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san4es73 [151]
3 years ago
14

Kendall Swam (n) laps in the pool. Sophia swam 12 less than Kendall. How many laps did they swim altogether.

Mathematics
1 answer:
dezoksy [38]3 years ago
7 0

Kendall and Sophia swam (2n - 12) laps together

<em><u>Solution:</u></em>

Given that, Kendall Swam (n) laps in the pool

To find: Number of laps swam together

From given statement,

Number of laps by Kendall = n

Also, Sophia swam 12 less than Kendall

Therefore, number of laps swam by Sophia is 12 less than the number of laps by Kendall

Number of laps by Sophia = Number of laps by Kendall - 12

Number of laps by Sophia = n - 12

<em><u>How many laps did they swim altogether ?</u></em>

Number of laps swam together = Number of laps by Kendall + Number of laps by Sophia

Number of laps swam together = n + n - 12 = 2n - 12

Thus they swam (2n - 12) laps together

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3 years ago
Find AM, if AM = 6y-4 and MC = 2y+12.
aleksley [76]

Answer: 20

Step-by-step explanation:

Since Line l is a segment bisector, we know that AM and MC are equal to each other.

6y-4=2y+12        [subtract both sides by 2y]

4y-4=12              [add both sides by 4]

4y=16                 [divide both sides by 4]

y=4

Now that we have y, we plug that into AM.

6(4)-4                 [multiply]

24-4                   [subtract]

20

Now, we know that AM is 20.

6 0
3 years ago
A line passes through the point (-1,-5) and has a slope of -5.
Anna71 [15]
<h3>hello!</h3>

We're given a point that the line intersects and its slope.

Let's use Point-slope:-

\boxed{y-y1=m(x-x1)}

y1 = -5

m=-5

x1=-1

\boxed{y-(-5)=-5(x-(-1)}

\boxed{y+5=-5(x+1)}

Convert to slope-intercept:-

\boxed{y+5=-5x-5}

\boxed{y=-5x-5-5}

Finally,

\bigstar{\boxed{\pmb{y=-5x-10}}

<h3>note:-</h3>

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

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2 years ago
Find maclaurin series
Mumz [18]

Recall the Maclaurin expansion for cos(x), valid for all real x :

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Then replacing x with √5 x (I'm assuming you mean √5 times x, and not √(5x)) gives

\displaystyle \cos\left(\sqrt 5\,x\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt5\,x\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^{2n}}{(2n)!}

The first 3 terms of the series are

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and the general n-th term is as shown in the series.

In case you did mean cos(√(5x)), we would instead end up with

\displaystyle \cos\left(\sqrt{5x}\right) = \sum_{n=0}^\infty (-1)^n \frac{\left(\sqrt{5x}\right)^{2n}}{(2n)!} = \sum_{n=0}^\infty (-5)^n \frac{x^n}{(2n)!}

which amounts to replacing the x with √x in the expansion of cos(√5 x) :

\cos\left(\sqrt{5x}\right) \approx 1 - \dfrac{5x}2 + \dfrac{25x^2}{24}

7 0
3 years ago
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