Studies show that the minimum half-life of Diazepam is 20 hours. Use the following to construct a function that will model the minimum amount of Diazepam left in the body after an initial dose of 30 mg. Q(t) = Pert Where Q(t) describes the amount of Diazepam left in the body after t hours following an initial dose of P mg. 1. Q(t): = 2. How long (in hours) will it take for the amount of Diazepam left in the body to reach 5 mg?

Q: dx Evaluate the integral d using trigonometric substitution. ſ √25-x²

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Q: Evaluate the line integral F F. dr, where C is given by the vector function r(t). F(x, y, z) =…

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Q: First make a substitution and then use integration by parts to evaluate the integral. r5 cos(x³) dr

A: We need to solve the integration by parts.

Q: 12. Use a half-angle identity to find the exact value of cos 105°.

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Q: 3) Given that f (x) = 2x + 8 g(x) = 5x – 2 / 4 and h(x) = 2x + 6 / X Find: - iv) hᴏf(x)= v)…

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Q: Use the result obtained in Problem 20 to find the area enclosedby f1x2 = - 5x2 + 8, the x-axis, and…

A: Given function is f(x)=-5x2+8. The objective is to find the area enclosed by f(x), x-axis. where…

Q: 6. The radical function fx) = √√x is graphed below, along with a few key points. Sketch the…

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A: given radius decreasing rate is 4 inches per hour radius is 5 inches v=43πr3drndr=nrn-1

Q: B. Instruction. Find the Inverse of each Function. 3. f(x) = x² +7 4. f(x) = 2x² - 3 5. f(x) = 2x+7…

A: We will find the inverse function letting y=f(x).

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

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A: The answer is given below:

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Q: The midpoint of the line segment from P1 to P2 is (5, - 4) If P2 = (7, - 2), what is P1?

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Q: Find the height of the trapezoid shown below, if the area is 134.54. 12.8 a 6.2 15.5 13.9 Q

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Q: 0 4 √t dt

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Q: equation of the line tangent to the curve at the point corresponding to the given value of t.…

A: Given query is to find the equation of the tangent.

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Q: please solve question : (b)

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Q: ∞ k=1 (-1)+¹(x - 1)k k

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Q: Solve the following basic calculus problems: d (e² cos x) dx a. X b. Sybdy c. Show: d. if df dx = वर…

A: As per the rules, we are supposed to answer the first question and rest others can be reposted.

Q: 1. dy = e3x+2y dx

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Q: Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x…

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Q: a. Use the given Taylor polynomial p2 to approximate the given quantity. b. Compute the absolute…

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Q: What can you say about the inflection points of a quadratic curve y = ax² +bx+c, a #0? Give reasons…

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Q: - 6 y = x² - x - 30, y = 0, x = -5, x = 4 y -4 -2 30 20 10 -10 -20 30 2 X

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Q: What is the sum of the first 14 terms of the series 9 + 2-5-12-19-...? -25 Ob -98 Oc -511 Od -518

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Q: Assume a population of fish grows exponentially. A pond is stocked initially with 500 fish. After 6…

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Q: Evaluate the definite integral by interpreting it in terms of areas. D = 16 D = √20 √√-2² + +16 dx

A: This question can be solved using the concept of some special integrals∫a2-x2dx=x2a2-x2+a22sin-1xa+C

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Q: The area of a rectangle with one of its sides s is A(s) = 17s². What is the rate of change of the…

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Q: Find by integration the area of ​​the triangle that has vertices at : (5,1), (1,3), (-1,-2)

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Q: Which of the following equations has no solution? 5. a. b. − ²)(a b) = (19) (²2) -77²) (²5) = (69) a…

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Q: the Shell Method to compute the volume of the solid obtained by rotating the region in the first…

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Q: 3. Verify that the function F(x) is an antiderivative of the function f(x), then find the given…

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Q: 1. The equation x² + y² = 1 defines the unit circle with its centre at the origin. The circle passes…

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Q: Let I be the length of a diagonal of a rectangle whose sides have lengths and y, and assume that and…

A: Here we have to use the concept of derivatives

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Q: Use Newton's method to estimate the one real solution of x³+4x+1=0. Start with x = 0 and then find…

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Q: Consider the following parametric equations. Answer parts a. through d.   x=t2​, y=t−3​; −4≤t≤4   a.…

A: Solve the following

Q: Use concepts learned in this module to complete this problem set: particle motion, applications…

A: We can find the limit of the function .

Q: Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by…

A: