Mathematics College

Solve for the following equation . x^6-9x^3+10=0

Answers

Answer 1

Answer:

x = ∛10x = -∛10/2 +(∛10√3)/2ix = -∛10/2 -(∛10√3)/2ix = -1x = 1/2 -(√3)/2ix = 1/2 +(√3)/2i

Step-by-step explanation:

You want to solve the 6th-degree equation x^6 -9x^3 +10 = 0.

Quadratic

The equation is basically quadratic in x^3. Substituting z = x^3, we have ...

z^2 -9z +10 = 0

(z -10)(z +1) = 0 . . . . . factored form

z = 10, z = -1 . . . . . . . values of z that make the factors zero

Cubics

Now, we have two cubic equations to solve:

x^3 = 10 ⇒ x = ∛10x^3 = -1 ⇒ x = ∛(-1) = -1

The real root is given by the cube root function. The imaginary roots are that value multiplied by 1∠±120° = (-1/2 ±(√3)/2i). Then the six roots are ...

x = ∛10x = -∛10/2 +(∛10√3)/2ix = -∛10/2 -(∛10√3)/2ix = -1x = 1/2 -(√3)/2ix = 1/2 +(√3)/2i

Additional comment

The product ∛10√3 can be simplified to ...

[tex]\sqrt[3]{10}\sqrt{3}=(10^{2/6})(3^{3/6})=(10^23^3)^{1/6}=\sqrt[6]{2700}\approx 3.7315903[/tex]

Related Questions

>
Suppose you want to have $300,000 for retirement in 35 years. Your account earns 10% Interest.
How much would you need to deposit in the account each month?

Answers

Answer: 79.02

Step-by-step explanation:

set present value to 0

set future value to 300000

set number of time periods to 35 * 12 = 420

set interest rate percent per time period to 10/12 = 0.833333.

Equation:

See attachment

Evaluate x²-5xy for x = -3 and y = -2

Answers

Answer: -21

Step-by-step explanation:

x = -3 and y = -2

x²-5xy=

(-3)²-5(-3)(-2)=

9-5(-(-6))=

9-5(6)=

9-30=

-(30-9)=-21

What is the equation?

Answers

Answer:

Answer = (2)n+(2)

Step-by-step explanation:

As the first step try to examine the distribution on both sides carefully.And as a general rule of thumb, try calculating the difference between 2 consecutive terms on "OUT" side. (if the difference is the same for every 2 consecutive terms, then the distribution is arithmetic)In this case it is (-4) - (-2) = -2.After that, try writing the first OUT term in terms of both that difference (most of the time difference comes in multiplication with n) and the first term on IN side.If that cannot be achieved in one go, then either add or subtract a suitable amount of value. it is as follows,

first difference = -2

Now, -2 = -2 × (n) + (0) if n = 1

or -2 = -2 × (n) + (-6) if n = -2

or -2 = |-2| ×(n) + 2 :::: -2 = 2n +2 if n = -2

Now all the 3 arrangements are okay but except for the third one, others do not comply with higher terms in the distribution.Therefore, the third one turns out to be the correct arrangement.

the circumference of earth is approximately 2.49x10^4 miles. If Philip traveled around the circumference of Earth 20 times, what would the approximate number of miles he traveled

Answers

The approximate no . of miles Philip traveled are 4 . 98 * ( 10 ^ 5 ) miles .

Given : the circumference of earth 2.49 x ( 10^4 ) miles

To calculate : the approximate number of miles Philip traveled

Philip traveled 20 times

⇒ 20 * circumference of circle

⇒ 20 * [ 2.49 x ( 10^4 ) ]

( 2 * 2.49 ) * ( 10 ^ 5 )

= 4 . 98 * ( 10 ^ 5 )

Hence , the approximate no . of miles Philip traveled are 4 . 98 * ( 10 ^ 5 ) miles .

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Given g (x) =3^2+2x-4, find g(1.5)

Answers

Answer:

Step-by-step explanation:

[tex]g(x)=3^2+2x-4=5+2x \\ \\ g(1.5)=5+2(1.5)=8[/tex]

Express each fraction as an expression using a negative exponent organ than -1.
1/25=?

Answers

Answer:

A negative exponent flips the fraction and turns the exponent positive, and vice versa.

1/121 = 1/1211 = 121-1

As an example, 5-2 = 1/25, and 1/5-2 = 25.

true or false?????????????????

Answers

The equation: 1/2 + 1/6 = 2/3

Is true.

Is the equation true or false?

Here we have the equation:

1/2 + 1/6 = 2/3

First, we need to find a common denominator for the two fractions, if we multiply and divide the first one by 3 we get:

(3/3)*(1/2) = 3/6

Replacing that in the equation:

3/6 + 1/6 = 2/3

4/6 = 2/3

Now we can simplify the fraction in the left by dividing both numerator and denominator by 2:

4/6 = 2/3

2/3 = 2/3

Thus, the equation is true.

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if z=10, find the value of z raised to 3-3(z-10)

Answers

The value of the expression when z = 10 is 1000

How to evaluate the expression?

The given parameters are

z = 10

z^3 - 3(z-10)

Substitute z = 10 in z^3 - 3(z-10)

So, we have

10^3 - 3(10-10)

Evaluate the expression

10^3 - 3(10-10) = 1000

hence, the value of the expression when z = 10 is 1000

Answers

(45°F − 32) × 5/9 = 7.222°C
Therefore B is correct

Work out 10.3% of 853.93km
Give your answer rounded to 2 DP.

Answers

Answer: 87.96 km

Step-by-step explanation:

10.3% of 853.93km= 87.96 km

87.95
tdp so you round up

In 1995, the standard bus fare in a city was $1. In 2022, the standard bus fare was $2.25. Find the percent
increase. (Round to the nearest tenth of a percent.)
Answer:
Submit Question

Answers

I assume what was meant was $1.50 for the original value here because it is the only solution that would make sense for this case. There was a 50% increase from 1995 to 2022.

The formula for percent change is:

New value - old value / old value

Given the formula, we can set up an equation:

2.25 - 1.50 = 0.75

0.75 / 1.50 = 0.50

Therefore, the percent change would be 50% if $1.50 was meant here.

what is 2,722 rounded to the nearest thousand

Answers

The 2,722 to the nearest thousand is 3000.

In the given statement is :

What is 2,722 rounded to the nearest thousand

Number is => 2722

Number at thousand place is = 2Now, we need to find the digit at the right side of thousand place = 77 is greater then or equal to 5, now we have to increase the thousand place digit by 1. => 2 + 1 = 3Now after rounding digit 3, all numbers at the right side becomes zero, then rewrite the numbers.

Hence, the 2,722 to the nearest thousand is 3000.

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help me with this question

Answers

Answer:3

Step-by-step explanation:

Find the smallest number by which 6300 must be multiplied to make it a perfect
square.

Answers

To get a perfect square, the smallest number to be multiplied by 6300 is 7.

Multiplication is the process of calculating the result when a number is taken times. Each of the numbers is referred to as a factor of the product, which is the outcome of a multiplication.

Consider the number 6300 which can also be written as:

6300 = 2 × 2 × 3 × 3 × 5 × 5 × 7

Now, 2, 3, and 5 are in pairs. Only 7 is not in pair.

Now, we will multiply 6300 by 7.

Then,

6300 × 7 = 44100

Therefore, the number 44100 is the number that makes the perfect square.

Let's say x² = 44100,

Taking square root on each side of the equation:

x² = 44100

√x² = √44100

x = √[ 21 × 21 × 10 × 10 ]

x = 210

Therefore the smallest number by which 6300 is multiplied to get a perfect square is 7.

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Consider the system of linear equations.

−4x+6y = 4

2x−3y = k

Determine the constant so that the system of linear equations has infinitely many solutions. (Hint: Graph the equations in the same coordinate plane. What should you see in order for the system to have infinitely many solutions?)

Answers

The value of the constant k such that the system has infinitely many solutions is; -2.

What is the value of k such that the system has infinitely many solutions?

It follows from the task content that the system of equations given upon observation are multiples.

Hence, by multiplying the second equation by -2; we have;

-4x +6y = 4

-4x +6y = -2k

Hence, for the system to have infinitely many solutions; 4 = -2k.

Ultimately, k = -2 by dividing both sides of the equation above by -2.

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A long year-end status report for work is 130 pages long. You need to print 17 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.44 each. S Give your answer to the nearest cent, only for the paper you use

Answers

Answer:

$17.20

Step-by-step explanation:

You need to print (130)(17) = 2210 pages.

This means you need 2210/500 reams, which rounds up to 5.

So, the cost is 5(3.44) = $17.20

Answer:

7602.40

Step-by-step explanation:

Based on the given conditions

Formulate:

3.44×30×17

447.2×17

7602.4

Round 7062.4

=7062.40

Need help with median question here

Answers

Answer:

36.5 is median Temperature for girls

Step-by-step explanation:

Let's first calculate the median Temperature for boys to show you how it is done;

Below are the Temperature, they are not in ascending order

37.0,36.1,37.1,37.3,36.3,36.4,36.7,36.7,36.7,35.8

Now let's arrange them in ascending order

35.8, 36.1, 36.3, 36.4, (36.7, 36.7, )36.7, 37.0, 37.1, 37.3

In the middle are 36.7 and 36.7 as seen in the bracket

to find median = 36.7+36.7/2

➟ 73.4/2

➟ 36.7

∴36.7 is median Temperature for boys

Now that I've shown you example with boys temperature let's go find the actual temperature which is girls

Below are temperature for girls

34.7,35.8,35.9,36.2,36.4,36.6,36.6,36.8,36.8,36.9

Let's arrange them in ascending order

34.7, 35.8, 35.9, 36.2,( 36.4, 36.6, )36.6, 36.8, 36.8, 36.9

In the middle are 36.4 and 36.6 as seen in the bracket

to find median = 36.4+36.6/2

➟ 73/2

➟ 36.5

∴36.5 is median Temperature for girls

please refer to the image below!!

Answers

The expression of f(x) = -2x² - 10 which is h(x) = -2x² - 6 would be vertically upward by 3 units, it becomes the graph of a function for f(x).

What is a function?

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The function h is defined as follows.

h(x) = -2x² - 6

If the graph of his translated vertically upward by 3 units, it becomes the graph of a function for f(x)

To determine the expression for f(x).

Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit, add 1 to the function

If shift down by 4 units, subtract 4 from the function

Here h + 4 because adding 2 to the h coordinate would shift it up 2

⇒ h(f(x)) = ( x, y +4 )

⇒ f(x) + 4 = -2x² - 6

⇒ f(x) = -2x² - 6 -4

⇒ f(x) = -2x² - 10

Hence, the expression of f(x) = -2x² - 10 which is h(x) = -2x² - 6 would be vertically upward by 3 units, it becomes the graph of a function for f(x).

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solve the following equation for d. 4hd=3f-g3

Answers

The equation solved for 'd' gives d = 3f - g³/ 4h

What is subject of formula?

The subject of a formula is defined as the variable expressed in terms of the other variables.

It is also the variable that is worked out in a given equation or expression;

Given the equation;

4hd = 3f - g³

To solve for 'd'

Divide both sides by the coefficients of d, we have;

4hd/ 4h = 3f - g³/ 4h

We then have

d = 3f - g³/ 4h

Thus, the equation solved for 'd' gives d = 3f - g³/ 4h

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Given b = −14.

Which equation is true?

b/2 + 7.4 = 1.4

2b + 8 = 20

-28 +2b =53

b/7 + 18 =16

Answers

Answer:

D) b/7 + 18 =16

Step-by-step explanation:

Let's solve your equation step-by-step.

b/7+18=16

Step 1: Simplify both sides of the equation.

1/7b+18=16

Step 2: Subtract 18 from both sides.

1/7b+18−18=16−18

1/7b=−2

Step 3: Multiply both sides by 7.

7*(1/7b)=(7)*(−2)

b=−14

If COS theta =2√2/4, calculate the value of Sin theta

Answers

Answer: [tex]\frac{1}{\sqrt{2}}[/tex]

Step By Step Explanation:

[tex]=\frac{2\sqrt{2}}{2\cdot \:2}[/tex]

[tex]=\frac{\sqrt{2}}{2}[/tex]

[tex]=\frac{\sqrt{2}}{\sqrt{2}\sqrt{2}}[/tex]

[tex]=\frac{1}{\sqrt{2}}[/tex]

It’s 0.25 because of the divided sign twice

5 3/8 as a whole number

Answers

Answer:

Exact Form: 43/8

Decimal Form: 5.375

Rounding to the Nearest whole number: 5

5.3 ………………………………………..

find(-18)+(-15)+10 ..........

