Differential Equations Dilemma
Show directly that the given functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the
following functions that vanishes identically.
f(x) = 4x, g(x) = 2x², h(x) = 8x-12x²
Enter the non-trivial linearcombination.
(16)4x + (__)2x²+ (__)(8x-12x²) = 0
Answers
The equation with nontrivial linear combination is (16)4x + ( -48 )2x²+ (-8 )(8x-12x²) = 0
We can solve this problem following some steps.
Let's assume the value is A for blank one and it is B for blank two.
Now we can rewrite the equation as,
(16)4x + (A) 2x²+ (B)(8x-12x²) = 0
Or, 64x + 2Ax² + 8Bx - 12Bx² = 0
After rearrangement, we can write this equation as,
x ( 64 + 8B) + x²( 2A - 12B) = 0
We can consider the whole equation as zero, only when the coefficient of both x and x² is zero, To complete a nontrivial combination, we have to write,
∴ ( 64 + 8B) = 0 [ Coefficient of x ]
Or , 8B = -64
Or, B = -64/8 = -8
Again following the previous concept we can also write, ( 2A - 12B ) = 0
[ Coefficient of x² ]
Now, we should put the value of B = -8
∵ ( 2A - 12B ) = 0
Or, 2A + 96 = 0
Or, 2A = - 96
Or, A = - 48
So, the value of A is -48, and the value of B is -8
Now we can conclude,
(16)4x + ( -48 )2x²+ ( -8 )(8x-12x²) = 0
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Related Questions
Solve the following triangle completely.
(a). in triangle ABC, B = 25.6° C = 124.4° C= 39.2m
(b) B = 101.15°, b= 17.23cm and C= 10.86cm.
Answers
Answer:
The answers is below in bold.
Step-by-step explanation:
(a) A = 180 - 25.6 - 124.4 = 30 degrees.
Next use the Sine Rule:
b / sin B = c / sin C
b / sin 25.6 = 39.2/sin 124.4
b = (39.2 * sin 25.6) / sin 124.4
b = 20.53 m.
Also
a / sin A = c / sin C
a / sin 30 = 39.2 / sin 124.4
a = (39.2 * sin 30 / sin 124.4
a = 23.75 m.
b). This is solved in a similar way to (a).
First find angle C using the sine rule.
Then you will know angle A from the 180 degree Rule.
Then you can find the length of a using the Sine Rule.
what is the nearest hundreth in 1.2983 if you round it
Answers
Answer:
1.3000
Step-by-step explanation:
To Round Numbers...
1 ) Decide which is the last digit to keep ( In this case it would be the hundredths )
2 ) Leave it the same if the next digit is less than 5 (this is called rounding down)
3 ) But increase it by 1 if the next digit is 5 or more (this is called rounding up)
Hope this helps! :)
Jeane bought 2 books to read while on vacation.
• The first book cost $15.45
• The second book cost $9.87
About how much did Jeane spend on her new books?
Answers
All you do is add the amount of money she spent to get the total.
15.45
+
9.87
A race car traveled for 2 1/2hours with an average speed of 132 5/8 km per hour. Find the total distance it covered.
Answers
Answer: The total distance covered by the car is 331 9/16 km.
Step-by-step explanation:
We know that, speed= distance/time taken
Therefore, distance = speed x time taken
= 132 5/8 x 2 1/2
= 5/2 x 1061/8
= 5305/16
= 331 9/16 km
Therefore, total distance is 331 9/16 km.
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The function f(x) = -2(4)²+1 +140 represents the number of tokens a child has x hours after arriving at an arcade.
What is the practical domain and range of the function?
Enter your answer by filling in the boxes to correctly complete the statements. If necessary, round to the nearest hundredth.
The practical domain of the situation is ?
The practical range of the situation is ?
Answers
The practical domain of the situation is all real numbers, since there is no restriction on the number of hours the child can spend at the arcade.
The practical range of the situation is [1,140], since the minimum value of the function is 1 and the maximum value is 140.
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 3.5? (1 point)
A rectangle is shown. The length of the rectangle is labeled as 8 cm, and the width is labeled as 6 cm.
1.Perimeter = 98 cm, area = 109.25 cm2
2.Perimeter = 98 cm, area = 588 cm2
3.Perimeter = 42 cm, area = 109.25 cm2
4.Perimeter = 42 cm, area = 588 cm2
Answers
Answer:
2. Perimeter = 98 cm, área = 588 cm²
The selling price of a refrigerator, is $540.10.
