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3 years ago

Find the oth term of the geometric sequence 9, -18, 36, ...

Mathematics

1 answer:

Sphinxa [80]3 years ago

3 0

Answer:

2304

Step-by-step explanation:

Given :-

A geometric sequence is given to us which is 9 , -18 , 36.

And we need to find out the 9th term of the sequence. Here firstly we should find the Common Ratio and then we can substitute the respective values in the formula to find the nth term of a geometric sequence .

Common Ratio :-

$:\implies$ CR = -18÷ 9 = -2

The 9 th term :-

$:\implies$ T_n = arⁿ - ¹

$:\implies$ T_9 = 9× (-2) ⁹ - ¹

$:\implies$ T_9 = 9 × (-2)⁸

$:\implies$ T_9 = 9 × 256

$:\implies$ T_9 = 2304

Hence the 10th term is 2304.

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a rocket was launched into the air from a platform above the ground. The height, in feet, of the rocket above the ground t secon

vova2212 [387]

For this case we have the following expression:
h (t) = -16t ^ 2 + 64t + 80
For t = 0 we have:
h (0) = -16 (0) ^ 2 + 64 (0) + 80
h (0) = -0 + 0 + 80
h (0) = 80 feet
Therefore the number 80 represents the initial height of the rocket
Answer:
the 80 in the expression represented:
the initial height of the rocket

5 0

2 years ago

Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

3 years ago

Write an expression for the next 3 even numbers that are greater than P

Alisiya [41]

Every even number is 2 away from the last.
0, 2, 4, 6, 8, 10, 12, 14...etc.

If we had an even number p, then the next three even numbers would be
p+2, p+4, and p+6.

(If we had an odd number p, then the next three even numbers would be
p+1, p+3, and p+5. I'm not sure if p is even is implied in the question. Technically the answer would be p - p mod 2 + 2, where p is an interger...that gets into more technical function stuff, though.)

5 0

3 years ago

Read 2 more answers

Is 6^-2 positive or negative? Explain.

Gnoma [55]

Answer:

It's positive when you have 6^-2 it's the same as having $(\frac{1}{6})^{2} \\$ . So 6^-2 it's 1/36.