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2 years ago

How can the equation of a parabola be derived when given the focus and the directrix

1 answer:

7 0

If the focus<span> of a </span>parabola<span> is and the </span>directrix<span> is , find the</span>equation<span> of the </span>parabola. Let ( x 0 , y 0 ) be any point on theparabola. Find the distance between ( x 0 , y 0 ) and the focus. Then find the distance between ( x 0 , y 0 ) and directrix<span>.</span>

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The radioactive element americium-241 has a half-life of 432 years. How many years will it take a 10 gram mass of americium-241

geniusboy [140]

<h2>Answer: 816 years</h2>

This problem can be solved using the <u>Radioactive Half Life Formula: </u>

<u />

$A=A_{o}.2^{\frac{-t}{h}}$ (1)

Where:

$A=2.7g$ is the final amount of the material

$A_{o}=10g$ is the initial amount of the material

$t$ is the time elapsed (the quantity we are asked to find)

$h=432y$ is the half life of americium-241

Knowing this, let's find $t$ from (1):

$2.7g=(10g).2^{\frac{-t}{432y}}$

$\frac{2.7g}{10g}=2^{\frac{-t}{432y}}$

$0.27g=2^{\frac{-t}{432y}}$

Applying natural logarithm in both sides:

$ln(0.27g)=ln(2^{\frac{-t}{432y}})$

$-1.309=-\frac{t}{432y}ln(2)$

$-t=\frac{(-1.309)(432y)}{0.693}$

<u></u>

<u>Finally:</u>

$t=816y$

3 0

3 years ago

In April, a customer buys 1 MCS Oct 50 call for 9 and sells 1 MCS Jul 50 call for 4. What will the customer's profit or loss be

Alexandra [31]

Answer:

The net gain or profit is $600

Step-by-step explanation:

Firstly, we should know the losses of the customer which were:

9 when the customer bought 1 MCS Oct 50

1 when the customer bought back 1 MCS Jul 50

Therefore the total losses were 10.

And the gains were:

4 when the customer sold 1 MCS Jul 50

12 when the customer sold 1 MCS Oct 50

Therefore the total gains were 16.

Therefore (16 - 10)×100 = $600

Therefore the net gain or profit is $600

5 0

3 years ago

If -2 and 3 are zeroes of quadratic polynomial xsquare + (a+1)x+b then find the value of and b

ohaa [14]

Answer:

a = - 2, b = - 6

Step-by-step explanation:

Substitute the values of the zeros into the polynomial and equate to zero.

x² +(a + 1)x + b

x = - 2 → (- 2)² - 2(a + 1) + b = 0 , that is

4 - 2a - 2 + b = 0

2 - 2a + b = 0 ( subtract 2 from both sides )

- 2a + b = - 2 → (1)

x = 3 → 3² + 3(a + 1) + b = 0, that is

9 + 3a + 3 + b = 0

12 + 3a + b = 0 ( subtract 12 from both sides )

3a + b = - 12 → (2)

Subtract (1) from (2) term by term to eliminate b

5a = - 10 ( divide both sides by 5 )

a = - 2

Substitute a = - 2 into either of the 2 equations and evaluate for b

Substituting into (2)

3(- 2) + b = - 12

- 6 + b = - 12 ( add 6 to both sides )

b = - 6

Thus a = - 2 and b = - 6

4 0

3 years ago

1 2 3 4 5 6 7 8 9 10

Maslowich

The graph that represents viable values for y = 2x is Option A.

<h3>What is a Straight Line Function ?</h3>

A straight line function is given by y = mx +c , where m is the slope and c is the y intercept.

The given equation is y = 2x

here m = 2

x is the number of pounds of rice scooped and purchased from a bulk bin

y is the total cost of the rice

as both the data cannot be negative , Option C , D is out of choice

The Option 1 represents a straight line and it starts at the origin which is satisfied by y = 2x as y = 0 , at x = 0

ends at point (2.5, 5) giving a slope of m =2 ,

Therefore , The graph that represents viable values for y = 2x is Option A.

To know more about Straight Line equation

brainly.com/question/959487

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6 0

2 years ago

Which expression is equivalent to 364ab7c9?

charle [14.2K]

What do you mean is there an image

6 0

2 years ago