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2 years ago

Find the minimum or maximum value of f (x) = x2 - 6x + 13.

Mathematics

1 answer:

Greeley [361]2 years ago

7 0

Minimum value is (3, 4)

It is the minimum value because the coefficient of x^2 is positive.

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In the state of North Carolina, the mean SAT Math score is 535 with a standard deviation of 95 points. Savannah,

konstantin123 [22]

Answer:

675

Step-by-step explanation:

6 0

2 years ago

Please look at the picture, I need help ASAP.

forsale [732]

See below for the proof that the areas of the lune and the isosceles triangle are equal

<h3>How to prove the areas?</h3>

The area of the isosceles triangle is:

$A_1 = \frac 12r^2\sin(\theta)$

Where r represents the radius.

From the figure, we have:

$\theta = 90$

So, the equation becomes

$A_1 = \frac 12r^2\sin(90)$

Evaluate

$A_1 = \frac 12r^2$

Next, we calculate the length (L) of the chord as follows:

$\sin(45) = \frac{\frac 12L}{r}$

Multiply both sides by r

$r\sin(45) = \frac 12L$

Multiply by 2

$L = 2r\sin(45)$

This gives

$L = 2r\times \frac{\sqrt 2}{2}$

$L = r\sqrt 2$

The area of the semicircle is then calculated as:

$A_2 = \frac 12 \pi (\frac{L}{2})^2$

This gives

$A_2 = \frac 12 \pi (\frac{r\sqrt 2}{2})^2$

Evaluate the square

$A_2 = \frac 12 \pi (\frac{2r^2}{4})$

Divide

$A_2 = \frac{\pi r^2}{4}$

Next, calculate the area of the chord using

$A_3 = \frac 12r^2(\theta - \sin(\theta))$

Recall that:

$\theta = 90$

Convert to radians

$\theta = \frac{\pi}{2}$

So, we have:

$A_3 = \frac 12r^2(\frac{\pi}{2} - \sin(\frac{\pi}{2}))$

This gives

$A_3 = \frac 12r^2(\frac{\pi}{2} - 1)$

The area of the lune is then calculated as:

$A = A_2 - A_3$

This gives

$A = \frac{\pi r^2}{4} - \frac 12r^2(\frac{\pi}{2} - 1)$

Expand

$A = \frac{\pi r^2}{4} - \frac{\pi r^2}{4} + \frac 12r^2$

Evaluate the difference

$A = \frac 12r^2$

Recall that the area of the isosceles triangle is

$A_1 = \frac 12r^2$

By comparison, we have:

$A = A_1 = \frac 12r^2$

This means that the areas of the lune and the isosceles triangle are equal

Read more about areas at:

brainly.com/question/27683633

#SPJ1

5 0

11 months ago

What is the slope of the line that lies between the points (0, -1) and (-1,2)?

Shkiper50 [21]

Answer:

m=-3

Step-by-step explanation:

3 0

2 years ago

Just b I need to know, I need explanation also.

Nastasia [14]

Answer:

$\implies \: 2.6851 \text{ \: ft}$

$\\$

Step-by-step explanation:

$\boxed{\boxed{ \blue\bigstar \red{ \bold{ \: \: math \: \: }} \blue\bigstar}}$

$\pink{\implies = \sqrt{ {36.1}^{2} - {36}^{2}} }$

$\orange{ \implies = \sqrt{1303.21} - 1.296}$

$\green{ \implies = \sqrt{7.21} }$

$\red{ \implies = 2.6851 \: \text{ft}}$

4 0

2 years ago

What is the midpoint of this segment??

Korvikt [17]

Answer:

A) 6,3

Why?

The midpoint, which is somewhat self-explanatory thanks to its name, is a point in the center of a line.

To answer this question properly, you need to analyze the line and assess the situation.

How did it go from x = 2 to x = 10? Let's see, if we count by two's across the line, you'll notice it makes more sense. So now we know that every square goes up by two. x = 6 is the exact center of the line.

I hope this wasn't confusing, it's tough to explain it!

3 0

2 years ago

Read 2 more answers