Use v=-0.0098 t+c ln R , where v is the velocity of the rocket, t is the firing time, c is the velocity of the exhaust, and R is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. Find the velocity of a spacecraft whose booster rocket has a mass ratio of 20 , an exhaust velocity of 2.7km/s, and a firing time of 30 s . Can the spacecraft achieve a stable orbit 300km above Earth?

Answer:7 and a half

Step-by-step explanation:

Simple enough, if it seven inches and grows half an inch a week than after a week it grows half an inch, so its just 7 + a half, your awnser is 7 and a half

Answer:

The values of x for the equation 5x² - 9x - 10 is x = 9 ± √(281) / 10.  

Step-by-step explanation:

In this question we need to solve the given equation that is 5x² - 9x - 10 to obtain the value of x using the complex solution method.

Now, the given equation is 5x² - 9x - 10 in which we need to apply the quadratic formula to find the solution;

So, the quadratic formula is => -b ± √(b² - 4ac) / 2a

Now, on comparing the equation 5x² - 9x - 10 we get the values;

a = 5

b = -9

c = -10

Further, on substituting the values given above in the quadratic formula to obtain the value of x.

=> -(-9) ± √((-9)² - 4(5×(-10)) / 2×5

=> 9 ± √(81 +200) / 10

=> 9 ± √(281) / 10

After simplifying the above equation we obtained the value of x that is;

=> x = 9 ± √(281) / 10

Now, the final values of x from the above condition are;

=> x = 9 + √(281) / 10  

and

=> x = 9 - √(281) / 10

It can be further represented in the decimal form;

=> x = 2.57630546...

and

=> x =  −0.77630546...

Thus, the values of x for the equation 5x² - 9x - 10 is x = 9 ± √(281) / 10.  

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Using the mean absolute deviation concept, it is found that:

1. One set of possible locations is given as follows: (40, 40, 40, 60, 60, 60).

2.  Another set of possible locations is given as follows: (39, 40, 41, 59, 60, 61).

Hence, for a mean of 50 and a mean absolute deviation of 10, with 6 pennies, we want data-sets with these following characteristics:

Hence:

1. One set of possible locations is given as follows: (40, 40, 40, 60, 60, 60).

2.  Another set of possible locations is given as follows: (39, 40, 41, 59, 60, 61).

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The solution for the inequality | x | + 9 ≤ 7 is (option d) x ≤ -2 and x > -16

You can solve an inequality by: adding the same amount to each side; taking the same amount away from each side; multiplying or dividing each side by the same positive amount. The inequality symbol needs to be turned around if either side is multiplied or divided by a negative number. Therefore, the answer is x > 1.

Given,

The expression:   | x | + 9 ≤ 7

If | x | ≤ a ⇒ -a ≤ x ≤ a

Then,

-7 ≤ | x | + 9 ≤ 7

⇒ -7 - 9 ≤ x ≤ 7 - 9

⇒ -16 ≤ x ≤ -2

That is x ≤ -2 and x > -16.

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The equation to find the nth term of the sequence is aₙ = 4n - 17

The equation of the sequence can be represented as follows;

a₃ = - 5, a₄ = - 1, a₅ = 3, a₆ = 7, a₇ = 11

Therefore, let's find the equation of the nth term.

Using arithmetic formula,

aₙ = a + (n - 1)d

where

Therefore,

d = 11 - 7 = 4

Hence, let's find the first term using 7th term

11 = a + 6(d)

11 = a + 6(4)

11 - 24 = a

a = - 13

Therefore, the equation to find the nth term of the sequence is as follows:

aₙ = -13 + (n - 1)4

aₙ = - 13 + 4n - 4

aₙ = - 13 - 4 + 4n

aₙ = 4n - 17

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Following is domain and range for given function -

A)The function's range is -5≤ a≤50.

The function's range is -50≤c≤150.

B) The information we got from equation of the function is used to determine domain and range.

Given,

The whole amount spent is $750.

