The range of values of x that satisfy sec(x) = -√(2) and π/2 is:
x = 3π/4, 5π/4, 0.453, 5.829.
What are the range of values of x?The range of values of x is calculated as follows;
Since sec(x) = 1/cos(x), we can use the identity cos^2(x) + sin^2(x) = 1 to solve for cos(x).
First, we consider the case where sec(x) = -√(2).
We know that sec(x) = 1/cos(x), so we can write:
1/cos(x) = -√(2)
Multiplying both sides by cos(x) gives:
1 = -√(2)cos(x)
Dividing both sides by -√(2) gives:
-1/√(2) = cos(x)
So, x is an angle whose cosine is -1/√(2). This occurs in the second quadrant, where cosine is negative. We can find the reference angle for this value of cosine by taking the arccosine of its absolute value:
arccos(|-1/√(2)|) = π/4
Therefore, x is either:
x = π - π/4 = 3π/4
or
x = π + π/4 = 5π/4
Next, we consider the case where sec(x) = π/2. We know that sec(x) = 1/cos(x), so we can write:
1/cos(x) = π/2
Multiplying both sides by cos(x) gives:
1 = π/2 cos(x)
Dividing both sides by π/2 gives:
2/π = cos(x)
So, x is an angle whose cosine is 2/π. This occurs in the first quadrant, where cosine is positive. We can find the reference angle for this value of cosine by taking the arccosine:
arccos(2/π)
Using a calculator, we find that:
arccos(2/π) ≈ 0.453
Therefore, x is either:
x = 0.453
or
x = 2π - 0.453 ≈ 5.829
So the range of values of x that satisfy sec(x) = -√(2) and π/2 is:
x = 3π/4, 5π/4, 0.453, 5.829
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The complete question is below:
If sec(x) = -√(2) and π/2, find the range of values of x
A company borrows $891,000 at 5%, 6% and 9% interest. It owed $54,000 in annual interest. The amount borrowed at 5% was four times the amount at 6%. How much was borrowed at 9%?
Answer:
$274,526
Step-by-step explanation:
A lorry travels 320km and uses 40 litres of petrol, work out the average rate of petrol usage. Amswer in km. Litre
If a lorry travels 320km and uses 40 litres of petrol, the average rate of petrol usage for the lorry is 8 km per liter.
To find the average rate of petrol usage for the lorry, we need to divide the total distance traveled by the amount of petrol used. This will give us the number of kilometers traveled per liter of petrol.
In this case, the lorry traveled 320 km and used 40 liters of petrol, so we can calculate the average rate of petrol usage as follows:
Average rate of petrol usage = Total distance traveled / Amount of petrol used
= 320 km / 40 litres
= 8 km/litre
This means that for every liter of petrol used, the lorry can travel an average of 8 kilometers. This metric can be useful in comparing the fuel efficiency of different vehicles or in calculating the cost of a particular journey based on the price of petrol per liter.
In summary, calculating the average rate of petrol usage involves dividing the distance traveled by the amount of petrol used, resulting in a unit of km per liter.
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how many ternary sequences of digits chosen from {0, 1, 2} of length twelve have exactly three 1's and two 0's?
It can be stated that there exist 63,360 ternary sequences of digits selected from {0, 1, 2} with a length of twelve, which contain precisely three 1s and two 0s.
The problem is asking us to find out how many ternary sequences of digits are there that are chosen from {0, 1, 2} of length twelve, and have exactly three 1's and two 0's.
Therefore, there will be a total of 7 digits (12 - 3 - 2 = 7) that could be 1 or 2. So, let's solve it in steps.
Step 1: The number of ways we can choose 3 positions out of 12 for 1s is C (12,3).
Step 2: The number of ways we can choose 2 positions out of 9 (because there are already 3 1s and 2 0s) for 0s is C (9,2).
Step 3: We have three digits left that can be either 1 or 2. So, there will be 2 options for each of these digits, and the total number of options will be
2 × 2 × 2 = 8.
Step 4: So, the total number of sequences will be obtained by multiplying the results of Steps 1, 2, and 3. i.e.
