During the decay of a radioactive substance, the rate of decay(the rate at which the mass is lost) is proportional to the mass present at that instant. Let M denote the mass in grams of radioactive Thorium 229 at time t in years after it has been introduced, where the initial amount of Thorium-229 was Mo = 112

g. Now M satisfies the differential equation

ball is thrown off a cliff. Its height (in feet) after 𝑡 seconds is given by the function ℎ(𝑡) = 200 + 100𝑡―16𝑡2Graph this function in Desmos. Use the Graph Settings button (the wrench) to set the X-axis to go from ―2 to 10 and the Y-axis from 50 to 500. Use the graph to answer the following questions. Give the values as they appear on the graph. Include units.

A coconut is fired from a cannon at the edge of a cliff over the water. The height of the coconut above the water is

hx=-32x2502+x+250

where x is the horizontal distance of the coconut from the face of the cliff. Height and horizontal distance are both measured in feet.

Graph the function in Desmos. Move/zoom as needed to see the graph.

Display the coordinates of all intercepts, maximum points, and minimum points by clicking on each point. Take a screenshot. Paste the screenshot below, then answer the questions about this scenario.

Scenario: A reclamation facility uses raw sewage as a source of water.

• Calculate microbial concentrations that meet daily acceptable risk. Assume that people drink 2 L of water daily. The daily intake dose based on probability of infection [D(Pi)] is 4.62 x10-7 for rotavirus, 5.61 x10-5 for Shigella, and 6.52 x10-5 for Cryptosporidium.

• How many log10 reductions are required to protect public health? Assume that the sewage contains the following concentrations of pathogens: rotavirus (enteric virus) 104 /100mL, Shigella 103 /100mL, and Cryptosporidium 105 /100mL

3. (6 pts) Determine whether the function

f(t) = 8/(1+t)

satisfies the hypotheses of the Mean Value Theorem on the interval [0, 3]. If so, find a value e in [0, 3] that satisfies the conclusion of the Mean Value Theorem

Which of the following committee recommended for Panchayati Raj System in India?

How many tiers are in the Panchayati Raj system of India?

(a) One-tier

(b) Two-tier

(c) Three-tier

(d) Four-tier

Which of the following system is established on the basis of the direct election?

(a) Gram Panchayat

(b) Block Committee

(c) Zila Parishad

(d) Both b and c

Which of the following statements is not correct?

(a) Panchayati Raj was established in India by Jawahar Lal Nehru

(b) Madhya Pradesh was the first state which implemented The Panchayati Raj system in India

Which of the following statements is not correct?

(a) Panchayati Raj was established in India by Jawahar Lal Nehru

(b) Madhya Pradesh was the first state which implemented The Panchayati Raj system in India

(c) 73rd Constitutional amendment was implemented in 1992

(d) Tamil Nadu has adopted the bicameral method

Which of the following Article is related to Panchayati Raj?

(a) Article 243

(b) Article 324

(c) Article 124

(d) Article 73

What was the main purpose behind bringing the Panchayati Raj system in India?

(a) To Prevent criminalization of politics

(b) Development of villages

(c) Decentralisation of the political power to the general peoples

(d) To reduce election expenses