Угол при основании равнобедренного

PLZ HELP THIS IS TIMED!!!!

mihalych1998 [28]

Answer:

For the sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

Hence the formula $f(x)=-\frac{2}{3}(6)^{x-1}$ for x=1,2,3,... represents the given geometric sequence

Step-by-step explanation:

Given sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

To find the formula to describe the given sequence :

Let $a_1=\frac{-2}{3}$ , $a_2=-4$ , $a_3=-24$ ,...

First find the common ratio

$r=\frac{a_2}{a_1}$ here $a_1=\frac{-2}{3}$ and, $a_2=-4$

$=\frac{-4}{\frac{-2}{3}}$

$=\frac{4\times 3}{2}$

$=\frac{12}{2}$

$r=6$

$r=\frac{a_3}{a_2}$ here $a_2=-4$ and $a_3=-24$

$=\frac{-24}{-4}$

$=6$

$r=6$

Therefore the common ratio is 6

Therefore the given sequence is geometric sequence

The nth term of the geometric sequence is

$a_n=a_1r^{n-1}$

The formula which describes the given geometric sequence is

$f(x)=a_1r^{x-1}$ for x=1,2,3,...

$=\frac{-2}{3}6^{x-1}$ for x=1,2,3,...

Now verify that $f(x)=a_1r^{x-1}$ for x=1,2,3,... represents the given geometric sequence or not

put x=1 and the value of $a_1$ in $f(x)=a_1r^{x-1}$ for x=1,2,3,...

we get $f(1)=-\frac{2}{3}(6)^{1-1}$

$=-\frac{2}{3}(6)^0$

$=-\frac{2}{3}$

Therefore $f(1)=-\frac{2}{3}$

put x=2 we get $f(2)=-\frac{2}{3}(6)^{2-1}$

$=-\frac{2}{3}(6)^1$

$=-\frac{12}{3}$

Therefore $f(2)=-4$

put x=3 we get $f(3)=-\frac{2}{3}(6)^{3-1}$

$=-\frac{2}{3}(6)^2$

$=-\frac{2(36)}{3}$

Therefore $f(3)=-24$

Therefore the sequence is f(1),f(2),f(3),...

Therefore the sequence is $-\frac{2}{3}$ ,-4 ,-24 ,-144 ,...

Hence the formula $f(x)=a_1r^{x-1}$ for x=1,2,3,... represents the given geometric sequence is verified

Therefore the formula $f(x)=-\frac{2}{3}(6)^{x-1}$ for x=1,2,3,... represents the given geometric sequence

7 0

4 years ago

Read 2 more answers

Which of the following pairs of lines are perpendicular? Select all that apply

ad-work [718]

Perpendicular lines will have negative reciprocal slopes

B. y = -4x+ 5 and y = 1/4x + 4
D. y = x + 4 and y = -x + 4
E. y = -3 and x = -3

4 0

3 years ago

A circle has diameter endpoints at (7,2) and (p,8), p > 0, and the circle is tangent to the x axis. The circle’s equation can

ycow [4]

Answer:

yes

Step-by-step explanation:

7 0

3 years ago

Marianna would like to create a mosaic using pieces that have only four angles. Which shapes could Marianna use?

viva [34]

Answer:

Step-by-step explanation:

Cube

8 0

3 years ago

Read 2 more answers

indicate whether the measures 8, 14, and 16 can be the side lengths of a triangle. if they can, classify the triangle.

Aleksandr-060686 [28]

Answers:

A triangle is possible.

The triangle is acute and scalene

=============================================================

Explanation:

We use the triangle inequality theorem to see if a triangle is possible with these side lengths.

Consider the side lengths a, b, and c. A triangle is possible if and only if the following 3 conditions hold true

a+b > c
a+c > b
b+c > a

Basically pick any two sides. If the sum is larger than the third side, then a triangle is possible.

-----------------

In this case we have: a = 8, b = 14, c = 16. The order of the a,b,c values doesn't really matter.

Then:

a+b = 8+14 = 22 which is larger than c = 16. So a+b > c is true.
a+c = 8+16 = 24 is larger than b = 14. So a+c > b is true.
b+c = 14+16 = 30 is larger than a = 8. So b+c > a is true.

All three inequalities mentioned are true; therefore, a triangle is possible with these side lengths.

-----------------

We'll use those a,b,c values in the converse of the pythagorean theorem to determine what kind of triangle this is. So far we know it's scalene because all three side lengths are different. It would be isosceles if it had exactly two equal sides, and equilateral if all 3 sides were the same length.

$a^2+b^2 = c^2\\\\8^2+14^2 = 16^2\\\\260 = 256\\\\$

The last equation is false, which tells us this triangle is not a right triangle. It's either acute or obtuse.

Since $a^2+b^2 > c^2$ is the case here, we can conclude the triangle is acute

If $a^2+b^2 < c^2$ was the case, then the triangle would be obtuse.

-----------------

Summary:

A triangle is possible with side lengths a = 8, b = 14, c = 16.
This triangle is scalene and acute

4 0

1 year ago