C (12,3) × C (9,2) × 8
⇒ ¹²C₃ × ⁹C₂ × 8
⇒ 220 × 36 × 8 = 63360.
Therefore, there are 63,360 ternary sequences of digits chosen from {0, 1, 2} of length twelve that have exactly three 1s and two 0s.
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Geometry: solve this problems, it’s urgent
1. triangle = 180
7x7 = 49
180-49 = 131
2. 10x10 = 100 but since its a pyramid its degrees is 180
180-100=80
What are all the zeros of the polynomial function
[tex]f(x)=x^4-2x^3-8x^2+10x+15[/tex]
Answer:
The correct option is A. x = -1, x = 3, x = ±√5.
We found the zero x = -1 through synthetic division, and then we factored the cubic polynomial using the Rational Root Theorem and synthetic division to obtain (x + 1)(x^3 - 3x^2 - 6x + 15). We found that the remaining zeros of the polynomial function are the roots of the quadratic factor x^2 - 3x - 5, which are x = (3 ± √29))/2.
Therefore, the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3, x = (3 + √(29))/2, and x = (3 - √(29))/2, which simplifies to x = (3 ± √(5))/2.
Option A lists all of these zeros, so it is the correct option. Options B and C do not list all of the zeros of the polynomial function.
STEPS: Here are the steps to find all the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15:
Write the polynomial function in descending order of degree: f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15.
Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±3, ±5, ±15.
Use synthetic division to test each possible zero. We start with x = -1:
-1 │ 1 -2 -8 10 15
│ -1 3 -5 -5
└───────────────
1 -3 -5 5 10
x = -1 is a zero of the polynomial function. We can write f(x) as:
f(x) = (x + 1)(x^3 - 3x^2 - 5x + 10)
Use the Rational Root Theorem and synthetic division to factor the cubic equation x^3 - 3x^2 - 5x + 10:
3 │ 1 -3 -5 10
│ 3 0 -15
└─────────────
1 0 -5 -5
x = 3 is not a zero of the polynomial function.
-3 │ 1 -3 -5 10
│ -3 24 -57
└────────────
1 -6 19 -47
x = -3 is not a zero of the polynomial function.
The only remaining possible rational zeros are ±1/1 and ±5/1, but testing these values using synthetic division does not yield any more zeros.
Solve for the remaining zeros of the polynomial function by factoring the quadratic equation x^2 - 3x - 5 using the quadratic formula or factoring by grouping:
x = (3 ± √(29))/2
These are the remaining zeros of the polynomial function.
Therefore, the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3, x = (3 + √(29))/2, and x = (3 - √(29))/2, which simplifies to x = (3 ± √(5))/2.
Option A lists all of these zeros, so it is the correct option.
Hope this helps! I'm sorry if it doesn't! :]
Is 4.284 an irrational number?
Answer: "An irrational number is a number that cannot be expressed as a ratio between two integers and is not an imaginary number.
Since 4.284 is not the square root of a negative number, it is not imaginary
Since 4.284 is a rational number from above, 4.284 is not an irrational number"
Step-by-step explanation: /\ I looked at a calculator for irrational numbers. Should be right, considering how it's well explained. Just search for "irrational number calculator". Dont rely on that. But it's there if
you need it! :)
No
It is a rational number since it is a fraction/decimal that isn't non-terminating, not is it pi or
i need help asappppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer: A ♀️
Step-by-step explanation:
A Nigerian visiting India changed N70200 to rupees at the rate of 3 naira to 35 rupees. He spent 224 000 rupees and invested the remaining amount in the State Bank of India at 41.5% simple interest per annum. At the end of 8 months, he transferred the capital and interest to his account in the Modern Bank of Nigeria at the rate of 21 rupees to 2 naira. What was the amount, in naira, credited to his account, to the nearest naira?
According to the solving this to the nearest naira, the amount credited to his account is 580,163 Nigerian naira.
Describing percentage:A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.
