An equilateral triangular plate with sides 12 m is submerged vertically in a liquid of density 865 kg/m³ so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s² for the acceleration due to gravity.) Show all steps clearly.

Q: (a) Estimate the volume of the solid that lies below the surface z = xy and above the following…

A: Step 1:Step 2:

Q: (a) Suppose that k is an odd integer and w is a k-form. Show that w^w = 0. (b) Note: This question…

A:

Q: Find the length of the curve Arc length = x = 1 √(y – 3), 1≤ y ≤ 9.

A: Step 1:       Step 2: Step 3: Step 4:

Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Order your…

A:

Q: Sketch the graph is f(x) for all of these, they are apart of 1 question. I need poi, critical…

A: Step 1: Determine Points of Inflection: Since this function is a rational function, there are no…

Q: factorize  -7x3+ 7/ 3x2-x-2

A:

Q: Solutions to question 1 please

A: Step 1:It is asked to solve question 1 only.  (i) e2y+x=y .......(1)  (a) Differentiating on both…

Q: Use the remainder theorem to determine the remainder when P(x)= 3x^5 - 3x^2 - x+ 2 Is divided by…

A:

Q: Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it…

A: For this question, we have to analyze the given diagram. First analyze x axis. When moving along x…

Q: 26. A carpenter is constructing a large cubical storage shed. The volume of the shed is given by 3…

A: The objective of this question is to find the average rate of change in volume of the cubical…

Q: An ice cube tray filled with tap water is placed in the freezer, and the temperature of the water is…

A: Given,Temperature of water is changing at the rate of -9e-0.2t degrees Fahrenheit per hour. a) To…

Q: Use known Maclaurin series and operations on power series to nd Maclaurin series for the following…

A: Step 1: To find the Maclaurin series for x^7cos(4x^5), we can use the Maclaurin series for cos(x)…

Q: Given Ś Ś cos (y²) dy doc (a) Write down o x inequalities in xy for ?εχε? Ly the region R of…

A:

Q: 13. Let v(4,8, 12). Which of the following vectors is parallel to v? Which point in the same…

A: Two vectors are parallel if they are scalar multiples of each other. This means that each component…

Q: 3. Illustrate each limit on the graph. Limit as x approaches negative infinity: Limit as x…

A: Step 1:Step 2:​From the given graph:Let the function be f(x)We know that for a function f(x), If y=a…

Q: Calculus I May I please have the solution for the following question? Thank you,

A: Step 1:     Step 2: Step 3: Step 4:

Q: Evaluate this double integral

A: Consider,∫xndx=n+1xn+1​∫1 dx=x(a−b)2=a2+b2−2ab∫ab​x dx=[2x2​]ba​=2a2​−2b2​Integrating x terms with…

Q: If you use the rst three non-zero terms of the Maclaurin series of 2/3+ x^5, what is the approximate…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the limit. lim x→0+ sin(6x) x4 = 6 ✓

A: Step 1:To find the right-hand limit of f(x)=−x4sin(6x)​ as x approaches 0, we evaluate f(x) as x…

Q: 2. (a) Find the Maclaurin series of 2/3+x^5 from the Maclaurin series for 1/1 - x and power series…

A: Step 1:part a) Step 2:part b) Step 3: Step 4:

Q: Find the absolute maximum and minimum values of the function over the indicated interval. f(x)=4x²…

A: The objective of this question is to find the absolute maximum and minimum values of the function…

Q: Consider the series Σ n=1 (2x)n n2

A: The objective of this question is to determine the values of x for which the Ratio Test is…

Q: Use the square root method to solve the equation. 3x²=45 A. 22.5 B. 16 C. ±√1 OD. ±15

A:

Q: 9. Describe in words and a simple sketch the solid given by the following inequalities (a) 0p≤2, 0…

A: The objective of the question is to describe and sketch the solid defined by the given inequalities…

Q: Polar Coordinates

A:

Q: Given u = and v = u+v = Λ

A: The objective of this question is to perform vector addition and subtraction. In this case, we are…

