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3 years ago

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A sign says that the price marked on all music equipment is 35% off the original price. You want to buy an electric guitar for t

he $315. Write an equation to represent the total cost c for the price p with a 35% discount

1 answer:

zaharov [31]3 years ago

8 0

Step-by-step explanation:

c=p-0.35p

If the guitar is 315 dollars, then the price with discount is 204.75

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Find a formula for the sum of n terms. Use the formula to find the limit as n → [infinity]. lim n → [infinity] n 2 + i n 8 n i =

Masteriza [31]

Complete Question

Find a formula for the sum of n terms. $\sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )$

Use the formula to find the limit as $n \to \infty$

Answer:

$K_n = \frac{n + 73 }{n}$

$\lim_{n \to \infty} K_n = 1$

Step-by-step explanation:

So let assume that

$K_n = \sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )$

=> $K_n = \sum\limits_{i=1}^n ( \frac{16}{n} + \frac{2i}{n^2} )$

=> $K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)$

Generally

$\sum\limits_{i=1}^n (k) = \frac{1}{2} n (n + 1)$

So

$\sum\limits_{i=1}^n (8) = \frac{1}{2} * 8* (8 + 1)$

$\sum\limits_{i=1}^n (8) = 36$

$K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)$

and

$\sum\limits_{i=1}^n (i) = \frac{1}{2} n (n + 1)$

Therefore

$K_n = \frac{72}{n} + \frac{2}{n^2} * \frac{1}{2} n (n + 1 )$

$K_n = \frac{72}{n} + \frac{1}{n} (n + 1 )$

$K_n = \frac{72}{n} + 1 + \frac{1}{n}$

$K_n = \frac{72 + 1 + n }{n}$

$K_n = \frac{n + 73 }{n}$

Now $\lim_{n \to \infty} K_n = \lim_{n \to \infty} [\frac{n + 73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [\frac{n}{n} + \frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 + \frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 ] + \lim_{n \to \infty} [\frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = 1 + 0$

Therefore

$\lim_{n \to \infty} K_n = 1$

5 0

3 years ago

Find the distance between the two points. (-5,5) (1,-2)

makkiz [27]

Answer:

The distance between the points is 9.219544457292887

Step-by-step explanation:

7 0

2 years ago

Mr. Smith drew an obtuse triangle with side lengths of 4 cm, 6 cm, and 8 cm. In addition to being an obtuse triangle, what kind

Ulleksa [173]

Answer:

Scalene

Step-by-step explanation:

With this question, it's best to draw it out or we can use process of elimination.

We can rule out Right as the triangle is already obtuse (it can't be both).

We can rule out Equilateral as all the sides are not equal.

We can also rule out Isosceles as this triangle requires 2 sides to be equal, which clearly, they aren't.

Therefore, we are left with Scalene (C) which is your answer.

A scalene triangle has no identical sides or angles, and can be obtuse, right or acute.

Hope this helps,

Cate

3 0

3 years ago

Please help! I've been working on this for a few days and I just don't understand, it's due in a few hours. Thank you.

never [62]

Answer:

Part A: α = arc tan (y/x) = tan⁻¹ (y/x)

Part B: quadrant II α = arc tan (- y/x) = arc (- tan (y/x)) = - tan⁻¹ (y/x) 180°>α>90°

quadrant III α = arc tan (-y)/(-x) = arc tan (y/x) = tan⁻¹ (y/x) 270°>α>180°

quadrant IV α = arc tan (- y/x) = arc (- tan (y/x)) = - tan⁻¹ (y/x) 360°>α>270°

Part C: quadrant II 180°>α>90° α = tan⁻¹ (-6/1) = - tan⁻¹ 6 = 180° - 80.53° = 99.47°

Step-by-step explanation:

PART A:

In this case we will use trigonometric function tanα to calculate angle α:

tanα = y/x => α = arc tan (y/x) = tan⁻¹ (y/x)

This formula is use in general way and in first quadrant 90°>α>0°

Part B:

But in the other quadrants you must know to use unit circle to reduce angle from II, III and IV quadrant to the first quadrant.

If angle is in the quadrant II 180°>α>90° then

tanα = - tan (180°-α)

If angle is in the quadrant III 270°>α>180° then

tanα = tan (α-180°)

If angle is in the quadrant IV 360°>α>270° then

tanα =- tan (360°-α)

Part C:

vector w (x,y) = (-1,6) this vector lies in quadrant II 180°>α>90°

180°- α = tan⁻¹ (-6/1) = - tan⁻¹ 6 = 80.53° => 180° - α = 80.53°

α = 180° - 80.53 = 99.47°

It's not easy to understand this, but it's not easy for me to explain.

God with you!!!

5 0

2 years ago

Kari has x green apples and y red apples. Which statement explains why x + y and y + x will each find the total number of apples

ehidna [41]

X+y and y+x are the same as stated by the commutative law.
This is because let’s say x=2 and y=3,
2+3=5 and 3+2=5

3 0

2 years ago