According to the given information:The Nigerian visitor changed N70200 to rupees at a rate of 3 nairas to 35 rupees. Therefore,
70200 Nigerian naira = 70200 * 35 / 3 = 819500 Indian rupees
He spent 224,000 rupees, so the amount he invested at 41.5% per annum was:
819500 - 224000 = 595500 rupees
The simple interest he earned after 8 months at a rate of 41.5% per annum is:
595500 * (41.5/100) * (8/12) = 129702.5 rupees
So, the total amount he had after 8 months was:
595500 + 129702.5 = 725202.5 rupees
He then transferred this amount to his account in the Modern Bank of Nigeria at a rate of 21 rupees to 2 naira. Therefore,
725202.5 rupees = (725202.5 / 21) * 2 = 580162.5 Nigerian naira
this to the nearest naira, the amount credited to his account is 580,163 Nigerian naira.
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you are playing super mario bros together with 2 of your friends. you got to level 4, where you encounter your nemesis bowser. bowser is very strong, and he is defeated only 41% of the times. each of you will play level 4 one time. (a) (2 points) let x be the total number of times that bowser is defeated. what is the distribution of x? (b) (3 points) what is the probability that only 1 of you defeats bowser? (c) (2 points) you want to understand how likely it is to correctly predict the number of times bowser is defeated. what is the variance of x? (d) (1 point) what is the probability that you beat bowser - regardless of whether your friends beat him or not? suppose that, after your friends are gone, you decide to play level 4 until you beat bowser. let y be the number of times you play level 4. (e) (3 points) what is the distribution of y? (f) (3 points) what is the probability that you play less than 3 times? (g) (3 points) what is the expected number of times that you play?
(a) The distribution of x is a binomial distribution with n=3 and p=0.41, where n is the number of trials (each of you playing level 4 one time) and p is the probability of success (defeating Bowser).
(b) The probability that only 1 of you defeats Bowser is given by the binomial probability formula:
P(x=1) = (3 choose 1)(0.41)^1(0.59)^2 = 0.411
(c) The variance of x is given by the formula:
Var(x) = np(1-p) = 3(0.41)(0.59) = 0.726
(d) The probability that you beat Bowser, regardless of whether your friends beat him or not, is simply the probability of success in one trial, which is 0.41.
(e) The distribution of y is a geometric distribution with p=0.41, where p is the probability of success (defeating Bowser).
(f) The probability that you play less than 3 times is given by the sum of the probabilities of playing 1 or 2 times:
P(y<3) = P(y=1) + P(y=2) = (0.41)^1(0.59)^0 + (0.41)^1(0.59)^1 = 0.651
(g) The expected number of times that you play is given by the formula:
E(y) = 1/p = 1/0.41 = 2.439
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solve for b??
5b-3 > 9b+4
Answer: b<-7/4
Step-by-step explanation:
Let's collect numbers with same variables to the same side:
-3-4>9b-5b
-7>4b
b<-7/4
solve this problem for me
The discounted price of the camera is $270 and the price of the camera after the 40% increase is $378.
When the store offered a 40% discount on the original price of $450, the discounted price of the camera can be calculated as follows:
Discounted price = Original price - Discount
Discounted price = $450 - 40% x $450
Discounted price = $450 - $180
Discounted price = $270
Therefore, the discounted price of the camera is $270.
After the sale, the discounted price of the camera was increased by 40%. We can calculate the new price of the camera as follows:
New price = Discounted price + 40% x Discounted price
New price = $270 + 40% x $270
New price = $270 + $108
New price = $378
Therefore, the price of the camera after the 40% increase is $378.
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Consider the following set of numbers:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
What is the probability of drawing an odd number or a
multiple of 3?
Answer:
Probability of drawing an odd number.
Number of odd numbers = 5
Number of numbers in the set = 10
So it's a 5 in 10 chance or 1 in 2 chance.
Probability of drawing a multiple of 3.
Multiples of 3 in the set = 3, 6 and 9 = 3 multiples of 3
Number of numbers in the set = 10
So it's a 3 in 10 chance
Need some help in math
Answer: A all you have to do is look where the line is going
Answer:
C
Step-by-step explanation:
under a reflection in the line y = - x
a point (x, y ) → (- y, - x ) , then
(- 1, 6 ) → (- 6, - (-1) ) → (- 6, 1 )
(- 3, 2 ) → (- 2, - (- 3) ) → (- 2, 3 )
20 POINTS, URGENT!!
A. the area of a rectangular deck is (8d² + 20d). The deck is (4d) meters long. Determine a polynomial that represents the width of the deck.
B. What are the dimensions and area of the deck when d is 4 meters?
I think the answer to A is (2d + 5) but what I need help with is B
In response to the given question, we can state that With d = 4 metres, polynomials the deck dimensions are 16 metres by 128 metres, and the deck area is 2048 square metres.
what are polynomials?A polynomial is a mathematical statement composed of equations and uncertainty that exclusively uses additions, addition and subtraction, multiplications, and real number powers of variables. The form x2 4x + 7 indicates a single determinate x algebraic. A polynomial expression in mathematics is made up of determinants (also known as freshly made) and equations that may be added, deducted, multiplied, then raised to minus integer powers of semi. A polynomial is an algebraic statement that includes variables and coefficients. An expressions can really only incorporate the operations add, subtraction, duplication, and non-negative integer factors. These expressions are referred to as polynomials.
substituting d = 4 into the formulas given in the problem.
Then, using the polynomial you discovered in Part A, we can calculate the breadth of the deck when d = 4.
8d2 + 20d = 8(42) + 20(4) = 128 width
With d = 4 metres, the breadth of the deck is 128 metres.
Next, we may utilise the supplied deck length, 4d = 4(4) = 16 metres, to calculate the deck area when d = 4:
16 × 128 = 2048 Area = Length x Width
With d = 4 metres, the deck dimensions are 16 metres by 128 metres, and the deck area is 2048 square metres.
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SHOW STEPS! PLS HELP
Answer:
chocolate = $1.25
soft drink = $1.85
Step-by-step explanation:
Given price of chocolate is c and price of soft drink is s
Olivia: 5c + 2s = 9.95
Taylor: 6c + 6s = 18.60
6c + 6s = 18.60
divided by 6, we have
c + s = 3.1
=> s = 3.1 - c
Substitute s = 3.1 - c into
5c + 2s = 9.95
5c + 2(3.1 - c) = 9.95
5c + 6.2 - 2c = 9.95
3c = 9.95 - 6.2
3c = 3.75
c = 3.75/3 = 1.25
s = 3.1 - c = 3.1 - 1.25 = 1.85
A number is chosen from 1 to 20. Find the probability that the number chosen is a odd prime number
The probability of choosing an odd prime number from 1 to 20 is 0.35
The probability is the ratio of the number of favorable outcomes to the total number of outcomes
The odd prime numbers between 1 and 20 are 3, 5, 7, 11, 13, 17, and 19. There are 7 odd prime numbers in this range.
The total number of possible choices is 20 (since there are 20 numbers in the range 1 to 20).
Therefore, the probability of choosing an odd prime number is:
number of odd prime numbers / total number of possible choices
= 7 / 20
= 0.35
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Jocelyn and Lorlesha are comparing the size of their villages in the Clash of Clans app. The area of Jocelyn’s village is represented by the polynomial, 2w^2 + 10w + 12. The area of Lorlesha’s village is represented by the polynomial, 3w^2 + 4w -5, where w represents the width, in meters of their Town Hall.
Jocelyn's village additional area is (-w² + 6w + 17) m². The combined total area of both is (5w² + 14w + 7) m².
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
Let w represent he width of the town hall.
Area of Jocelyn's village = 2w² + 10w + 12
Area of Lorlesha's village = 3w² + 4w - 5
The difference in their area = (2w² + 10w + 12) - (3w² + 4w - 5) = -w² + 6w + 17
The sum of their area = (2w² + 10w + 12) + (3w² + 4w - 5) = 5w² + 14w + 7
Jocelyn's village additional area is (-w² + 6w + 17) m². The combined total area of both is (5w² + 14w + 7) m².
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At the start of the day, a painter rested a 3m ladder against a vertical wall so that
the foot of the ladder was 50cm away from the base of the wall.
During the day, the ladder slipped down the wall, causing the foot of the ladder to
move 70cm further away from the base of the wall.
How far down the wall, in centimetres, did the ladder slip?
Give your answer to the nearest 1 cm.
The ladder slipped down the wall by approximately 296 cm to the nearest 1 cm.
What is the distance slipped by the ladder?We can use the Pythagorean theorem to solve this problem.
Let the distance the ladder slips down the wall be represented by x (in cm).
Then, at the start of the day, we have a right triangle formed by the wall, the ground, and the ladder, with the ladder being the hypotenuse.
The length of the ladder is 3m = 300cm, and the distance from the foot of the ladder to the wall is 50cm.
Therefore, we have:
(300)² = x² + (50)²
Simplifying this equation, we get:
90000 = x² + 2500
Subtracting 2500 from both sides, we get:
87500 = x²
Taking the square root of both sides, we get:
x = √87500
x = 295.8 cm
x ≈ 296 cm
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Angela can shovel the snow from her driveway in 2 hours. When Franklin joins her, the driveway can be finished in just 54 minutes. How long would it take Franklin to shovel the driveway alone?
By speed formula, it would take Franklin 2 hours and 30 minutes (or 150 minutes) to shovel the driveway alone.
What is speed?
Speed is defined as the distance travelled by an object in a given amount of time. Speed is a scalar quantity, meaning that it has magnitude but no direction.
Mathematically, speed is calculated as follows:
speed = distance / time
where "distance" is the distance travelled by the object, and "time" is the time it takes for the object to travel that distance.
Let's assume that Angela's shoveling rate is "a" and Franklin's shoveling rate is "f" (measured in driveways per hour). We can use the formula:
time = distance / rate
where "distance" is the length of the driveway (which we can assume to be 1 driveway) and "rate" is the shoveling rate (in driveways per hour).
According to the problem, Angela can shovel the driveway in 2 hours, so her shoveling rate is:
a = 1/2
When Franklin joins her, they can finish the driveway in 54 minutes, or 9/10 of an hour. Therefore, their combined shoveling rate is:
(a + f) = 1 / (9/10) = 10/9
We can now set up a system of equations to solve for "f".
First, we know that Angela and Franklin can finish the driveway in 9/10 of an hour:
1/2 + f = 1 / (9/10)
Multiplying both sides by 10/9, we get:
5/9 + (10/9)f = 1
Simplifying, we get:
(10/9)f = 4/9
f = (4/9) * (9/10)
f = 4/10
f = 2/5
Therefore, Franklin's shoveling rate is 2/5 of a driveway per hour. To find how long it would take him to shovel the driveway alone, we can use the formula:
time = distance/rate
time = 1 / (2/5)
time = 5/2
time = 2 1/2 hours
Therefore, it would take Franklin 2 hours and 30 minutes (or 150 minutes) to shovel the driveway alone.
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A machine takes 2.8 hours to make 9 parts. At that rate, how many parts can the machine make in 28.0 hours?
Answer:
The machine can make 9 parts in 2.8 hours.
To find the rate of production, we can divide the number of parts by the time: 9 parts / 2.8 hours = 3.214 parts per hour.
Now that we know the machine's rate of production, we can use it to answer the question:
In 28.0 hours, the machine will produce: 3.214 parts per hour x 28.0 hours = 89.9 parts.
Therefore, the machine can make 89.9 parts in 28.0 hours at the given rate. We can round this to 90 parts.
Step-by-step explanation:
Pls help me I don’t know the answer and don’t understand it
If the length of rectangle is 5.25, then the area of rectangle will be less than 25 square meters.
What is area of rectangle?
Area of rectangle is the region covered by the rectangle in a two-dimensional plane. A rectangle is a type of quadrilateral, a 2d shape that has four sides and four vertices.
We know the perimeter of rectangle is 20 meters. So according to formula of Perimeter of rectangle = 2 (L + B) we can conclude that sum of length and width will be 10 meters.
We are given length as 1, 3, 5, 7, and 9.
So width of the rectangle will be 9, 7, 5, 3 and 1.
Area of Rectangle = L x B
So area of rectangle will be 9, 21, 25, 21, and 9.
If the length of rectangle is 5.25, then the area of rectangle will be less than 25 square meters.
Values are changing in a linear way and not in an exponential way.
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if 4x+y=7 is a true equation what would be the value of −5(4x+y)
Answer:
-32
Step-by-step explanation:
since 4x+y equals 7, multiply -5 by 7
Answer:
40x - 5y = -40x - 5(4x + y) = -40x - 20x - 5(7) = -60x - 35
Step-by-step explanation:
To find the value of -5(4x+y), we first need to simplify the expression inside the parentheses:
-5(4x + y) = -5(4x) - 5(y) = -20x - 5y
Now, we can substitute the value of y from the given equation:
-20x - 5y = -20x - 5(4x + y) = -20x - 20x - 5y = -40x - 5y
Since we know that 4x + y = 7, we can substitute this into the above equation:
-40x - 5y = -40x - 5(4x + y) = -40x - 20x - 5(7) = -60x - 35
(20P) Help please and thankyou it’s due soon
10.6.3 Test (CST): Factoring Polynomials
Question 3 of 25
What are the zeros of f(x) = x²-x-20?
OA. x=-2 and x = 10
B. x= -4 and x = 5
OC. x=-10 and x = 2
OD. x= -5 and x = 4
Therefore, the zeros of the function f(x) are x = 5 and x = -4.
What is polynomial?A polynomial is a mathematical expression consisting of variables and coefficients, combined using the operations of addition, subtraction, multiplication, and non-negative integer exponents. It can have one or more terms, and the degree of a polynomial is the highest power of the variable in the expression.
Here,
To find the zeros of the function f(x) = x² - x - 20, we need to solve for x when f(x) = 0:
x² - x - 20 = 0
We can factor the left side of this equation as:
(x - 5)(x + 4) = 0
Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero. Therefore, we can set each factor equal to zero and solve for x:
x - 5 = 0 or x + 4 = 0
Solving for x in each equation gives us:
x = 5 or x = -4
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What is the translation rule that describes the result of the composition of (x, y) --> (x+4, y-1) and (x, y) --> (x-5, y-5)?
The composition of the two translation rules is:
(x, y) → (x - 1, y - 6)
What is a translation rule?
A translation rule is a mathematical description of how to move each point in a geometric shape by a fixed distance in a certain direction. It is used to describe a transformation called a translation, which moves a shape without changing its size, shape, or orientation.
To find the composition of the two translation rules, we apply the second rule first and then apply the first rule to the result.
Let's consider a point (x, y). Applying the second rule (x, y) → (x - 5, y - 5) gives us a new point:
(x - 5, y - 5)
Now we apply the first rule (x, y) → (x + 4, y - 1) to this new point:
(x - 5 + 4, y - 5 - 1)
Simplifying:
(x - 1, y - 6)
Therefore, the composition of the two translation rules is:
(x, y) → (x - 1, y - 6)
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Solve this homogeneous differential equation
dy/dx=y^2+x^2/x^2
The solution to the given homogenous differential equation dy/dx = y² + x² / x^2 is y² = -x(y³ / 3 + Cy³ - 3Cx)
The given differential equation is: dy/dx = y² + x² / x^2
To solve this, we can first separate the variables by bringing all the y-terms on one side and all the x-terms on the other side:
(1/y²)dy = (x² / x² + y²)dx
Next, we can integrate both sides:
∫(1/y²)dy = ∫(x²/x² + y²)dx
Using the substitution u = y/x, we can simplify the integrals:
∫(1/y²)dy = ∫(1 + u²)dx
-1/y = x + (1/3)u³ + C
where C is the constant of integration.
Substituting back u = y/x, we get:
-1/y = x + (1/3)(y/x)³ + C
Multiplying both sides by -y³, we get:
y² = -x(y³ / 3 + Cy³ - 3Cx)
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What are all the zeros of the polynomial function?
[tex]f(x)=3x^3-5x^2-10x-6[/tex]
Answer:
The correct option is C. x=3, x=-2±√2/3.
