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Happiness Mahlalela

Happiness M.

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The half-life of bismuth-210, $ ^{210} Bi $, is 5 days. (a) If a sample has a mass of 200 mg, find the amount remaining after 15 days. (b) Find the amount remaining after $ t $ days. (c) Estimate the amount remaining after 3 weeks. (d) Use a graph to estimate the time required for the mass to be reduced to 1 mg.

The half-life of bismuth-210, $ ^{210} Bi $, is 5 days. (a) If a sample has a mass of 200 mg, find the amount remaining after 15 days. (b) Find the amount remaining after $ t $ days. (c) Estimate the amount remaining after 3 weeks. (d) Use a graph to estimate the time required for the mass to be reduced to 1 mg.

Calculus: Early Transcendentals

Functions and Models

Exponential Functions
An RL circuit has EMF $E(t)=10 \sin 4 t$ V. If $R=$ $2 \Omega, L=\frac{2}{3} \mathrm{H},$ and there is no current flowing initially, determine the current for $t \geq 0$.

An RL circuit has EMF $E(t)=10 \sin 4 t$ V. If $R=$ $2 \Omega, L=\frac{2}{3} \mathrm{H},$ and there is no current flowing initially, determine the current for $t \geq 0$.

Differential Equations and Linear Algebra

First-Order Differential Equations

Modeling Problems Using First-Order…

Questions asked

INSTANT ANSWER

Mathematics Paper 1 \& Paper 2 2023/12 \( 1 \& 2 \) QUESTION 8 Two trig functions namely, \( f(x)=a \cos x \) and \( g(x)=\sin b x \), are shown below for \( x \in\left[-180^{\circ} ; 180^{\circ}\right] \). 8.1 Determine; 8.1.1 the value of \( a \) and \( b \). 8.1.2 the range of \( f \). 8.1.3 the period of \( g \). 8.2 Use the graph to determine the values of \( x \) for which; 8.2.1 \( \cos x-0,5 \sin 2 x-1=-1 \) 8.2.2 \( f(x) \) is increasing and \( g(x) \) is decreasing. 8.2.3 \( g(x)>0 \) and \( f(x) \) increasing. 8.2.4 \( g(x)-f(x)=2 \)

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Melissa Munoz verified

Numerade educator

The cylinder shown below has a radius r cm, height of h cm and a volume of 500 cm³. Calculate h and the total surface area

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Keondre Parker verified

Numerade educator

The diagram below shows the cross-section of a solid made up of a hemisphere placed on top of a right circular cone with radius r and slant height s. The perpendicular height of the cone, h, is 6,5 cm and the volume of the cone is 83,38 cm³. Calculate, correct to TWO decimal places. 1.1. The radius r of the cone 1.2. The slant height s of the cone 1.3. The surface area of the solid 2. Consider the solid hemisphere with a radius of 4 cm. Calculate to 2 decimal places the: 2.1. Volume 2.2. Surface area of the solid 2.3. If the radius is doubled, what would be the ratio of the volume of the original sphere to the volume of the new sphere.

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Eduard Sanchez verified

Numerade educator

A frustrating is formed by removing a small right circular cone from a similar larger right circular cone. The height of the small right circular cone is 20 cm and the height of the larger circular cone is 40 cm. The diameter of the larger right circular cone is 30 cm. 1. Write down the radius of the smaller cone with reason. 2. Calculate the volume of the frustum in cm³.

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Oswaldo Jiménez verified

Numerade educator

Use the Lagrange Interpolation to find a quadratic polynomial that fits the data below, x0=1 f(x0)=0 x1=4 f(x1)=1.386294 x2=6 f(x2)=1.791759

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Kathleen Carty verified

Numerade educator

In 2000, the population of a country was approximately 5.63 million, and by 2050 it is projected to 10 million. Use the exponential growth model, in which t is the number of years after 2000 and P0 is in​ millions, by which year will the population be 12 million?

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Khushbu Rani verified

Numerade educator

A pot of soup starts at a temperature of 373.0 K, and the surrounding temperature is 293.0 K. If the cooling constant is k = 0.00150 1/s, what will the temperature of the pot of soup be after 20.0 minutes?

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Khushbu Rani verified

Numerade educator

Suppose a population of butterflies is growing according to the logistic equation. If the carrying capacity is 500 butterflies and k = 0.1 individuals/(individual x month), what is the maximum possible growth rate for the population?

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INSTANT ANSWER

\[ \begin{tikzpicture} \begin{axis}[ xlabel={Time (days)}, ylabel={Mass remaining (mg)}, xmin=0, xmax=40, ymin=0, ymax=800, xtick={0,5,10,15,20,25,30,35,40}, ytick={0,100,200,300,400,500,600,700,800}, legend pos=north east, grid style=dashed, width=10cm, height=7cm ] \addplot[color=blue,domain=0:40,samples=100]{800*exp(-ln(2)/5*x)}; \legend{Mass remaining} \end{axis} \end{tikzpicture} \]

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Danielle Fairburn verified

Numerade educator

Example 1: Solve a certain organism develops with a constant relative growth of 0.2554 per member per day. Suppose the organism starts on day zero with 10 members. Find the population size after 7 days. Example 2: A population of a small city had 3000 people in the year 2000 and has grown at a rate proportional to its size. In the year 2005 the population was 3700. (a.) Find an expression for the number of people in the city t years after the year 2000. (b.) Estimate the population of the city in 2006. In 2010. (c.) Find the rate of growth of the population in 2006. (d.) Assuming the growth continues at the same rate, when will the town have 25000 people?

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