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3 years ago

A 33 gram sample of a substance that's

Mathematics

1 answer:

Mazyrski [523]3 years ago

6 0

9514 1404 393

Answer:

6.2

Step-by-step explanation:

We presume your "k-value" is the k in the exponential decay term ...

e^(-kt) . . . where t is the number of time units

This is 1/2 when ...

ln(1/2) = -kt

t = ln(1/2)/(-k) = ln(2)/k

t = 0.69315/0.1124 ≈ 6.2

The half life is about 6.2 time units.

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Which these numbers cant round to 35 35.6 35.1 350.96 35.001 135.1

Ede4ka [16]

35.001 is the closest of the 5 to 35.

8 0

3 years ago

2. Find the next three terms of the sequence.

Fudgin [204]

Answer:

The correct answer is D. -2,592, -15,552, -93,312

Step-by-step explanation:

Each of the terms is the previous term multiplied by 6. You can find this by taking any term and dividing it by the one before it. The answer will always be 6.

-72/-12 = 6

-12/-2 = 6

So, in order to find the next 3, we take the last term and multiply it by 6.

-432 * 6 = -2,592

-2,592 * 6 = -15,552

-15,552 * 6 = -93,312

4 0

3 years ago

Describe how to find the number of seats on the middle and lower levels of the stadium when solving for the variable only gives

dezoksy [38]

Answer:

Use the value for the variable to solve for the other unknowns. Substitute the value for the variable into the expression for the number of seats on the middle level. Substitute the value for the variable into the expression for the number of seats on the lower level.

5 0

3 years ago

Read 2 more answers

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$