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3 years ago

8

The longest straight line you can draw within this circle is 3.6 inches long. What is the circumference of this circle?

1 answer:

nydimaria [60]3 years ago

3 0

Answer:

18 inches.

Step-by-step explanation:

We can connect two points of a circle in many ways, as you can see in the picture below.

The longest straight line that you can draw to connect two points is the diameter, that is, the straight line that passes through the center of the circle.

If the circle has 9 inches of radius the diameter will be 9+9 = 18 inches.

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Find a and b so that f(x) = x^3 + ax^2 + b will have a critical point at (2,3).

Digiron [165]

Using the critical point concept, it is found that a = -3 and b = 7.

<h3>What are the critical points of a function?</h3>

The critical points of a function are the values of x for which:

$f^{\prime}(x) = 0$

In this problem, the function is:

$f(x) = x^3 + ax^2 + b$

Hence, the derivative is:

$f^{\prime}(x) = 3x^2 + 2ax$

Then:

$f^{\prime}(x) = 0$

$3x^2 + 2ax = 0$

$x(3x + 2a) = 0$

$x = 0$

$3x + 2a = 0$

$3x = -2a$

$x = -\frac{2a}{3}$

Since the critical point is at x = 2, we have that:

$-\frac{2a}{3} = 2$

$-2a = 6$

$2a = -6$

$a = -3$

Then:

$f(x) = x^3 - 3x^2 + b$

Critical point at (2,3) means that when $x = 2, y = 3$ , then:

$3 = 2^3 - 3(2)^2 + b$

$8 - 12 + b = 3$

$b = 7$

You can learn more about the critical point concept at brainly.com/question/2256078

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1 year ago

A plane flying horizontally at an altitude of 3 mi and a speed of 440 mi/h passes directly over a radar station. find the rate a

Licemer1 [7]

The distance is increasing at a rate that is the speed of the plane multiplied by the cosine of the angle between its flight path and the direct line to the radar station. That cosine is 4/√(3²+4²) = 4/5, so the distance is increasing at
440 mi/h × 4/5 = 352 mi/h

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3 years ago

Plase help me I already set the equation up I just need you to solve it.

masya89 [10]

$\sf \frac{6}{30} = \frac{x}{100}$

Solve for x by cross multiplication

$\sf6 \times 100 = x \times 30$

Multiply the numbers

$\sf \: 600 = 30x$

Swap the sides of equation

$\sf \: 30x = 600$

Divide both sides of equation by 30

$\boxed{ \tt \: x = 20}$

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MAVERICK [17]

I have done this question yesterday it is 1 and 3

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Nastasia [14]

Answer:

B is correct

Step-by-step explanation:

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