A rocket is fired upward from ground level with an initial velocity of 1600ft/sec . When will the rocket be above 1000ft? Show your work. Round your answer to the nearest tenths. Write the answer in set notation.

[tex] \green{\large\underline{\sf{Solution-}}}[/tex]

Given expression is

[tex]\rm :\longmapsto\:\dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } [/tex]

can be rewritten as

[tex]\rm \:  =  \: \dfrac{5 \times { {(5}^{2} )}^{n + 1} - {5}^{2} \times {5}^{2n} }{5 \times {5}^{2n + 3} - {( {5}^{2} )}^{n + 1} } [/tex]

We know,

[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ {( {x}^{m} )}^{n} \: = \: {x}^{mn}}}} \\ [/tex]

And

[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}} \\ [/tex]

So, using this identity, we

[tex]\rm \:  =  \: \dfrac{5 \times {5}^{2n + 2} - {5}^{2n + 2} }{{5}^{2n + 3 + 1} - {5}^{2n + 2} } [/tex]

[tex]\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 4} - {5}^{2n + 2} } [/tex]

can be further rewritten as

[tex]\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 2 + 2} - {5}^{2n + 2} } [/tex]

[tex]\rm \:  =  \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2} - 1)} [/tex]

[tex]\rm \:  =  \: \dfrac{4}{25 - 1} [/tex]

[tex]\rm \:  =  \: \dfrac{4}{24} [/tex]

[tex]\rm \:  =  \: \dfrac{1}{6} [/tex]

Hence,

[tex]\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } = \frac{1}{6} }}[/tex]

Answer:

i think it is same let me know

[tex] - \frac{2}{ \sqrt{2} } \\ \\ in \: \: alternate \: \: form \\ \\ = - 0.7070107[/tex]

hope it helps

Answer:

300,621

Step-by-step explanation:

Answer:

angle x is 86

angle y is 38

Step-by-step explanation:

Answer:

y = -2x + 9 or y = 9 - 2x

Step-by-step explanation:

First find the gradient

Next, look at where the line intercepts (goes through) the y-axis: 9

The equation of the line is y = -2x + 9

Tip: The gradient is negative because the line is going downwards from left to right; if the line was going upwards, the gradient would be positive.

Hope this helps!

Answer: 24 boxes

Step-by-step explanation:

Answer:

Arianna can move 24 boxes

5

3:5

256 fluid ounces

Step-by-step explanation:

Answer:

its 34/5

Step-by-step explanation:

change that mixed fraction by simply multiplying 6×5 then add 4 you'll get 34 then place it over the denominator 5 =34/5........ hope it helps

Answer:

k=50º

m=90º

Step-by-step explanation:

a line is 180º total

so 130+k=180

k=50

a triangle also is 180º total

so 180-40-k=m

180-40-50=m

90=m

Step-by-step explanation:

Answer:

B) or C)

Step-by-step explanation:

Answer:

result is $6432.00 | 221.43

Answer:

442

Step-by-step explanation:

Answer:

Step-by-step explanation:

6) At y-intercept , x = 0

So, y-intercept = 3

5) Slope = Change in y/ change in x

              [tex]= \dfrac{3-1}{0-[-3]}\\\\= \dfrac{2}{0+3}\\\\= \dfrac{2}{3}[/tex]

Answer:

[tex]v = \frac{1}{2} a {t}^{2} \\ a = \frac{2v}{ {t}^{2} } [/tex]

'a' can be expressed in terms of 'v' and 't' as -

[tex]$a=\frac{2v}{t^{2} }[/tex]

We have the following expression -

[tex]$v = \frac{1}{2} at^{2}[/tex]

We have to express → a in terms of v and t.

On solving, we get -

Sin([tex]2n\pi x[/tex]) = 0.785

Sin([tex]2n\pi x[/tex]) = Sin ([tex]\frac{\pi }{4}[/tex])

2n[tex]\pi[/tex]x =  [tex]\frac{\pi }{4}[/tex]

x =  [tex]$\frac{1}{8n}[/tex]

According to the question, we have -

[tex]$v = \frac{1}{2} at^{2}[/tex]

[tex]$a=\frac{2v}{t^{2} }[/tex]

Hence, 'a' can be expressed in terms of 'v' and 't' as -

[tex]$a=\frac{2v}{t^{2} }[/tex]

To solve more questions on Rearranging expressions, visit the link below-

brainly.com/question/8864600

#SPJ2

Answer:

k = 6

Step-by-step explanation:

Answer:

270.15

Step-by-step explanation:

