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3 years ago

What is the 100th term of 1, 6, 11, 16

Mathematics

1 answer:

Advocard [28]3 years ago

6 0

Answer:

496

Step-by-step explanation:

a+99d

1+ 99 (5)

1+ 495

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Is the line for the equation x = 4 horizontal or vertical? What is the slope of the line? Select the best answer

Arlecino [84]

Answer:

x=4 is vertical line it's an undefined slope

7 0

3 years ago

Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66

Ipatiy [6.2K]

Answer:

Summation notation is:

$\sum_{n=1}^{16}[5(x-1)-9]$

If you prefer it a little more simplified:

$\sum_{n=1}^{16}(5x-14)$

Step-by-step explanation:

First my favorite part, finding a pattern between the consecutive terms.

This is an arithmetic series because the terms are going up by 5 each time.

So arithmetic sequence, think linear equations:

x | y

1 -9

2 -4

3 1

4 6

..................

n 66

We are going to have to find that n but will will eventually...

The equation for a line in point slope form is $y-y_1=m(x_x_1)$ where $(x_1,y_1)$ is a point on the line and m is the slope.

We are already have the slope is 5 (the slope is the common difference in arithmetic sequence).

I'm going to use the first point (1,-9).

So the equation in point slope form is $y-(-9)=5(x-1)$

Subtract 9 on both sides:

$y=5(x-1)-9$

Now we need to know how many terms we are adding so what is x if y=66.

$66=5(x-1)-9$

Add 9 on both sides:

$75=5(x-1)$

Divide both sides by 5:

$15=x-1$

Add 1 on both sides:

$16=x$

We have 16 terms in this sequence where the 16th term is 66.

Summation notation is:

$\sum_{n=1}^{16}[5(x-1)-9]$

You could simplify the 5(x-1)-9.

Distribute: 5x-5-9

Add like terms: 5x-14

3 0

3 years ago

Read 2 more answers

A wooden plank is leaning against a wall. The bottom of the plank is 3 feet from the wall. Answer each of the following question

Nadusha1986 [10]

AB = ==> distance between the bottom of the plank; and the wall ===> 3 ft.

C ====> 49 degrees

For letter a, to solve for AC:

AC ==> HYPOTENUSE. The angle C is the OPPOSITE side of AB.

use sine :

sin A ===> opposite/hypotenuse

Solve:

sin 49 ====> 3/AC

AC ====> 3 / sin 49

AC ====> 3.96 ft.

For letter b, to solve for BC:

We are now given with the base (3 ft.); and; the hypotenuse (3.96 ft.) so we can use the Pythagorean theorem:

a^2 + b^2 = c^2

Let:

a ===> AB

b ===> BC

c ===> AC

(AB)^2 + (BC)^2 ===> (AC)^2

3^2 + (BC)^2 ===> (3.96)^2

(BC)^2 ===> (3.96)^2 - 3^2

(BC)^2 ===> 6.6816

sqrt (BC)^2 ===> sqrt 6.6816

Answer: BC ===> 2.58 ft.

Hope that helps!!!! : )

3 0

3 years ago

Distance formula derived from Pythagorean theorem

allsm [11]

Answer:

The Distance Formula itself is actually derived from the Pythagorean Theorem which is a 2 + b 2 = c 2 {a^2} + {b^2} = {c^2} a2+b2=c2 where c is the longest side of a right triangle (also known as the hypotenuse) and a and b are the other shorter sides (known as the legs of a right triangle).

Step-by-step explanation:

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3 years ago

Read 2 more answers

82. Close shave Which of two brands (X or Y) of electric

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