Contestants ABCDEFG and I are in a 10k race. In how many ways can C finish first and A finish second?

Answer:

- sin (x)

Step-by-step explanation:

hope this helps :)

Answer:  tan(-x) cos(-x) = -sin(x)

Step By Step Explanation:

tan(-x) cos(-x)

Use the negative angle Identity to get:

Cos (x) (-tan(x))

Remove the parenthesis to get:

-Cos (x) tan (x)

Express with sin,cos to get:

-sin(x)

I got my explanation from www.symbolab.com

https://www.symbolab.com/solver/simplify-calculator/tan%5Cleft(-x%5Cright)%20cos%5Cleft(-x%5Cright)%20%3D?or=input

,  Hope this Helps :)

Have a great day!!

The given curve has equation

r(θ) = 9 + 8 cos(θ)

and its derivative is

dr/dθ = -8 sin(θ)

When θ = π/3, we have r (π/3) = 13, and dr/dθ (π/3) = -4√3.

Differentiate these with respect to θ :

dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)

dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)

In polar coordinates, we have

y(θ) = r(θ) sin(θ)

x(θ) = r(θ) cos(θ)

and when θ = π/3, we have y (π/3) = 13√3/2 and x (π/3) = 13/2.

The slope of the tangent line to the curve is dy/dx. By the chain rule,

dy/dx = dy/dθ • dθ/dx = (dy/dθ) / (dx/dθ)

dy/dx = (dr/dθ sin(θ) + r(θ) cos(θ)) / (dr/dθ cos(θ) - r(θ) sin(θ))

When θ = π/3, the slope is

dy/dx = (-4√3 sin(π/3) + 13 cos(π/3)) / (-4√3 cos(π/3) - 13 sin(π/3))

dy/dx = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))

dy/dx = - 1/(17√3)

So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is

y - 13√3/2 = -1/(17√3) (x - 13/2)

y = -(x - 338)/(17√3)

9514 1404 393

Answer:

  center (-5, 3)

  radius 3

Step-by-step explanation:

Compare the given equation to the standard form equation of a circle:

  (x -h)² +(y -k)² = r² . . . . . . circle with center (h, k) and radius r

This shows us that ...

  -h = +5   ⇒   h = -5

  -k = -3   ⇒   k = 3

  r² = 9   ⇒   r = √9 = 3

Then the circle center is (h, k) = (-5, 3), and the radius is r = 3.

13/51 hours per pound

EXPLANATION

= 2 3/5 hours : 10 1/5 pound

= 13/5 hours : 51/5 pound

= 13/5 × 5/51 hours per pound

= 65/255 hours per pound

= 13/51 hours per pound

#LearnWithEXO

Answer:

Step-by-step explanation:

Let the width is x, then the area is:

Solving we get:

So correct choice is B

Answer:

1 1/4

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

3 3/4 ÷ 2 1/2

3/2

= 1.5

Answer:

A

Step-by-step explanation:

Answer:

The Correct answer is A

Step-by-step explanation:

The rate of inflation between year 1 and year 2, based on the CPI, is  c. 33.33%.

The Consumer Price Index (CPI) allows us to calculate inflation. To find the inflation across these years, use the formula:

= (CPI₂ - CPI₁) / CPI₁ x 100%

Solving gives us:

= (200 - 150) / 150 x 100%

= 33.3%

In conclusion, the inflation is 33.3%.

Find out more at https://brainly.com/question/17329174.

Answer:

6.75

Step-by-step explanation:

First, I just gave you the answer.

Second, just use it.

