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0 A spherical tank of radius 8 feet is half full of oil that weighs 50...
Give parametric equations that describe a full circle of radius R, centered at the origin with...
Give parametric equations that describe a full circle of radius
R, centered at the origin with clockwise orientation, where the
parameter t varies over the interval [0,22]. Assume that the
circle starts at the point (R,0) along the x-axis.
Consider the following parametric equations, x=−t+7, y=−3t−3;
minus−5less than or equals≤tless than or equals≤5. Complete parts
(a) through (d) below.
Consider the following parametric equation.
a.Eliminate the parameter to obtain an equation in x and y.
b.Describe the curve and indicate...
1 6 at the point with X-coordinate 3. Find the For f(x) = the slope of...
1 6 at the point with X-coordinate 3. Find the For f(x) = the slope of the graph of y = f(x) is known to be equation of the tangent line at that point. 2 4 + x 169 (Type an equation. Use integers or fractions for any numbers in the equation.) Find the particular solution determined by the given condition. ds 17t2 + 3t - 8; s = 110 when t=0 dt The particular solution that satisfies the given...
1) A tank contains 200 gallons of water in which 50 pounds of salt are dissolved. A brine solutio...
please solve all three questions, will upvote thank you
1) A tank contains 200 gallons of water in which 50 pounds of salt are dissolved. A brine solution containing 4 pounds of salt per gallon is pumped into the tank at the rate of 6 gallons per minute. The mixture is stirred well and is pumped out of the tank at the same rate. Let A(t) represent the amount of salt in the tank at time t a) Write down...
17. Consider the differential equation given by dy/dx = xy/2
17. Consider the differential equation given by dy/dx = xy/2 (A) On the axes provided, sketch a slope field for the given differential equation. (B) Let f be the function that satisfies the given differential equation. Write an equation for the tangent line to the curve y (x) through the point (1, 1). Then use your tangent line equation to estimate the value of f(1.2) (C) Find the particular solution y=f(x) to the differential equation with the initial condition f(1)=1. Use your solution...
Consider the differential equation: -9ty" – 6t(t – 3)y' + 6(t – 3)y=0, t> 0. a....
Consider the differential equation: -9ty" – 6t(t – 3)y' + 6(t – 3)y=0, t> 0. a. Given that yı(t) = 3t is a solution, apply the reduction of order method to find another solution y2 for which yı and y2 form a fundamental solution set. i. Starting with yi, solve for w in yıw' + (2y + p(t)yı)w = 0 so that w(1) = -3. w(t) = ii. Now solve for u where u = w so that u(1) =...
Can you please help with this question? Please answer the question in MATLAB coding. Thank you in advance!! A storage tank (shown below) contains a liquid at depth y where y 0 when the tank is half f...
Can you please help with this question? Please answer the
question in MATLAB coding. Thank you in advance!!
A storage tank (shown below) contains a liquid at depth y where y 0 when the tank is half full. Liquid is withdrawn at a constant flow rate Q to meet demands. The contents are resupplied at a sinusoidal rate 3Qsin2(t) A. The change in volume can be written as d(y) 30 sin2(t) Q dt where A is the surface area and...
Question 8: [20 marks] a) Determine the type of the differential equation+3)xy+(x* +6x +9)cosx (is +9...
Question 8: [20 marks] a) Determine the type of the differential equation+3)xy+(x* +6x +9)cosx (is +9 coSx (15S it linear/ nonlinear, separable/non-separable, homogeneous/non-homogeneous)? b) Find the particular solution subject to the initial condition y(0) 6.
4. [3/8 Points) DETAILS PREVIOUS ANSWERS SCALCCC4 9.5.013. Consider the line that passes through the point...