As a result, our equation is

ca = 750

calculating c,

c = 750 / a

The function's domain and range are:

a ≤ 5

Each prize now needs to be under 50.

= 50 ≤ c

Using the formula, ac = 750

A's maximum value is 75.

we can say that domain is

5 ≤ a ≤ 50

Finally, by substituting a = 5 we can see that the maximum for c is 150.

This gives range for c as -

50 ≤ c ≤ 150

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The simplified form is [tex]5x^{3} y^{9}[/tex].

Simplify is to make something less complicated or much less cluttered. An instance of simplification is when you provide an explanation for a difficult math idea in truly smooth phrases for a kid to understand. An example of simplifying is whilst you chop out a whole lot of the activities that were making you busy and careworn. To turn out to be less difficult.

The phrase simplifies the approach to make something simpler to do or understand. So, by lowering or simplifying the fractions approach we make the fraction as simple as viable. We do this by dividing the numerator and the denominator via the biggest range that may divide into each number precisely.

Factoring the number,

[tex]125=5^{3}[/tex]

[tex]\sqrt[3]{5^{3} x^{6} y^{9} }[/tex]

Applying radical rule,

[tex]\sqrt[3]{5^{3} } =5^{9}[/tex]

[tex]5x^{3} y^{9}[/tex]

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Answer:

[tex] \sf \: x=0.4[/tex]

Step-by-step explanation:

-0.5x-3.69=x-1.9-2.39

Step 1: Simplify both sides of the equation.

−0.5x−3.69=x−1.9−2.39

−0.5x+−3.69=x+−1.9+−2.39

−0.5x−3.69=(x)+(−1.9+−2.39)(Combine Like Terms)

−0.5x−3.69=x+−4.29

−0.5x−3.69=x−4.29

Step 2: Subtract x from both sides.

−0.5x−3.69−x=x−4.29−x

−1.5x−3.69=−4.29

Step 3: Add 3.69 to both sides.

−1.5x−3.69+3.69=−4.29+3.69

−1.5x=−0.6

Step 4: Divide both sides by -1.5.

−1.5x/−1.5 = −0.6/−1.5

x=0.4

The value of x will be 0.4.

In mathematics, an equation is a connection of two expressions that is expressed as an equality on all sides of the corresponding sign.  A statement that uses the equal sign to show that both of the expressions possess the same value is called an equation. Mathematical equations are made up of figures, an equal sign, and an optional variable in the position of an unknowable value.

-0.5x-3.69=x-1.9-2.39

-0.5x - x = -1.9 - 2.39+3.69

Simplifying the given equation:

-1.5 x = - 0.6

x = 0.6 / 1.5

x = 0.4

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Answer:

[tex]\frac{1}{y^9}[/tex]

Step-by-step explanation:

Exponent rule → [tex]a^{-b}=\frac{1}{a^b}[/tex]

Using exponent rule → [tex]y^{-9}=\frac{1}{y^9}[/tex]

Final result → [tex]=\frac{1}{y^9}[/tex]

Answer: 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number =x

So, x*12*2=144

=12x=144/2

=12x=72

=x=72/12

=x=6

So the answer is 6 because 6*12=72 and doubling 72 gives us 144.

Have a great day!!!

Answer:

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

Given inequality:

Simplify and collect like terms:

The Solution for equation 2 ln x=4 is 7.4088.

2 ln x=4

( [tex]x^{2}[/tex]) = [tex]e^{4}[/tex]

[tex]x^{2}[/tex] = 54.598

x = √54.598

x = 7.4088

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Two expressions joined by the equals symbol ("=") form an equation. The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero.

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Answer:

+ x = 116/9

- x = 40

* x = -2/3 and x = 59/3

/ x =  -2/3

Step-by-step explanation:

Since it's unclear what operations here are all of them, plus, minus, multiply and divide. If you need Steps, let me know.

Answer:

34

Step-by-step explanation:

I really don't know I just wanted to answer for points

Answer:

The solution to this equation is (9t)^(12) / (4a)^(6).

