An rectangular metal box without a top is to be made with panels that are 0.5 inch thick. The inside length is 8 inches, the inside width is 5 inches and the inside height is 3 inches. Approximate the amount of metal to be used using differentials. Clearly identify all your variables.

Q: A cylindrical water tank has a height of 6 m and a radius of 4 m. How much work is required to empty…

A:

Q: 4. Find differential dy for each function. (A) y = f(x) = 200x -. (B) y = f(x) = (3x + 5)².

A:

Q: At an amusement park, the pendulum ride's movement from its starting position in meters can be…

A: Given :

Q: Find the area of the surface generated by revolving the curve x=t, y=4-2t [0,4] about the x-axis.

A: We will find the required.

Q: What are all the solutions to the equation sin 2x = 2cos x in the interval [0, 2TT)? O {TT} O {0,…

A: We can find the correct answer and mark the option in the below steps.

Q: 2. Find d if y= 2² +25 da

A:

Q: Suppose x = 11.5, 0 = y = ㅠ 5 A X z = 3πT radians and = radians in the figure, which is not drawn to…

A:

Q: a. Find the Divergence of the Vector. b. Use divergence Theorem to calculate the Surface integral;…

A:

Q: Let the velocity vector be v(t) = (6 cos(3t), 4t³, 9 exp(3t)) and the initial position vector be…

A:

Q: Closest points are (If there is more than one closest point, enter a comma-separated list.)

A:

Q: For the following expression, find the correct partial fraction decomposition. -5x² - 19x +38 (3x −…

A:

Q: f(x, y) = 2x - 8y 7x² + 5y

A: f(x)=2x-8y7x2+5y

Q: z Find the Taylor polynomial på for f(x) = xe at z = 2.

A: we have to find the taylor polynomial P3   for function f(x)=xe-x  at  x =2   f(x) = xe-x   ⇒f(2)=…

Q: Given that n=0 (-1, 1), find the power series for 0. X 1 1 X to x = N): Σ x" with convergence in n=0…

A:

Q: 4. Given function g(x) = { -1, 1, if is an even integer; if x is not an even integer. (A) Graph…

A: The given function gx=-1,if x is an even integer1,if x is not an even integer We have to sketch the…

Q: 42. lim √√x = 0 0-x

A: Given query is to find the limit of the expression.

Q: x² dx + y(x - 1)dy = 0

A:

Q: A note card company has found that the marginal cost per card of producing x note cards is given by…

A:

Q: The population P(t) of a herd of deer on an island can be modeled by P(t)= 900/1+2e-0.01t where t…

A:

Q: A honey bee population starts with 100 bees and increases at a rate of N (t) bees per 15 week. What…

A: given  population start with 100 bees inceasing rate is  N(t)  bees per week

Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

A:

Q: Find a. a. Əw dx ?w A). ax y and b. (2,2,-2) aw dz 2 at the point (x,y,z) = (2,2, - 2) if w= x² + y²…

A:

Q: 3. lim (x² 3x) = -2 x-2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Suppose that in a memory experiment the rate of memorizing is given by M′(t)=−0.009t2+0.2t where…

A: Topic:- application of integration

Q: Find the points on the curve x = t² – 4t – 3, y = t² + 18t + 6 that have: - A. a horizontal tangent…

A: To find the points where the given curve has horizontal and vertical tangents.

Q: Find the order 3 Taylor polynomial T3(x) of the given function at x = 0. Use exact values. ƒ(x) =…

A: As we know that the nth order Taylor's polynomial at x=x0 is given by:…

Q: The price-demand function and the cost function for the production of HDTVs are as follows:…

A:

Q: 2. Find the exact values or state that the expression is undefined. ¹ (¹) b. cos ¹(1.5) a. sin c.…

A: If x = sin -1(y) then y= sin(x) If x = cos -1(y) then y= cos(x) If x= tan -1(y) then y= tan(x)

Q: O Evaluate the integral 1- -5x ln(x) dx;

A: solving the problem by finding the value of the integration.

Q: Explain why, to find maxima and minima for f(x), one thing we do is solve f'(x) = 0.

A: We can explain why , to find maxima and minima for f(x) , one thing we do is solve f'(x) =0.

Q: Verify the Divergence Theorem for the vector field and region: F = (3x, 2z, 2y) and the region x² +…

A: Given that F=3x,2z,2y  and the region x2+y2≤1, 0≤z≤4

Q: ind the Maclaurin Series for f(x) =1/(1+8x) and its interval of convergence.

A:

Q: Use l'Hospital's rule to find the limit. You must show the indeterminate form, etc. All details for…

A:

Q: 5. Find and simplify expression f(5+h)-f(5) if ƒ(x) = x² – 1.

A:

Q: g(r, t, z) = 7r(5 – cos(t)) – 2z dg ər dg Ət ag дz ... ... m ... ...

A: To determine the partial derivatives with respect to each variable.gr, t, z=7r5-cost-2z

Q: 39. If 2x − 1 ≤ f(x) ≤ x² for 0 < x < 3, find limx→1 f(x).

A:

Q: Let f (x)=5. Which of the following statements is true about the graph of f?

A:

Q: dy 1) Find if y=3(x - 6x + 1) dx

A:

Q: Find the k-component of (curl F) for the following vector field on the plane. F = (x¹)i + (5ye*)j…

A:

Q: For each of the described curves, decide if the curve would be more easily given by a polar equation…

A: (a)   given radius is 5 and centre is (1,2)equation of circle is standard form is  (x-h)2+(y-k)2=r2…

Q: Find the derived functions of each of the following functions: y=sin 1/x

A:

Q: Find the points on the curve t² 16t+ 6, y X = = A. a horizontal tangent line B. a vertical tangent…

A: Given the curve is x=t2-16t+6  and y=t2+4t+3

Q: √3n+1 2+√√n

A: Solve the following

Q: Find the point on the plane x + 2y + 3z = 18 closest to the point (1,1,1). The closest point is).…

A:

Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

A: (a).   Given                          F⇀ (x,y) =(4x,4y)         {vector field}Compute the…

Q: Justin stands at the top of a cliff. On the ground, 250 feet below, Justin spots a coyote. a. When…

A: Justin stands at the top of a cliff. On the ground, 250 feet below, Justin spots a coyote.

Q: The question is asking for CM/min. Are you sure this is the solution to

A:

Q: An arithmetic sequence has a15 = 86 and a34 = 200. Find a150. an = a₁ + (n − 1)d -

A: NOTE: Refresh your page if you can't see any equations. . it is given that

Q: Suppose you do not know the rotation of the broken compass. Instead of a 30° counterclockwise…

A: Suppose you do not know the rotation of the broken compass. Instead of a 30° counterclockwise…

Q: √2x √2x + 1 dx

A: