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EBK DIFFERENTIAL EQUATIONS AND LINEAR A
- If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.arrow_forward#1,2 Please write clearlyarrow_forwardIf f ( x) = 3x^3 − 4x − 3 and g( x) = 7 − ( x − 3)^2 , a.) Solve for x: f ( x) = g( x) (Answers correctly rounded to the nearest .001) b.) Solve for x: f ( x) < g( x)arrow_forward
- Find (i) ?’(?) and (ii) ?’’(?) of the following functions. a)h(?)= 1 −9√?,b)?(?)=6?4−√? ,c)?(?)= ?4 −5?−5?arrow_forwardInstructions: In problems 1-15, use the derivative rules to find the derivative of y in each case. 1. y = (2x-7)³ 2. y = (3x² +1)* 3. y=3x (4-9x)* 4. y=(3 + x)² (1 − x²)³ 5. y=(9-x²) ²/3 7. y = √√9x² + 2x + 7 10. y= x + 1 x-1 13. y=(x+¹)* 1 (ii) 8. y= lim to+ 11. y 17. Bonus Set M=(1,0), N= (0, 1), O = (0,0), and P,= (t,√t) for t> 0. Compute: (i) Area(AMOP) lim t-0+ Area(ANOP) - 2x + 1 Perimeter (AMOP) Perimeter (ANOP,) 6x - 5 2 x + 1 6. y=√√3-2x 2x³ 1 M 9. y 12. (4x-1)³ 14. y = x²(x −1)² 2x² +1 16. Bonus Use calculus to find the coordinates of the two points along the graph of y=4-x² whose tangent lines pass through point P = (1,7). Then sketch a graph which displays the parabola and both of its tangent lines which intersect at P. Also, determine the angles of inclinations of these tangent lines. (Recall, m = tan a, if a is the inclination of the line with slope m.) Hint: Describe the parabola parametrically to find the two points - refer to problem 4 of Worksheet 5. y=√x y = 15. y =…arrow_forward4. (a) X, y and z are such that x varies directly as z and inversely as the cube root of y. If x = 8, y = 27 and z = 4, find: (i) an expression for x in terms of y and z. value(s) of y when x = 12 and z = 10. (ii) (b) The area of a rectangle is 6m². If the length is 1m longer than the width. Find the dimension of the rectangle (a) In the diagram below, RS is a tangent at S. The circle PQS is the circum-circle of APQS. If QRS 34° and P$Q = 61°. Calculate QŜR. %3D P NOT DRAWN TO SCALE 61 340 R The probability that Afua can solve a particular mathematical problem is 0.7 and the pr that Kojo can not solve the same problem is 0.4. What is the probability that: (b) all of them solve the problem? at least one of them solves the problem? (1) (ii)arrow_forward
- solve for x if CDy=4(x-E)arrow_forwardIf f(x) = 2x + ln x, find f-1(2).arrow_forwardx2 + 1, Problem 2. Find the shaded area in the picture below. The three functions are f(x) g(x) = 2x4, and h(x) = 2x (you will have to compute the intersection points yourself; don't worry, I made them nice). f(x) g(x) h(x)arrow_forward
- Problem 3. Use the formula to find the derivative of below functions. 1 (1) f(x) = = (32+x) · (2 – √√5x+x²), (2) g(x) = ( 5x²7x+2 2³-9arrow_forward1. A child lets go of a helium-filled balloon from a height of 4 feet above ground. The value of r(t) is the rate of change, in feet per second, of the balloon's height after t seconds have elapsed. Write an expression, involving an integral, that gives the balloon's height after 5 seconds. Briefly explain your answer.arrow_forwardSolve number 3arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning