(b) Suppose a rocket, as designed, cannot provide enough velocity to achieve a stable orbit. Could alterations to the rocket make a stable orbit achievable? Explain.

The missing value of direct variation is 56/3

The direct variation property states that , whenever the division of values of two quantities is a constant value then there is same variation between these two corresponding values. Or we can also say that if the divisible nature of two corresponding values is constant, then one quantity is directly varies with second quantity. That mean if one quantity increase other will also increase and vice versa.

Let say if x and y are two values and k is a constant value, then

According to direct variation

k = y/x or y = k x

In the given question,

Take the order pair (3,7)

As it is an direct variation, we can substitute it

y=k x  

7=k (3)

K=7 / 3

Now find the direct variation equation

y=k x

Also, k=7/3

Solve this equation for the second pair (8,y)

As, y=7/3 x

   y= 7/3 (8) = 56/3

Therefore, missing value is 56/3

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In mathematics, an inverse function is one that "reverses" another function. The inverse of each function y = 3x + 1 is y = x−13.

The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f is bijective.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.

Let the function be y = 3x+1

Replacing f(x) with y, we get

y = 3x+1

simplifying the above equation, we get

x = 3y + 1

Subtracting 1 from both sides to get

3y = x − 1

Dividing both sides by 3, we get

y = x−13

Replace y with f⁻¹(x), we get

f⁻¹(x) = x−13

The inverse of each function y = 3x+1 is f⁻¹(x) = x−13.

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Answer: x=8

Step-by-step explanation: i did this exact question on OW

The required simplification of an expression is 2(x + 1) / (x + 4)(x + 4).

What is an expression?

An expression is any statement in mathematics written using numbers, variables and at least one operation present.

Simplification of the expression: 2x - 8 / x² - 16 . x² + 5x + 4 / x² + 8x + 16

Given an expression,

2x - 8 / x² - 16 . x² + 5x + 4 / x² + 8x + 16

On simplifying, we get,

(2x - 8).(x² + 5x + 4) / (x² - 16).(x² + 8x + 16)

For the numerator, (2x - 8).(x² + 5x + 4), we have,

= 2(x + 1)(x - 4)(x + 4)

For the denominator,  (x² - 16).(x² + 8x + 16)

= (x + 4)(x - 4)(x + 4)(x + 4)

Now, (2x - 8).(x² + 5x + 4) / (x² - 16).(x² + 8x + 16)

= 2(x + 1)(x - 4)(x + 4) / (x + 4)(x - 4)(x + 4)(x + 4)

= 2(x + 1) / (x + 4)(x + 4)

The restriction to the given expression is that the denominator,  x + 4 should not be 0.

Hence, the required simplification of an expression is 2(x + 1) / (x + 4)(x + 4).

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Answer:

100

Step-by-step explanation:

a quadrilateral has a total of 4 angles

so the sum of all four angles is 360degre

so let the two equal angles be 2x

so 110+50+2x=360

    2x=360-160

    2x=200

     x=200/2

therefore x = 100

log x-log y = log ( x/y) we  use this properties Quotient in the equation.

A logarithm is defined simply?

How does exponential growth utilise e?

You use this properties Quotient in the equation -

log x-log y = log ( x/y)

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Answer:

151 cm² (i don't know what unit you were given so im going to use cm)

Step-by-step explanation:

Part One: finding the missing side (h)

h = a² = b² + c²

13² = 12² + c²

169 = 144 + c²

169 - 145 = c²

= 25

square root of 25 = c

5 = c

area of top triangular area = ½ b × h

= ½ × 12 × 5

= 30 cm²

Part Two

area of rectangle = l × b

= 12 × 8

= 96 cm²

Part Three

area of square = l × l

= 5 × 5

= 25 cm²

total surface area = (30 + 96 + 25) cm²

= 151 cm²

Using logarithmic quotient rule, we expand each logarithm function log√2x/y as 1/2 log (2x) - log (y).

According to the question, we need to expand  we expand logarithm function log√2x/y .In Logarithms, the power is raised to some numbers (usually, base number) to get some other number. It is an inverse function of exponential function.

Quotient rule for logarithm: log (a/b) = log (a) - log(b).