Step-by-step explanation:

It is given that [(4a³t²)/(9at^6)]^-3 which is to be simplified and solved to get the final answer.

Now,

let us have a look at the equation and observe the powers given;

=> [(4a³t²)/(9at^6)]^-3

So, let us convert the powers using the rules;

=> [(4a²)/(9t^4)]^-3

Further, we will apply the rule known as product of powers and we get an equation that is;

=> (4a)^(-6) / (9t)^(-12)

Now, after reciprocating both the powers as per the rules we get;

=> (9t)^(12) / (4a)^(6)

Therefore, the solution to this equation is (9t)^(12) / (4a)^(6).

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Answer: Letter C

Step-by-step explanation:

just look at the problem a little closely

The solution of the equation  x² - 24 x + 144 = 0  is  x = 12 .

It is a quadratic equation , it will have 2 roots .

Using factorisation ,

x²-24 x+144=0

( [tex]x^{2}[/tex] - 12 x - 12 x + 144 ) = 0

x ( x - 12 ) - 12 ( x - 12 ) = 0

( x - 12 ) * ( x - 12 ) = 0

x = 12

Both roots are same and are equal to 12 .

Hence , the solution of the equation x² - 24 x + 144 = 0 is 12 .

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Answer:

[tex] \sf \fbox{46.296 British Pounds}[/tex]

Step-by-step explanation:

1 shower job requires 3 hours of work,

plumber will fix only 1 shower that means he will work for 3 hours,

Charges of 1 hour = 25$

Charges of 3 hour = 25× 3 = 75$

The currency that plumber accept is British pound (£),

1 British pound (£) = 1.62 dollar ($)

x British pound = 75 dollar

[tex] \frac{1}{x} = \frac{1.62}{75} [/tex]

taking reciprocal both the side,

[tex] \frac{x \cancel £}{1\cancel£} = \frac{75 \: \cancel\$ }{1.62 \:\cancel \$} [/tex]

[tex]x = 46.296[/tex]

Jamar need to pay 46.296 British Pounds to plumber for the shower job.

The two units that were cancelled was Dollar & Pound.

It is required to cancel units because, mathematical operation does not work for different units. For e.g. If I have given two measurement one is volume(cm³) & another is length(cm) so I cannot add them.

[tex] \sf Volume + Length = Not \: possible [/tex]

Same thing happens with division Operation of two different units, the magnitude gets cancelled but unit still remains there.

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After rotating a parallelogram 270° counterclockwise points of D will be (2,7).

There are 4 types of translation they are, translation, rotation, and dilation.

We know when we rotate a shape 270° counter-clockwise the coordinates (x,y) becomes (y, -x) that is we switch x and y and make x negative.

Given a parallelogram with points C(-4,6), D(-7,2), E(6,6) and F(3,2).

Assuming point D when rotated 270° becomes D'.

∴ The points of D will switch which is (2,-7) and then we will make x negative.

So, D' becomes (2,7).

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If the concentration of hydrogen ions in household dish detergent is 10⁻¹² , then the calculated pH level of household dish detergent is 12.

Given that the concentration of hydrogen ions in household dish detergent is 10⁻¹² .

We are told to find the pH level of household dish detergent.

pH is basically a measure of how acidic/basic water is. The range of pH ranges from 0 - 14, with 7 being neutral.

We have to find the negative value of log value of concentration level to find pH of the solution.

pH=-log ([tex]10^{-12}[/tex])

pH=-(-12)log (10)          [We know that [tex]log a^{b}[/tex]=b log a]

pH=12*1

pH=12

Hence if the concentration of hydrogen ions in household dish detergent is 10⁻¹² , then the calculated pH level of household dish detergent is 12.

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An absolute value equation that has the given solution is  mathematically given as

I3 + xI - 7 = 0 where the solutions (or roots) are in X= 4 and X= -10

This is further explained below.

Generally, in this case, we want an absolute value equation that has the solutions x = 4 and x= -10.

