Doctors use radioactive iodine as a tracer in diagnosing certain thyroid gland disorders. This type of iodine decays in such a way that the mass remaining after t days is given by the function m(t) = 6e-0.089t where m(t) is measured in grams. (a) Find the mass at time t = 0. grams (b) How much of the mass remains after 5 days? (Round your answer to three decimal places.) grams

Q: 25. 4 3. 2.

A: To evaluate the area of the shaded region, we have to find the equation of the parabola first.Equati...

Q: Consider a cone with a radius of 5cm and a height of 10 cm. Find the change in the volume of the con...

A: Given data: The given radius of the cone is r=5 cm. The given height of the cone is h=10 cm. The cha...

Q: Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the ...

A: The logarithm is given as,log2 15 . The property of natural logarithm is, loga b=lnalnb Apply the pr...

Q: find the distance between points P1 and P2. P1(-1, 1, 5), P2(2, 5, 0)

A: Given points are: P1=(-1, 1, 5) and P2=(2, 5, 0) The formula to find the distance between two point ...

Q: Evaluate x(x2 + 1)3 dx.

A: Given ∫x(x2+1)3dx

Q: -p? Suppose the demand for a certain brand of a product is given by D(p) = 207 + 150, where p is the...

A: The demand function is Dp=-p2207+150 where p is the price in dollars. Now, the price is defined as p...

Q: write a differential formula that estimates the givenchange in volume or surface area. The change in...

A: a) To write the differential formula which gives the change in volume of a right circular cylinder w...

Q: 4n2 +n (a) Check the convergence of the series E using limit comparison test. n=o n°+6n2 – n (b) For...

A:

Q: The graph of f(x) = x3_______ to the left and______ to the right.

A: Given function - f(x) = x3Let us draw the curve for the point x=-5 to x=5, by finding corresponding ...

Q: Factor completely, or state that the polynomial is prime.: 5x3 - 45x

A: To factorize 5x3-45x 

Q: determine the general solution to thegiven differential equation y(iv) − 16y = 0.

A: Determine the generalsolution of given differential equation. yiv-16y=0

Q: A weather balloon is released and rises vertically such that its distance s(t) above the ground duri...

A: Given data: The expression for the distance of the balloon is s(t)=6+2t+t2. (a) The expression for t...

Q: Evaluate  algebraic expression for x = 2 and y = -5. | x - y|

A: Given x=2 and y=-5 we have to evaluate the algebraic expression x-y  

Q: (a) Use a graph of              ______________       ______________f(x) = √3 x2 + 8x + 6  -  √3 x2 +...

A: From the graph, the value of  f(x) to one decimal place islimx→∞ 3x2 + 8x + 6 - 3x2 + 3x + 1 ≈ 1.4

Q: Improper integrals Evaluate the following integrals or state that they diverge.

A: ∫lnxx2 dx=∫lnx·x-2 dx=lnx·∫x-2 dx-∫dlnxdx·∫x-2 dx dx=lnx·x-2+1-2+1-∫1x·x-2+1-2+1 dx=-lnxx+∫1x2 dx=-l...

Q: Begin by graphing the absolute value function, f(x) = lxl. Then use transformations of this graph to...

A: Given f(x) = lxl

Q: Solve the polynomial inequality -x2 + 2x ≥ 0and graph the solution set on a real number line. Expres...

A: Given inequality, -x2+2x≥0                 

Q: Fill in the blank/s: The formula for nCr has the same numerator as theformula for nPr but contains a...

A: We have to fill in the blanks: The formula for Crn has the same numerator as the formula for Prn but...

Q: Determine the following indefinite integral. Check your work by differentiation.

A: To evaluate the integral: ∫16cos2w-81sin2w4cosw-9sinwdw Solution: We know that cos2θ-sin2θ=cosθ+sinθ...

Q: Find the mass of the lamina described by the inequalities 0 ≤ x ≤ 2, 0 ≤ y ≤ 4 − x2, given that its ...

A: to find the mass of the lamina

Q: - 5 f(x) - If lim X-4 X - 2 1, find lim f(x). %3D

A: Given limx→4fx-5x-2=1 To find limx→4fx

Q: Rationalize the denominator : √2 /√5 ?

A: To rationalize the denominator of 25. Rationalizing the denominator of given expression. 25=25×55=2×...

Q: A cube's volume increases at a rate of 108 ft3/min. At what rate is the cube's edge length changing ...

A:

Q: Expand and evaluate numerical terms: ln (e19x20)

A: Consider the given logarithm  lne19x20

Q: The division (7 + 4i)/(2 - 5i) is performed by multiplying the numerator anddenominator by________ .

A:

Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area amo...

A: Given information: V=64 m3  

Q: Evaluate the integrals . Some integrals do notrequire integration by parts. ∫x (ln x)2 dx

A: Given: I=∫xlnx2dx for evaluating given integral, we use integral by parts theorem according to integ...

Q: I| Fx.y)dxdy, the change of order is For

A:

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x4 - ...

A: Increasing and decreasing functions: f(x)=x4-4x3+4x2 Increasing function Let y=f(x) be a differentia...

Q: Determine whether the statement is true or false. If it is false, explain why or give an example tha...

A: Given information: The function is an even function,  

Q: Use the Binomial Theorem to expand the binomial (x + 2y)5 and express the result in simplified form.

A: Given: x+2y5

Q: Consider the line whose equation is 2x + y - 6 = 0. The slope of any line that is parallel to this l...

A: Given equation of line - 2x+y-6 = 0Rewriting it - y =-2x+6Comparing this equation with general equat...

Q: The vertices of a triangle are (1, 2, 0), (0, 0, 0), (−2, 1, 0). Determine whether the triangle is a...

A: Suppose the given vertices of the triangle be P1 , 2 , 0 , Q0 , 0 , 0 and  R-2 , 1 , 0 So, the sides...

Q: Given P(x) = x³ + 3x2 + 4x + 12. Write P in factored form (as a product of linear factors). Be sure ...

A:

Q: Find the derivative of the function. 6. s(t) = 49 (6t - 7) %3D s'(t) =D %3D

A: Use the formula for derivative of a power of a function.

Q: Explain why each of the following integrals is improper.

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If y...

Q: Find the exact value of cos 15°.

A: To find value of cos15°. We know that cosa-b=cosa cosb+sina sinb Therefore, using the above formula....