Step-by-step explanation:
To find all the zeros of the polynomial function f(x) = 3x^3 - 5x^2 - 10x - 6, we can follow the steps outlined in the previous answer:
Write the polynomial function in descending order of degree: f(x) = 3x^3 - 5x^2 - 10x - 6.
Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±2, ±3, ±6, ±(1/3), ±(2/3).
Use synthetic division to test each possible zero. We start with x = 1:
1 │ 3 -5 -10 -6
│ 3 -2 -12
└─────────────
3 -2 -12 -18
x = 1 is not a zero of the polynomial function.
We continue testing the remaining possible zeros:
-1 │ 3 -5 -10 -6
│ -3 8 2
└────────────
3 -8 -2 -4
x = -1 is not a zero of the polynomial function.
2 │ 3 -5 -10 -6
│ 6 2 -16
└─────────────
3 1 -8 -22
x = 2 is not a zero of the polynomial function.
-2 │ 3 -5 -10 -6
│ -6 22 -24
└────────────
3 -11 12 -30
x = -2 is not a zero of the polynomial function.
3 │ 3 -5 -10 -6
│ 9 12 6
└─────────────
3 4 2 0
Since the remainder is zero, we have found a zero of the polynomial function at x = 3.
We can use synthetic division to factor the polynomial function:
3x - 1
(x - 3)(3x^2 + 13x + 2)
Now we can solve for the remaining zeros of the polynomial function by factoring the quadratic equation using the quadratic formula or factoring by grouping. Either way, we find that the remaining zeros are approximately x = -4.87 and x = -0.435.
Therefore, the zeros of the polynomial function f(x) = 3x^3 - 5x^2 - 10x - 6 are x = -4.87, x = -0.435, and x = 3.
It's C because we found the zero x = 3 through synthetic division, and then we used the quadratic formula to find the other two zeros. The quadratic formula gave us two solutions, which we simplified to x = -2 + sqrt(2)/3 and x = -2 - sqrt(2)/3.
If we substitute these solutions back into the original polynomial function f(x), we get:
f(-2 + sqrt(2)/3) = 3(-2 + sqrt(2)/3)^3 - 5(-2 + sqrt(2)/3)^2 - 10(-2 + sqrt(2)/3) - 6
≈ 0
f(-2 - sqrt(2)/3) = 3(-2 - sqrt(2)/3)^3 - 5(-2 - sqrt(2)/3)^2 - 10(-2 - sqrt(2)/3) - 6
≈ 0
Both of these values are approximately zero, which means that -2 + sqrt(2)/3 and -2 - sqrt(2)/3 are also zeros of the polynomial function.
Therefore, the zeros of the polynomial function f(x) = 3x^3 - 5x^2 - 10x - 6 are x = 3, x = -2 + sqrt(2)/3, and x = -2 - sqrt(2)/3, which matches option C.
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25 cm 7 cm 15 cm what is the area of triangle
The area of the triangle with side lengths of 25 cm, 7 cm, and 15 cm is approximately 209.27 cm².
To calculate the area of a triangle with side lengths of 25 cm, 7 cm, and 15 cm, we can use Heron's formula, which is a formula for finding the area of a triangle when only the side lengths are known:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of its sides. The semi-perimeter is half the sum of the three sides:
s = (a + b + c) / 2
Substituting the given values, we get:
s = (25 + 7 + 15) / 2 = 23.5
Now we can use Heron's formula to calculate the area:
Area = √(23.5(23.5-25)(23.5-7)(23.5-15))
= √(23.5 * (-1.5) * 16.5 * 8.5)
= √(43,822.5)
≈ 209.27 cm²
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98 kilometers in 7 hours = how many kilometers per hour
Answer:
[tex]\huge\boxed{\sf 14 \ km}[/tex]
Step-by-step explanation:
Given that,7 hours = 98 km
Divide both sides by 7
7/7 hour = 98/7 km
1 hour = 14 km[tex]\rule[225]{225}{2}[/tex]
help asap assignment closes soon!
Answer:
a = 12.56637061
Step-by-step explanation:
a= 4 · π · r²
a= 4 · π · 1²
a= 4π
a= 12.56637061
a= 12.57