Answers

Answer:

-23

Step-by-step explanation:

Just add left to right

2. What does it mean if P(-4) for the polynomial function P(x) = x3 + 11x²
+34x + 24 equals zero?

Answers

Answer:

It means that the -4 is one of the solutions for this polynomial. In other words, -4 is a point in the x axis of the graph where the function touches said axis.

The value of the polynomial at P(-4) will be 0.

What is a polynomial?

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given that the polynomial function is P(x) = x³ + 11x² + 34x + 24. The value of the function at P(-4) will be calculated as:-

P(x) = x³ + 11x² + 34x + 24

P(-4) = (-4)³ + 11(-4)² + 34(-4) + 24

P(-4) = -64 + 176 - 136 + 24

P(-4) = 200 - 200

P(-4) = 0

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In a lab experiment, 5300 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 10 hours. How many bacteria would there be after 12 hours, to the nearest whole number?

Answers

There will be roughly 12,000 bacteria after 12 hours.

What are mathematical operations?A mathematical "operation" is the process of calculating a value using operands and a math operator. The math operator symbol contains predefined rules that must be applied to the given operands or numbers. A mathematical expression is a collection of numbers and operations.

So, there are 5300 bacteria and it gets doubles in 10 hours:

Then,

5300 + 5300 = 10,600 (In 10 hours)5300 × 1/5 = 1060 (In 2 hours)In 12 hours = 10,600 + 1060 = 11,660After rounding off: 12,000

Therefore, there will be roughly 12,000 bacteria after 12 hours.

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Sachin can drive 110 more miles before he has to get gas.He has to drive 67 miles to his friends house and 32 miles to his moms.Use rounding to estimate whether he will have enough gas to go to both places

Answers

Rounding to an estimate, Sachin will have enough gas to go to both places before he runs out of gas.

What is an estimate?

An estimate is an equivalent numerical value obtained by rounding off.

The result of an estimate is not an exact value. The value represents the nearest rounded value.

For instance, 75.9% can be estimated or rounded off to 76%. 32 minutes can be rounded off or approximated to ¹/₂ hour.

Data and Calculations:

Driving distance before getting gas = 110 miles

The distance to his friend's house = 67 miles

The distance to his mom's house = 32 miles

The total distance to be covered on the available gas = 99 miles

Estimated distance to be covered = < 100 miles

Thus, using estimation, Sachin will still have more than 10 miles to drive before he gets gas.

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What value of x makes this equation true?

x/2 − 6 = 10

Drag and drop the number that correctly completes the equation.

x = blank

30 31 32 33 34

Answers

The answer is 32 because 32/2 is 16 and 16 minus 6 is 10

A car dealership sells SUVs and passenger cars. For a recent year, 30 more SUVs were sold than passenger cars. If a total of 540 vehicles were sold, determine the number of each type of vehicle sold.

Answers

The number of each type of vehicle sold are :

SUVs : 300

Passenger cars : 270

Number of SUVs were sold more than passenger cars = 30

Total number of cars sold = 540

Let the number of Passenger car sold = x

Then, The number of SUVs sold = x + 30

So, Total number of cars sold = Number of Passenger car sold + Number of SUVs sold

540 = x + (x + 30)

2x + 30 = 540

2x = 540

x = 540/2

x = 270

We got, the number of Passenger car sold (x) = 270

The number of SUV's sold = x + 30

The number of SUV's sold = 270 + 30 = 300

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455 times 6 step by step

Answers

Answer: 2,730

Step-by-step explanation:

Explained in mental math proccess:

In 455, the one value will be multiplied by 6. 5x6= 30.

In 455, the tens value will be multiplied by 6. 50x6= 300.

In 455, the hundreds value will be multipled by 6. 400x6= 2,400.

Find the sums of all products multiplied by 6. 30+300+2,400= 2,730.

455x6= 2,700

DETERMINE WHETHER THE LINES ARE PARALLEL, PERPENDICULAR, OR NEITHER
5X+2y=14 AND y=-5x+9

Answers

The lines are neither, nor perpendicular

How to determine the relationship?

The equations of the lines are given as

5x + 2y = 14

y = -5x + 9

Make y the subject in both equations

So, we have

y = -2.5x + 7

y = -5x + 9

The slopes of the above equations are

m1 = -2.5

m2 = -5

The above slopes are neither equal not opposite reciprocals

Hence, the lines are neither, nor perpendicular