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Morgarella [4.7K]

3 years ago

9

The probability of Roger winning the tournament, given that Stephan wins, is 0. The probability of Stephan winning the tournamen

t, given that Roger wins, is 0. Given this information, which statement is true?

1 answer:

Fofino [41]3 years ago

7 0

They're both true. Both statements, together, make one
single fancy way of saying "Only one man can win.".

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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:

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

So, the point of contact between the tangent line and C is (-1, -3).

7 0

2 years ago

A number d minus is less than -1

katrin [286]

$\boxed{d-4$

<h2>Explanation:</h2>

Hello! Recall you need to write complete questions in order to find exact answers. So in this problem I'll assume the question is:

<em>A number d minus 4 is less than -1</em>

<em />

So it is easy to know that we need to write an inequality here because of the words "less than", which implies that we must use the symbol <. So let's solve this step by step.

Step 1. A number d minus 4.

This statement includes the word "minus", so we need to use the symbol (-). Therefore:

$d-4$

Step 2. A number d minus 4 is less than

As we said above, here we need to use the symbol (<). So:

$d-4$

Step 3. A number d minus 4 is less than -1

Finally, we get:

$d-4$

<h2>Learn more:</h2>

Inequalities: brainly.com/question/9611462

#LearnWithBrainly

3 0

3 years ago

The quotient of the cube root of x and nine

miss Akunina [59]

Answer:

$\frac{ \sqrt[3]{x} }{9}$

Quotient means the answer after dividing two numbers.

8 0

3 years ago

Brainliest + points!<br><br> Please explain

zepelin [54]

Answer:

C

Step-by-step explanation:

Legs are the sides of an isosceles triangle that aren't the base, so in this case ZX would be the base. This rule is only for isosceles triangles. It doesn't apply to any other type of triangle.

Hope I helped, sorry if I'm wrong!

~Mschmindy

6 0

3 years ago

Read 2 more answers

The lines below are parallel. If the slope of the green line is -3, what is the

siniylev [52]

Answer:

m=-3

Step-by-step explanation:

Since the lines are parallel to each other, their gradients are equal.

∴ gradient of green line = gradient of red line

∴ m = -3

6 0

2 years ago

Read 2 more answers