⇒ log√2x/y

Applying quotient rule to the above logarithm function, we get

log√2x/y = log (√2x) - log (y)

= log (2x)^1/2 - log (y)  →(1)

Power rule for logarithm: log (a)ˣ = x log (a)

Applying power rule to the equation (1), we get

log (2x)^1/2 - log (y) = 1/2 log (2x) - log (y)

Hence, using logarithmic quotient rule, we expand each logarithm function log√2x/y as 1/2 log (2x) - log (y).

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David travelled 32 kilometres of the entire trip by foot

David travelled 4/5 of his trip by bicycle and the rese was done by foot

The whole trip was 160 km

The first step is to calculate the distance travelled with the bicycle

4/5 × 160

= 128

Therefore the distance travelled by foot can be calculated as follows

= 160-128

= 32

Hence David travelled 32km by foot

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Answer:32

Step-by-step explanation:32

Answer:

the answer is A

Answer:

Step-by-step explanation:

b is the aswswer

Answer:

x= 0 (B)

Step-by-step explanation:

hope this helps

The inverse of the function x^7 is x^-7 and it is also a function.

An inverse function or an anti function is defined as a function, which can reverse into another function.

A standard method to find inverse of a function is to set y=f(x)

let y= f(x)=x^7

thus

[tex]\sqrt[7]{y}[/tex]=x

thus [tex]f^{-1}[/tex](y)=[tex]\sqrt[7]{y}[/tex]

thus [tex]f^{-1} (x)=\sqrt[7]{x}[/tex]

(To verify this if a function is inverse or not we are required to check for the identity)

f([tex]f^{-1}[/tex](x))=[tex]f^{-1}[/tex](f(x))=x

Therefore, The inverse of the function x^7 is x^-7 and it is also a function.

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The value of the given equation is x = ln(4) / 3 ≈ 0.4621

The features of log are employed to expand (or compress) a single logarithm into numerous logarithms. A logarithm is simply another way to express exponents. Thus, logarithmic features are derived from exponentiation qualities.

e³x=12

Can be written as:

[e^x] [e^(2x)] = 4

Using the property of power multiplication utilizing the same base

e ^ (x + 2x) = 4

e ^ (3x) = 4

Applying logarithm  properties both side:

3x = ln(4)

ln(4) / 3 ≈ 1.38629 / 3 ≈ 0.4621

The value of the given equation is x = ln(4) / 3 ≈ 0.4621

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Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (8, 2 ) and (x₂, y₂ ) = (10, 2 )

m = [tex]\frac{2-2}{10-8}[/tex] = [tex]\frac{0}{2}[/tex] = 0

Answer: D

Explained: you find the solutions to x and the y axis to graph

Answer: i got no clue

Step-by-step explanation:

Answer:

32081.

Step-by-step explanation:

-9x-9+5^3x4^4

Using PEMDAS, the exponents are calculated first:

= -9 x -9 + 125 x 256

Next the multiplications:

= 81 + 32000

= 32081.

Answer:

The answer is 12.

Step-by-step explanation:

Let the smallest number = x and the largest number = x+2(since the three numbers are consecutive, we would have to use x+2. If we wanted the second largest number, it would be x+1)

We would write the statement "four times the smallest integer is equal to six more than more than three times the largest" as:

4x = 3(x+2) + 6

Now just solve.

4x = 3x+6+6     distributive property

4x = 3x+12        simplify

x  = 12               subtraction property

And since x is the smallest number, we have our answer.

Therefore, the answer is 12.

Answer:

Diagram A

Step-by-step explanation:

a line of best fit can only be drawn if thier is strong negative or positive correlation

well, double of 10000 is 20000, so hmmm happens in 12 years, ok

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$20000\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}[/tex]

[tex]20000=10000\left(1+\frac{~~ \frac{r }{100 } ~~}{1}\right)^{1\cdot 12} \implies \cfrac{20000}{10000}=\left( 1+\cfrac{r}{100} \right)^{12} \\\\\\ 2=\left( \cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{2}=\cfrac{100+r}{100}\implies 100\sqrt[12]{2}=100+r \\\\\\ 100\sqrt[12]{2}-100=r\implies {\LARGE \begin{array}{llll} \stackrel{\%}{5.95}\approx r \end{array}}[/tex]

now, what will it be after 10 years assuming we use 5.95%?  mind you that's a rounded figure, but close enough.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to 5.95\%\to \frac{5.95}{100}\dotfill &0.0595\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=10000\left(1+\frac{0.0595}{1}\right)^{1\cdot 10} \implies {\LARGE \begin{array}{llll} A \approx 17824.18 \end{array}}[/tex]

The probability that exactly two of selected are 75W is 0.2967 , probability that exactly two of the selected bulbs are rated 75W is 0.2637 , probability that one bulb of each type is selected is 0.0747  .