Q: Find an equation for the conic that satisfies the given conditions. ellipse, foci (0, -3), (4, -3),…

A:

Q: Bioengineers construct peptides with new functions by starting with a particular peptide, and then…

A: The objective of this question is to calculate the number of peptides that need to be screened in…

Q: Prove the identity 2 Sin²x = x tan ². 1 + tan²x Use a Pythagoras identity

A:

Q: 4. A particle with acceleration a(t) = − (t − 2)² + 1 m/s² is traveling in a straight line. If it…

A: Simply we are using calculs formulas for kinematics     So , distance will be 14 metre

Q: How to solve?

A: 1. To find the domain and range of each function, we consider the restrictions on the input x that…

Q: Calculate R5 for f(x)=4x2+6x over [-1,1]

A: The objective of this question is to calculate the Riemann sum, specifically R5, for the function…

Q: Let f (x) = arcsin(x²) arctan(2x). Evaluate f'(x) =

A: Given: f′(x)=arcsin(x2)arctan(2x)Getting the derivative, we…

Q: You approximate f (t) = e' by a Taylor polynomial of degree 2 about t = 0 on the interval [0, 0.5].…

A: The objective of this question is to determine whether the second-degree Taylor approximation of the…

Q: Find all points of intersection of the given curves. (Assume 0 ≤ 0 ≤ 2л and r≥ 0. Order your answers…

A: Step 1:Given that, the curves are r=6sin(2θ),r=3 and 0≤θ≤2π,r≥0 To find all the points of…

Q: მ Find 5e3zy Эх

A: If you have any questions let me know in comment box thankyou for your question.

Q: I need help with this problem and an explanation for the solution described below:

A:

Q: Evaluate ǝw (x, y, xz) ds where W = {(x, y, z) : x² + y² ≤ z ≤ 1}.

A: In the given problem we have to evaluate:∫∫∂W​⟨x, y, xz⟩⋅dSwhere:W={(x,y,z):x2+y2≤z≤1}Now using the…

Q: Test the series for convergence or divergence. Σ sin(3n) ח7 + 1 n = 1 convergent divergent

A:

Q: Problem #1: Set up the double integral that would be used to find the volume under the surface…

A: Step 1: Step 2: Step 3: Step 4:

Q: -y-x4-y₁ #21 Given f(y)= (a) Find the direction in which f(cy) decreases most rapidly at P. (0,0),…

A: Step 1:Step 2: Step 3: Step 4:

Q: Given the point (2, 3) on a tangent line to the curve f(x) = x^2 + 3x − 4 find the point(s) where…

A: Step 1:Step 2:Step 3:Step 4:

Q: please solve this step by step and quick please

A: For any query with the solution please ask in the comment box.

Q: A Publically traded company has issued $50M worth of stocks. The stock holders expect a rate of…

A: 1. Cost of Equity (Ke):The cost of equity is given as 12%.2. Cost of Debt (Kd):Kd = 10%3. Cost of…

Q: Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it…

A: The given vector field is:F=⟨cos(x)+2y, sin(y)−x⟩Now we have to find:∫C​F⋅dswhere C is the boundary…

Q: Find the absolute maximum and minimum, if either exists, for f(x) = x² - 4x+3.

A: The objective of this question is to find the absolute maximum and minimum values of the function…

Q: The vectors a-5b and a-b are perpundicular. If a and b are unit vectors, then find a.b

A:

Q: Calculate M6 for f(x)=sqr(3x) for [2,5]

A: Step 1: Divide the interval into subintervalsWe're approximating the definite integral using the…

Q: 1. Set up and simplify, but do not evaluate, an integral for the length of the curve y = ln(sinx), ≤…

A: Step 1:Solution- Correct option is C.Step 2: Step 3: Step 4:

Q: For the integral 2xy dy dx, sketch the region of integration and evaluate the integral. Your sketch…

A: Thanks for your patience!Kindly comment in case of any clarifications needed.