A cheap way to do this is to look for a number N that:

N + 4 = -(N - 10)

then, isolating N we get:

2N = 6 + 10 = 6

N = 6/2 = 3

then

=N +4  

= 3 + 4

= -8

and

=N - 10

= 3 - 10

= -7

In conclusion,  we know that I-7I = I7I = 7

now we can write our equation as:

I3 + xI - 7 = 0

where the solutions (or roots) are in X= 4 and X= -10

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The graph of a linear function is a straight line. One independent variable and one dependent variable make up a linear function.

What are the characteristics of a linear function?

What are the properties of equation?

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A real world situation that can be modeled by the equation. 19.25x =17.25x +26.77 is that a company charges 19.25 per hour and another company charges 17.25 per hour plus a one time fee of 26.77. What number of hours they have the same price?

It should be noted that an equation is used to show the relationship between the variables that are illustrated.

In this case, a real world situation that can be modeled by the equation. 19.25x =17.25x +26.77 is that a company charges 19.25 per hour and another company charges 17.25 per hour plus a one time fee of 26.77. What number of hours they have the same price?

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In mathematics, a variable is a symbol and placeholder for any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set

While multiplying two integer numbers, the rule is simple.

If both the integers have the same sign, then the result is positive.

If the integers have different signs, then the result is negative.

For example,

(+2) x (+3) = +6

(+3) x (-4) = – 12

The major Properties of Integers are:

Closure Property

Associative Property

Commutative Property

Distributive Property

Additive Inverse Property

Multiplicative Inverse Property

Identity Property

According to the distributive property of integers, if a, b and c are integers, then:

a x (b + c) = a x b + a x c

Example: Prove that: 3 x (5 + 1) = 3 x 5 + 3 x 1

LHS = 3 x (5 + 1) = 3 x 6 = 18

RHS = 3 x 5 + 3 x 1 = 15 + 3 = 18

Since, LHS = RHS

Hence, proved.

1) (a-b)+c

a= 0.5 , b= 2, c= -1

 (0.5- 2)+-1

=-1.5-1

=-2.5

2) a= 3 . b=-4, c=-2

(3-(-4)+-2

= (3 +4)+2

= 9

3) a= -8, b= 5, c= 3

 (-8+5)+3

=-3+3

= 0.

-(a-b)-c

1) a=0.5 , b= 2, c=-1

 -(o.5-2)-(-1)

=-0.5+2+1

= 2.5

2) a= 3, b= -4, c=-2

-(3-(-4)-(-2)

-(3+4)+2

-3-4+2

= -5

3) a= -8, b=5 ,c=3

-(-8-5)-3

=(8+5)-3

= 13-3

= 10.

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1) the mathematical model for given situation is f(t) = 2t + t, where t is the time in minutes

2) the amount of water in the pool after 50 minutes = 105 gallons

3) and the amount of time required to fill the pool =  12 hours 46 minutes

In this question,

a small pool hold 1500 gallons of water.

When there's is 5 gallons of water in the pool, the person decided

that not to stand outside and watch the pool fill.

This means, from the time he had decided, the amount of water in the pool = 5 gallons.

the water was filling the pool at a rate of 2.

Let t be the time in minutes.

So, the amount of water in the pool after 't' minutes would be,

f(t) = 2t + 5

We get an mathematical model for given situation,

f(t) = 2t + 5, where t is the time in minutes

We need to find the amount of water in the pool after 50 minutes

For t = 50 minutes

f(50) = 2(50) + 5

f(50) = 100 + 5

f(50) = 105 gallons

Also, we need to find the amount of time required to fill the pool.

1500 = 2t + 5

1495 = 2t

t = 747.5 minutes

t = 12 hours 46 minutes

Therefore, 1) the mathematical model for given situation is f(t) = 2t + t, where t is the time in minutes

2) the amount of water in the pool after 50 minutes = 105 gallons

3) and the amount of time required to fill the pool =  12 hours 46 minutes

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