Answer:

270.15

Step-by-step explanation:

u just add 52 and 18.72 and subtract it from 340.87

Answer:

x should equal 0

Step-by-step explanation:

Answer: 3x^2 +13x - 10

Step-by-step explanation:

(x+5)(3x-2) = x(3x-2) + 5(3x-2)

x(3x-2) + 5(3x-2) = 3x^2 - 2x + 15x - 10

3x^2 - 2x + 15x - 10 = 3x^2 + 13x - 10

Answer:

3x²+13x-10

Step-by-step explanation:

Answer:

15*4=60;60*3.5=210

Step-by-step explanation:

60 is the number of baskets Lucy makes in an hour,210 is her 3.5 hours of baskets

Answer:

answer is 1/4 × 3 1/2 =

3 1/8

Answer:

3 3/2x1/2

Step-by-step explanation:

Answer:

40.05

Step-by-step explanation:

multiplicas la cantidad de monedas por su valor:

2 monedas de 10 = 20

3 de 5 = 15

7 de 0.50 = 3.50

5 de 0.25 = 1.25

3 de 0.10 = 0.30

sumas lo multipicado:

40.05

Step-by-step explanation:

the answer is in the image above

The spider's movement is an illustration of a parabola.

(a) The equation

The spider passes through the origin.

So, we have:

[tex]\mathbf{(x,y) = (0,0)}[/tex]

The spider jumps to a maximum height of 10mm, midway 80mm.

So, the vertex is:

[tex]\mathbf{(h,k) = (40,10)}[/tex]

The equation of a parabola is:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

So, we have:

[tex]\mathbf{0 = a(0 - 40)^2 + 10}[/tex]

Subtract 10 from both sides

[tex]\mathbf{a(0 - 40)^2 =- 10}[/tex]

[tex]\mathbf{1600a =- 10}[/tex]

Solve for a

[tex]\mathbf{a =- \frac{1}{160}}[/tex]

Substitute [tex]\mathbf{a =- \frac{1}{160}}[/tex] and [tex]\mathbf{(h,k) = (40,10)}[/tex] in [tex]\mathbf{(h,k) = (40,10)}[/tex]

[tex]\mathbf{y = -\frac{1}{160}(x - 40) + 10}[/tex]

(b) The focus, directrix and the axis of symmetry

The focus of a parabola is:

[tex]\mathbf{Focus= (h, k + p)}[/tex]

Where:

[tex]\mathbf{p = \frac{1}{4a}}[/tex]

So, we have:

[tex]\mathbf{p = \frac{1}{4 \times -1/160}}[/tex]

[tex]\mathbf{p = -\frac{160}{4}}[/tex]

[tex]\mathbf{p = -40}[/tex]

So, we have:

[tex]\mathbf{Focus = (40,10-40)}[/tex]

[tex]\mathbf{Focus = (40,-30)}[/tex]

The axis of symmetry is:

[tex]\mathbf{x = h}[/tex]

So, we have:

[tex]\mathbf{x = 40}[/tex]

The directrix is:

[tex]\mathbf{y = k - p}[/tex]

[tex]\mathbf{y = 10 + 40}[/tex]

[tex]\mathbf{y = 50}[/tex]

Read more about parabolas at:

https://brainly.com/question/25237745

Answer:

22, 25, 28

Step-by-step explanation:

10 + 3 = 13

13 + 3 = 16

16 + 3 = 19

19 + 3 = 22

22 + 3 = 25

25 + 3 = 28.

all numbers go up by three points

Answer:

The width is: 11

The length is: 2

Step-by-step explanation:

The width is 5 feet longer than 3 times the length so

If the length is 2: 2 x 3 times = 6 plus the five = 11

The area of a rectangle is a = the width x the lenght

So 2 x 11 = 22 that is the area.

Answer:

I believe it helps the reader understand the mood of Frederick town. I hope this helps you! :)

Answer:

5.4772255750516 that's if it is x squared

Answer:

x=36

Step-by-step explanation:

first take six away from both sides to get 3/4x=27

then divide 27 by the numerator 3 to get 9. Then multiply 9 by the denominator 4 to get 36. So 3/4 of 36=27+6=33

3/4x+6=33

We move all terms to the left:

3/4x+6-(33)=0

Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R

We add all the numbers together, and all the variables

3/4x-27=0

We multiply all the terms by the denominator

-27*4x+3=0

We multiply elements

-108x+3=0

We move all terms containing x to the left, all other terms to the right

-108x=-3

x=-3/-108  

x=1/36

I hope this helps :)