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2 years ago

What is the exact distance from (-5, 1) to (3,0)?

1 answer:

8 0

Distance is calculated by the square root of (x2-x1)^2 + (y2-y1)^2

We simply substitute the values into this formula

Square root of (3--5)^2 + (0-1)^2

Which is 8

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Which expression is equivalent to log Subscript c Baseline StartFraction x squared minus 1 Over 5 x EndFraction?

Harrizon [31]

The equivalent expression of $\log_c(\frac{x^2 - 1}{5x})$ is $\log_c(x^2 - 1) - \log_c(5x)$

<h3>How to determine the equivalent expression?</h3>

The logarithmic expression is given as:

$\log_c(\frac{x^2 - 1}{5x})$

The law of logarithm states that:

log(a) - log(b) = log(a/b)

This means that the expression can be split as:

$\log_c(\frac{x^2 - 1}{5x}) = \log_c(x^2 - 1) - \log_c(5x)$

Hence, the equivalent expression of $\log_c(\frac{x^2 - 1}{5x})$ is $\log_c(x^2 - 1) - \log_c(5x)$

Read more about equivalent expression

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3 0

1 year ago

This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 681

aleksley [76]

Answer:

680 games

Step-by-step explanation:

Suppose that 681 tennis players want to play an elimination tournament.

1st round:

One of 681 players, chosen at random, sits out that round and 680 players play. There will be 340 winners plus one player which sits - 341 players for the next round and 340 games

2nd round:

There will be 170 winners plus one player which sits - 171 players for the next round and 170 games

3rd round:

There will be 85 winners plus one player which sits - 86 players for the next round and 85 games

4th round:

There will be 43 winners - 43 players for the next round and 43 games

5th round:

There will be 21 winners plus one player which sits - 22 players for the next round and 21 games

6th round:

There will be 11 winners - 11 players for the next round and 11 games

7th round:

There will be 5 winners plus one player which sits - 6 players for the next round and 5 games

8th round:

There will be 3 winners - 3 players for the next round and 3 games

9th round:

There will be 1 winner plus one player which sits - 2 players for the next round and 1 game

10th round - final:

1 champion and 1 game.

In total,

340 + 170 + 85 + 43 + 21 + 11 + 5 + 3 + 1 + 1 = 680 games

4 0

2 years ago

Brainliest for a math answer

erastovalidia [21]

Question 5- is 9
question 6- is 9
question 7-is 4
question 8-is 21
Question 9-is 2
question 10-not sure sorry :(

Tell me if your right ;)

5 0

2 years ago

Read 2 more answers

What is the volume of the solid?

kherson [118]

Answer:

The volume of a solid is the measure of how much space an object takes up. It is measured by the number of unit cubes it takes to fill up the solid. Counting the unit cubes in the solid, we have 30 unit cubes, so the volume is: 2 units⋅3 units⋅5 units = 30 cubic units.4

Step-by-step explanation:

I hope it's helpful u

6 0

2 years ago

A golfball is hit from the ground with an initial velocity of 200 ft/sec. The horizontal distance that the golfball will travel,

algol13

Answer:

The golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of $\pi/4$ .

Step-by-step explanation:

The formula from the maximum distance of a projectile with initial height h=0, is:

$d(\theta)=\frac{v_i^2sin(2\theta)}{g}$

Where $v_i$ is the initial velocity.

In the closed interval method, the first step is to find the values of the function in the critical points in the interval which is $[0, \pi/2]$ . The critical points of the function are those who make $d'(\theta)=0$ :

$d(\theta)=\frac{v_i^2\sin(2\theta)}{g}\\d'(\theta)=\frac{v_i^2\cos(2\theta)}{g}*(2)\\d'(\theta)=\frac{2v_i^2\cos(2\theta)}{g}$

$d'(\theta)=0\\\frac{2v_i^2\cos(2\theta)}{g}=0\\\cos(2\theta)=0\\2\theta=\pi/2,3\pi/2,5\pi/2,...\\\theta=\pi/4,3\pi/4,5\pi/4,...$

The critical value inside the interval is $\pi/4$ .

$d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\d(\pi/4)=\frac{v_i^2sin(2(\pi/4))}{g}\\d(\pi/4)=\frac{v_i^2sin(\pi/2)}{g}\\d(\pi/4)=\frac{v_i^2(1)}{g}\\d(\pi/4)=\frac{(200)^2}{32}\\d(\pi/4)=\frac{40000}{32}\\d(\pi/4)=1250ft$

The second step is to find the values of the function at the endpoints of the interval:

$d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\\theta=0\\d(0)=\frac{v_i^2sin(2(0))}{g}\\d(0)=\frac{v_i^2(0)}{g}=0ft\\\theta=\pi/2\\d(\pi/2)=\frac{v_i^2sin(2(\pi/2))}{g}\\d(\pi/2)=\frac{v_i^2sin(\pi)}{g}\\d(\pi/2)=\frac{v_i^2(0)}{g}=0ft$

The biggest value of f is gived by $\pi/4$ , therefore $\pi/4$ is the absolute maximum.

In the context of the problem, the golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of $\pi/4$ .

4 0

2 years ago