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3 years ago

A particle decays at a rate of 0.45% annually. assume and initial amount of 300 mg. (

1 answer:

6 0

The increase is an exponential increase in a multiplier
$100%+0.45%=100.45%$ and as decimal 1.0045

Final Value = Initial Value × $multiplier^{number of years}$
Final value = $300(1.0045)^{60}$
Final value = 393 mg (to the nearest whole number)

Half life = 0.5 years
Final value = $300(1.0045)^{0.5}$ =301 mg

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2 years ago

On a coordinate plane, a parabola opens up. It goes through (negative 2, 4), has a vertex at (0.25, negative 6), and goes throug

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The statements true about the the function f(x) = 2x2 – x – 6 are-

The vertex of the function is (one-quarter, negative 6 and one-eighth).
The function has two x-intercepts.

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The vertex of parabola is the point at the intersection of parabola and its line of symmetry.

Now the given function is,

f(x) = 2x^2 – x – 6

Also, it is given that the vertex is located at (0.25, -6) and the parabola opens up, the function has two x-intercepts.

Comparing the given function with standard form,

f(x) = a x^2 bx + c

By comprison we get,

a = 2

b = -1

c = -6

Now, x-coordinate of vertex is given as,

x = -b/2a

put the values we get,

x = -(-1)/2*2

or, x = 1/4

Put the value of x in given function, so y-coordinate of the vertex is given as,

f(1/4) = 2(1/4)² - 1/4 - 6

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The function has two x-intercepts.

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1 year ago

A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the

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The area of the square pyramid building is the amount of space on it

The maximum base length of the building is 67.42 cm

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The given parameters are:

Base = b

Slant height (l) = 5b

The lateral surface area is calculated using:

L = 2bl

So, we have:

L = 2 * b * 5b

Evaluate the product

L = 10b^2

The total surface area is calculated using:

T = L + b^2

So, we have:

T = 10b^2 + b^2

Evaluate the sum

T = 11b^2

The maximum surface area is 50,000 square feet

So, we have:

11b^2 = 50000

Divide both sides by 11

b^2 = 50000/11

Take the square root of both sides

b = 67.42

Hence, the maximum base length of the building is 67.42 cm