4. [3/8 Points) DETAILS PREVIOUS ANSWERS SCALCCC4 9.5.013. Consider the line that passes through the point and is parallel to the given vector. (4, -3,6) < 1, 2, -3> (a) Find symmetric equations for the line. 2-6 -(x-4)= 2 3 y +3 (b) Find the points in which the line intersects the coordinate planes. (5 X IX 0) (0,9 X -6 (4 x 0, 4 X) 1 Consider the line that passes through the point and is perpendicular to the...
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the...
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
A Water Tank Problem with Discontinuous Source A water tank contains V, > 0 liters of...
A Water Tank Problem with Discontinuous Source A water tank contains V, > 0 liters of pure water and Qo grams of salt. At time t = 0 we start pouring water into the tank with a rate r > 0 liters per minute with a salt concentration of q> 0 grams per litter, and we let the well-stirred water leave the tank at the same rate. After T > 0 minutes the process is stopped and fresh water is...
Give parametric equations that describe a full circle of radius
R, centered at the origin with clockwise orientation, where the
parameter t varies over the interval [0,22]. Assume that the
circle starts at the point (R,0) along the x-axis.
Consider the following parametric equations, x=−t+7, y=−3t−3;
minus−5less than or equals≤tless than or equals≤5. Complete parts
(a) through (d) below.
Consider the following parametric equation.
a.Eliminate the parameter to obtain an equation in x and y.
b.Describe the curve and indicate...
1 6 at the point with X-coordinate 3. Find the For f(x) = the slope of the graph of y = f(x) is known to be equation of the tangent line at that point. 2 4 + x 169 (Type an equation. Use integers or fractions for any numbers in the equation.) Find the particular solution determined by the given condition. ds 17t2 + 3t - 8; s = 110 when t=0 dt The particular solution that satisfies the given...
please solve all three questions, will upvote thank you
1) A tank contains 200 gallons of water in which 50 pounds of salt are dissolved. A brine solution containing 4 pounds of salt per gallon is pumped into the tank at the rate of 6 gallons per minute. The mixture is stirred well and is pumped out of the tank at the same rate. Let A(t) represent the amount of salt in the tank at time t a) Write down...
Consider the differential equation: -9ty" – 6t(t – 3)y' + 6(t – 3)y=0, t> 0. a. Given that yı(t) = 3t is a solution, apply the reduction of order method to find another solution y2 for which yı and y2 form a fundamental solution set. i. Starting with yi, solve for w in yıw' + (2y + p(t)yı)w = 0 so that w(1) = -3. w(t) = ii. Now solve for u where u = w so that u(1) =...
Can you please help with this question? Please answer the
question in MATLAB coding. Thank you in advance!!
A storage tank (shown below) contains a liquid at depth y where y 0 when the tank is half full. Liquid is withdrawn at a constant flow rate Q to meet demands. The contents are resupplied at a sinusoidal rate 3Qsin2(t) A. The change in volume can be written as d(y) 30 sin2(t) Q dt where A is the surface area and...
Question 8: [20 marks] a) Determine the type of the differential equation+3)xy+(x* +6x +9)cosx (is +9 coSx (15S it linear/ nonlinear, separable/non-separable, homogeneous/non-homogeneous)? b) Find the particular solution subject to the initial condition y(0) 6.
4. [3/8 Points) DETAILS PREVIOUS ANSWERS SCALCCC4 9.5.013. Consider the line that passes through the point and is parallel to the given vector. (4, -3,6) < 1, 2, -3> (a) Find symmetric equations for the line. 2-6 -(x-4)= 2 3 y +3 (b) Find the points in which the line intersects the coordinate planes. (5 X IX 0) (0,9 X -6 (4 x 0, 4 X) 1 Consider the line that passes through the point and is perpendicular to the...
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
A Water Tank Problem with Discontinuous Source A water tank contains V, > 0 liters of pure water and Qo grams of salt. At time t = 0 we start pouring water into the tank with a rate r > 0 liters per minute with a salt concentration of q> 0 grams per litter, and we let the well-stirred water leave the tank at the same rate. After T > 0 minutes the process is stopped and fresh water is...
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