A drug is administered intravenously for pain. The function ƒ(t) = 90 - 52 ln (1 + t), 0<=t<= 4 gives the number of units of the drug remaining in the body after t hours. a. What was the initial number of units of the drug adminis-tered? b. How much is present after 2 hours? c. Draw the graph of ƒ.

Q: Simplify the trigonometric expression. sin(x) csc(x) + cot(x)

A: To simplify,

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A:

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Q: Square CuN Sukstitdicm 13

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A: The area enclosed by two functions between x = a and x = b is given by:

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Q: You invest ​$1100. If the account grows by 6.3% per​ year, how quickly will the account be growing​ ...

A: We have P = $1100, r = 6.3% = 0.063, n = 1.

Q: Set  up the composite (gof)(x) when f(x)=2x^3-7x and g(x)=9x^2-7

A: Given function is

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Q: Find the derivative with respect to t. y= csc-1(et)

A: Given:

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A:

Q: Find the partial derivatives of the function f(x, y) = | cos(4t – 5t – 7) dt

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A: To express balloon’s volume V as the function of time.

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A: First consider the area bounded by y=|x| and y=mx+ 1, and evaluate the intersection points:

Q: *show work*

A: Find dy/dt.

Q: Exercises 1–6, sketch the given curves together in the appropriate coordinate plane and label each c...

A:

Q: For each of the following, solve △ABC, if possible. Round your answers to two decimal places. a. A= ...

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A: The given equation for displacement from equilibrium of an oscillating mass attached to a spring is,

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A: Given,

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Q: The rate of growth of the fish population was modeled by the equation G(t) = (60,000e^-0.6t)/(1+5e^-...

A: Given:

Q: If ƒ and g are real-valued functions, how are the domains of ƒ + g, ƒ - g, ƒg, and ƒ/g related to th...

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Q: find the domain and range of each function ƒ(x) = sqrt(5x+10)

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A: Given:

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Q: In Exercises 39 and 40, find a. (ƒ ∘ g) (-1).      b. (g ∘ ƒ) (2)  c. (ƒ ∘ ƒ) (x)          d. (g ∘ g...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Does the series converge absolutely, conditionally, or diverge?  sum (-1)^n (sqrt(n + 1) - sqrt(n)) ...

A: Given,

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A: Given that agricultural sprinkler distributes water within a circle of radius R = 50 ft.Also, it sup...

Q: Does the series convege absolutely, conditionally, or diverge? sum_(n=1)^∞ (-1)^n (sqrt(n + 1) - sqr...

A: For convergence test, checking for the type of convergence,

Q: State the range and domain.

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A: (a) Obtain the domain and range of the given function as follows.

Q: fa rock is dropped from a height of 217 ft, its poistion t seconds after it is dropped until it hits...

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Q: Evaluate the indefinite integral. Ja sin^(#)cos(z)dz = *(x)cos(x)dx Preview Get help: Video

A: Given integral:

Q: 4-x2 dx -2

A: The given integral is

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.