The half-life of radium-226 is 1620 yr. Given a sample of 1 g of radium-226, the quantity left Q(t) (in g) after t years is given by:Q(t)= 1/2^t/1620

Required:
a. Convert this to an exponential function using base e.
b. Verify that the original function and the result from part (a) yield the same result for Q(0), Q(1620), and Q(3240).

Answers

Answer 1
Answer:

Answer:

(a)e^(-0.000428 t)

Step-by-step explanation:

We are given that

Half life of radium-226=1620 yr

The quantity left Q(t) after t years is given by

Q(t)=((1)/(2))^{(t)/(1620)}

a. We have to convert the given function into an exponential function using base e.

Q(t)=((1)/(2))^{(t)/(1620)}

=(((1)/(2))^t)^{(1)/(1620)

=e^(ln(1/2) t/1620)

=e^({(ln(1/2))/(1620)t)

=e^(-0.000428 t)

(b)

Q(0)=e^(-0.000428 * 0)

=1

From original function

Q(0)=1

Q(1620)=((1)/(2))^{(t)/(1620)}

Q(1620)=(1)/(2)=0.5

From exponential function

Q(1620)=e^(-0.000428 * 1620)

=0.499\approx 0.5

Q(3240)=((1)/(2))^{(3240)/(1620))=0.25

Q(3240)=e^(-0.000428 * 3240)

Q(3240)=0.249=\approx 0.25

Hence, verified.


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B. We can't determine from the given information.
C. Exactly one
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Answers

The correct answer to this question is letter "B. We can't determine from the given information."

Using the information as stated, "If j and k are intersecting lines, A and B are points on j, and C and D are points on k," the number of planes that contain points A, B, C, and D cannot be determined because of the lack of information.

Please help the first people were wrong!!!

Answers

Answer:

The surface area is about 267.04 cm^2; the surface area would be divided by 4 if the slant height and diameter were to be cut in half

A parking lot is 100 yards long. What is the length of 3/4 of the parking lot, in feet? (Not in words)

Answers

1 yard = 3 feet.

100 yards x 3 = 300 feet.

300 feet x 3/4 = 225 feet.

The answer is 225 feet.

Answer:

225 ft hope it helps

What is the value of a + 4b / a + b if a = -4, b = 3

Answers

Answer:- 8

Step-by-step explanation:

-4 + 4(3)/ -4+3

-4 +12 / -1

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A rectangle is inscribed in a circle.Calculate the area of the circle. Use 3.14 for π. Round to the nearest hundredth.

1___ Square centimeters

2 Calculate the area of the rectangle.

3. Calculate the area of the shaded region. Use 3.14 for π. Round to the nearest hundredth.

Answers

Answer:

1. The area of the circle is 132.67 square centimeters

2. The area of the rectangle is 60 square centimeters

3. The area of the shaded region is 72.67 square centimeters

Step-by-step explanation:

* Lets explain how to solve the problem

- A rectangle is inscribed in a circle, that means the vertices of the

 rectangle lie on the circumference of the circle

∴ The diagonal of the rectangle = the diameter of the circle

- From the attached figure

∵ The diameter of the circle = 13 cm

∵ The radius of the circle is half the diameter

∴ The radius of the circle = 1/2 (13) = 6.5 cm

- The area of the circle = πr²

∵ π = 3.14

∴ The area of the circle = 3.14 × (6.5)²  = 132.67 cm²

1. The area of the circle is 132.67 square centimeters

- The area of any rectangle = length × width

∵ The length of the rectangle is 12 cm

∵ The width of the rectangle is 5 cm

∴ The area of the rectangle = 12 × 5 = 60 cm²

2. The area of the rectangle is 60 square centimeters

- The area of the shaded region is the difference between the

  area of the circle and the area of the rectangle

∵ The area of the circle = 132.67 cm²

∵ The area of the rectangle = 60 cm²

∵ The area of the shaded region = area of circle - area of rectangle

∴ The area of the shaded region = 132.67 - 60 = 72.67 cm²

3. The area of the shaded region is 72.67 square centimeters

Given tan(theta)= -2 and pi/2 < theta < pi; find cos theta)

Answers

Answer:

\cos \theta=-(1)/(√(5))

Step-by-step explanation:

Given\ \tan \theta=-2\ \ \ \ \ -(\pi)/(2)<\theta<\pi

Hence \theta is in second quadrant.

\tan \theta=(opposite)/(adjacent)=-2\n\nLength\ of\ opposite=2,\ \ Length\ of\ adjacent=1\n

Pythagorean Theorem:hypotenuse^2=opposite^2+adjacent^2

hypotenuse^2=(1)^2+(2)^2=1+4=5\nhypotenuse=√(5)

\cos \theta=(adjacent)/(hypotenuse)\n\n\cos \theta=(1)/(√(5))

But in the second quadrant \cos \theta will be negative.

Hence

\cos \theta=-(1)/(√(5))