Answer:

Sum: 17 + 11 = 28

Difference: 17 - 11 = 6

Step-by-step explanation:

The sum of x and y is 28. In other words, x plus y equals 28 and can be written as equation A:

x + y = 28

The difference between x and y is 6. In other words, x minus y equals 6 and can be written as equation B:

x - y = 6

Now solve equation B for x to get the revised equation B:

x - y = 6

x = 6 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 28

6 + y + y = 28

6 + 2y = 28

2y = 22

y = 11

Now we know y is 11. Which means that we can substitute y for 11 in equation A and solve for x:

x + y = 28

x + 11 = 28

X = 17

Summary: The sum of two numbers is 28 and their difference is 6. What are the two numbers? Answer: 17 and 11 as proven here:

Sum: 17 + 11 = 28

Difference: 17 - 11 = 6

Answer:

17 +11 = 28

hope this helps

There is no picture attached :)

Answer:

The answer is D

Step-by-step explanation:

-7.6+4.17= -3.43x

3.54-1.32= 2.22

Answer:

A. Personal vacation expenses

Step-by-step explanation:

Because everything else either helps the community or is a required expense

The sample will also be normally distributed, with same mean as the population, so µ = 70.5, but the standard deviation would be divided by the square root of the sample size, so σ = 2.6/√5 ≈ 1.16.

N(70.5, 1.16)

The sample will also be normally distributed, with the same mean as the population(µ = 70.5) and the standard deviation of 1.16 inches.

A normal distribution is a probability distribution that is used to represent events with a default behaviour and accumulated potential departures from it.

As it is given that the heights of male seniors in high school closely follow a normal distribution N(µ,σ) = N(70.5,2.6), where the units are inches.

Therefore, the mean will be the same (µ = 70.5), but the standard deviation for the sample size of the heights of five male seniors, can be written as,

[tex]s=\dfrac{\sigma}{\sqrt n} = \dfrac{2.6}{\sqrt5} = 1.16[/tex]

Hence, The sample will also be normally distributed, with the same mean as the population(µ = 70.5) and the standard deviation of 1.16 inches.

Learn more about Normal Distribution:

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Answer:

Step-by-step explanation:

n = 41

There are 41 students on each bus.

Answer:

The ages of all three brothers are 4,6,8 years.

Step-by-step explanation:

Here n is the smallest of the three consecutive even integers, the condition gives you this equation

2n + 3*(n+2) + (n+4) = 34.

2n + 3n + 6 + n + 4 = 34

6n = 24

n = 4.

Answer. The ages are 4, 6 and 8 years.

Hope this helps you.

The ages of the three brothers are 6, 8, and 10 years, respectively.

Let the ages of the three brothers be \(x\), \(x+2\), and \(x+4\).

The sum of the first even integer, three times the second even integer, and twice the third even integer is fifty:

\[x + 3(x+2) + 2(x+4) = 50\]

Simplify the equation:

\[x + 3x + 6 + 2x + 8 = 50\]

Combine like terms:

\[6x + 14 = 50\]

Subtract 14 from both sides:

\[6x = 36\]

Divide by 6:

\[x = 6\]

So, the ages of the three brothers are 6, 8, and 10 years, respectively.

Learn more about integer at https://brainly.com/question/17695139

#SPJ3

Answer:

Line A is represented by the function f(x) = 2x + 1.

Step-by-step explanation:

Answer:

Inspect the graph to see if any vertical line drawn would intersect the curve more than once.

Step-by-step explanation:

If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

Answer:

$29

Step-by-step explanation:

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1.6 pounds of lettuce costs :

1 pound of lettuce costs :

Answer:

mean of first five whole number = (0+1+2+3+4)/5 = 2

Step-by-step explanation:

Whole is starts from 0.

Answer:

uhhhh I can't explain how but the answer is B. -39,366.

Answer:

since 7 is a prime number, the prime factors are 1 and 7.

Step-by-step explanation:

Answer:

1 and 7

Step-by-step explanation:

Since 7 is a prime number (meaning that there are no other factors that can be multiplied to equal 7) the prime factors of 7 would be 1 and itself.

I attached a photo below that shows the factor tree for 7.

Hope this explanation clears up any confusion you may have had! Let me know if you have any other questions :D