Probability of an event E denoted by P(E) is defined as number of favorable outcomes divided by total number of outcomes.

In the given question

40W bulbs = 4

60W bulbs = 5

75W bulbs = 6

Total number of bulbs = 4+5+6=15.

Part(a)

probability that exactly two of the selected bulbs are rated 75-w

Selection of 3 bulbs from 15 bulbs can be done in C(15,3) ways.

[tex]=\frac{15!}{3!*12!}[/tex]

[tex]=\frac{15*14*13*12!}{12!*3!} \\ \\ =\frac{15*14*13}{3*2*1}[/tex]

=455 ways

Total number of ways = 455      ...(i)

Now,

Number of ways of selecting 2 ,75W bulbs and 1 bulb from the remaining is C(6,2)*C(9,1).    

= C(6,2)*C(9,1)

[tex]=\frac{6!}{2!*4!} *\frac{9!}{1!*8!} \\ \\ =\frac{6*5*4!}{2*4!} *\frac{9*8!}{8!}[/tex]

[tex]=\frac{6*5}{2} *9\\ \\ =15*9\\ \\ =135[/tex]

the probability that exactly two selected bulbs are rated 75W = 135/455 =0.2967

Part(b)

probability that one bulb of each type is selected .

Number of ways of selecting one bulb from each type = selecting 1 bulb from four 40W bulbs + 1 bulb from 60W bulbs + 1 bulb from 75W bulbs.

Number of ways of selecting one bulb from each type=C(4,1)*C(5,1)*C(6,1)

[tex]=C(4,1)*C(5,1)*C(6,1)\\ \\ =\frac{4!}{3!*1!} *\frac{5!}{4!*1!} *\frac{6!}{5!*1!}[/tex]

[tex]=\frac{4*3!}{3!} *\frac{5*4!}{4!} *\frac{6*5!}{5!}[/tex]   ...( as 1!=1)

[tex]=4*5*6\\ \\ =120[/tex]

Number of ways of selecting one bulb from each type = 120

Total number of ways = 455     ...from equation (i)

Probability that exactly two bulbs selected are rated 75W =120/455

=0.2637

Part(c)

probability that all three of the selected bulbs have the same rating

Number of ways three bulbs of same rating are selected = (all 3 from 40W bulbs )+(all 3 are from 60W bulbs )+( all 3 are from 75 W bulbs)

[tex]=C(4,3)+C(5,3)+C(6,3)[/tex]

[tex]=\frac{4!}{1!*3!} +\frac{5!}{2!*3!} +\frac{6!}{3!*3!} \\ \\ =\frac{4*3!}{3!} +\frac{5*4*3!}{2!*3!} +\frac{6*5*4*3!}{3*2*3!}[/tex]...( as1!=1)

[tex]=4+10+20[/tex]

[tex]=34[/tex]

Number of ways three bulbs of same rating are selected = 34

Total number of ways = 455     ...from equation (i)

Probability that all three of the selected bulbs have the same rating=34/455 = 0.0747

Therefore ,(a) the probability that exactly two of selected are 75W is 0.2967 , (b) probability that exactly two of the selected bulbs are rated 75W is 0.2637 (c)  probability that one bulb of each type is selected is 0.0747  .

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]6x-7y=-4\implies 6x=7y-4\implies 6x+4=7y \\\\\\ \cfrac{6x+4}{7}=y\implies \qquad \stackrel{\stackrel{m}{\downarrow }}{\cfrac{6}{7}} x+\cfrac{4}{7}=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

now, since we know that slope, let's check for a perpendicular line to it

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{6}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{6}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{6}}}[/tex]

so we're really looking for the equation of aline whose slope is -7/6 and that it passes through (-6 , 5)

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- \cfrac{7}{6}}(x-\stackrel{x_1}{(-6)}) \implies y -5= -\cfrac{7}{6} (x +6) \\\\\\ y-5=-\cfrac{7}{6}x-7\implies {\LARGE \begin{array}{llll} y=-\cfrac{7}{6}x-2 \end{array}}[/tex]

Answer:

Please read and try to understand it :>

Step-by-step explanation:

[tex]6x-7y=-4[/tex] is not the standard format for a straight line so you have to rearrange it:

[tex]y=\frac{6}{7} x +\frac{4}{7}[/tex]

To find the equation of a perpendicular line to the given equation, you have to first find the negative reciprocal of the gradient:

[tex]-\frac{7}{6}[/tex]

Since you want to find the equation of a perpendicular line that passes a certain point, you have to substitute the coordinates to the equation to find the y-intercept:

[tex]5=-\frac{7}{6} (-6)+c[/tex]

Solving:

[tex]5=-\frac{7}{6} (-6) +c\\ \\ 5=\frac{42}{6} +c\\ \\-\frac{42}{6} +5=c\\ \\-7+5=c\\\\ -2=c[/tex]

Final equation: [tex]y=-\frac{7}{6} x -2[/tex]

The distance of the earth from the star is mathematically given as

2.537 x 10¹⁵ miles

Generally, the Coefficients for the problem are mathematically given a

Coefficients =4.6 x 5.9

Coefficients =27.14

For Exponents

Exponents  10² x 10¹² = 10⁽²⁺¹²⁾

Exponents =10¹⁴

In conclusion, After that, we put them together once again to produce a scientific notation:

25.37 x 10¹⁴

2.537 x 10¹⁵ miles

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Answer:

31 minutes in total

Step-by-step explanation:

Going step by step, where m = minutes after the first 3:

0.58 + 0.15m = 4.78

We want to solve for m, so we need to isolate it. The first step is to get rid of 0.58 to simplify our equation.

0.15m = 4.78 - 0.58

Now we have:

0.15m = 4.20

To isolate further, we need to remove 0.15.

m = 4.20 / 0.15

m = 28

Now, we add the first 3 minutes to m to get our total time.

28 + 3 = 31

Answer:

Can I see a diagram?

Step-by-step explanation:

The taxi ride was 11.2 miles

Fabian took a ride from his house to the airport

The taxi company charged 4.80 and 4 per miles

The total fare amount was 44.80, the fee was not inclusive

The number of miles can be calculated as follows

= 44.80/4

= 11.2

Hence the taxi ride was 11.2 miles

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Answer:

Step-by-step explanation:-12+4x-7x=12-3x.

UR MOM IS GONNA BE SO PROUD OF YOU!!!!!!!!!!!!!

When thinking about the small group as a system, the key component that connects all of the system's relevant parts is D. Communication.

It should be noted that the system framework is important as it reminds us that the piece of puzzle interacts with each other.

Therefore, when thinking about the small group as a system, the key component that connects all of the system's relevant parts is communication.

The sender, also known as the communicator or source, is where communication starts. The sender wishes to share some kind of information with the recipient(s), such as a request, query, or idea.

Understanding comes through good communication. Four essential elements make up the communication process. These elements consist of encoding, transmission medium, decoding, and feedback.

It should be noted that communication links the parts together.

Therefore when thinking about the small group as a system, the key component that connects all of the system's relevant parts is Communication.

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The solution to the given inequality in inequality and interval notation form are x < 5 and ( -∞,5 ) respectively.

Given the inequality in the question;

4 + 6.5x < 36.5

First, move all terms not containing x to the right side of the inequality.

4 + 6.5x < 36.5

6.5x < 36.5 - 4

Subtract 4 from 36.5

6.5x < 36.5 - 4

6.5x < 32.5

Divide both sides by the coefficient of x

6.5x < 32.5

6.5x/6.5 < 32.5/6.5

x < 32.5/6.5

x < 5

The solution in inequality form is x < 5

The solution in interval notation is ( -∞,5 ).

Therefore, the solution to the given inequality in inequality and interval notation form are x < 5 and ( -∞,5 ) respectively.

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Answer:

X < 5

Step-by-step explanation:

The solution is so subtract the 4 with the 4 and 36.5 you cross out the 4 and subtract 4 form 36.5 which leaves you with 32.5. Then to get the variable by itself you divide 6.5 on both sides, then cross out the 6.5 and divide 6.5 on 32.5 which gives you 5. (I solved it by myself)

Expression as a single natural logarithm is 0.01234567901.

Given in the question an expression

ln 3 + 5 ln 3

ln 3 +  ln [tex]3^{5}[/tex]

Apply multiplication rule

ln (3/[tex]3^{5}[/tex])

[tex]3^{5}[/tex] = 243

so

expression as a single natural logarithm is 0.01234567901.

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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