph II :…

Q: Write an equation describing the relationship of the given variables. y varies inversely as the…

A: y varies inversely as the cube root of x and when x=125, y=3.

Q: 3. Find the linearization of f(t) = = this to estimate f(3.05). 3t t² +3 at t = 3 and use

A:

Q: rdan elimination. 2x + y = 12 2x-y+z=-5 (3x - 2y + 4z = -14

A: Given system is of the form Ax=b.

Q: Let f(x) be a function. The average rate of change between = a and * = b is equivalent to: O The…

A:

Q: tan( e + 4 ln(z))

A:

Q: Consider the function: f(x)=7x+1 Step 2 of 2 : Find the value of f(a+5)

A: Consider the function: f(x)=7x+1Step 2 of 2 :   Find the value of f(a+5).

Q: How to determine if it is continuous, without using a graph?

A: Given function:- fg=2g2-gif g≤0tangif g&gt;0

Q: 40. lim 3 cot(2x) sin-¹ x x→ 0+

A:

Q: Domain and Range The function f(x) is defined as a set or ordered pairs. Using that set of data,…

A: Values of x is the domain and values of f(x) is the range.

Q: Solve the given differential equation (where the function is subject to the given conditions) by…

A: Let's solve given diffential equation by using Laplace transform.