If the markup is 10% of the dealer's cost, what is the dealer's cost of the refrigerator?
Answers
Answer: $491
Step-by-step explanation:
Lines m and n lie in the standard (x, y) coordinate plane.
Line m includes the points (5, -3) and (5, 7). If line n is
perpendicular to line m, which of the following could be
the equation of line n?
Answers
A possible linear equation for line n is given as follows:
y = b. (in which b is any constant).
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope, representing the rate of change of the function.b is the y-intercept, representing the value of y when x = 0.When two lines are perpendicular, the multiplication of their slopes is of -1. Additionally, the perpendicular line to a vertical line is an horizontal line.
Two points on line m are given as follows:
(5, -3) and (5, 7).
Meaning that it is a vertical line, as the x-coordinate is constant.
Thus the perpendicular line n is an horizontal line, which has the definition given as follows:
y = b. (in which b is any constant).
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After drawing a square on the board, Mr. Hinkle asked his class to identify the shape. Timothy stated that Mr. Hinkle had drawn a rhombus. Which of the following statements is true?
Answers
The mean number of days construction workers miss per year is 11. The standard deviation is 2.3. The mean number of days factory workers miss per year is 8 with a standard deviation of 1.8. Which class is more variable in terms of days missed?
Please show work.
Answers
Answer:
Factory Workers
Explanation:
While a common mistake may be to take in count of only the standard deviation (like I had done previously), there is an equation to use that measures the dispersion of data points in a data set around the mean, called coefficient of variation.
\(CV=\frac{\sigma}{\mu} *100\) where sigma is the population standard deviation and mu is the population's mean.
The highest percentage of CV is considered more variable.
Let's do the math:
Construction workers: \(\frac{\sigma}{\mu} =\frac{2.3}{11} =0.209*100=20.9%\\\)
Factory workers: \(\frac{\sigma}{\mu} =\frac{1.8}{8} =0.225*100=22.5%\)
Since factory workers have a higher percentage, their data is more variable.
Select the true statement.
Answers
1 1/2 yards = 54 inches.
Answer: D) 54 inches = 1 1/2 yards
explanation: 1 1/2 yards = 54 inches.
Irene y Alejandro tienen 73 libros irene tiene el doble que Alejandro mas 1 cuantos libros tiene cada uno?
Answers
Irene has 49 Books, and Alejandro has 24 books.
Let's assume that Irene has x books, and Alejandro has y books. According to the given information, we can form the following equations:
1. Irene has twice as many books as Alejandro plus 1:
x = 2y + 1
2. The total number of books between Irene and Alejandro is 73:
x + y = 73
We can now solve this system of equations to find the values of x and y.
Substituting the value of x from equation (1) into equation (2), we have:
(2y + 1) + y = 73
3y + 1 = 73
3y = 72
y = 24
Now, we can substitute the value of y into equation (1) to find x:
x = 2(24) + 1
x = 49
Therefore, Irene has 49 books, and Alejandro has 24 books.
To verify our solution, we can check if the sum of their books equals 73:
49 + 24 = 7
So, our solution is correct.
In conclusion, Irene has 49 books, and Alejandro has 24 books.
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\Suppose that a person has an average heart rate of 88.6 beats/min. (Express your answers to problems in this section to the correct number of significant figures and proper units.) (a) How many beats does he or she have in 5.0 y
Answers
Answer:
He or she has 232,840,800 beats in five minutes.
Step-by-step explanation:
This question is solved by proportions.
In this question:
A year has 365 days.
Each day has 24 hours.
Each hour has 60 minutes.
Minutes in five years:
5*365*24*60 = 2,628,000 minutes.
How many beats in five minutes?
88.6 beats/min, 2,628,000 minutes. So the number of bears is:
88.6*2628000 = 232,840,800
He or she has 232,840,800 beats in five minutes.
Mark what answer it is
Answers
2/29
the i is imaginary
A. Only Sequence A
B. Only Sequence B
C. Both
D. Neither
Answers
Answer:
THE CORRECT ANSWER IS LETTER B.
Step-by-step explanation:
I HOPE IT'S HELP
HAVE A NICE DAY & NIGHT
10 times as many as 1 hundred is _____ hundreds are _____thousands.
Answers
10 hundreds or 1 thousand.
Further explanation
This question is related to place values.
10 times as many as a number is 10 multiplies the number.
Hence, 10 times as many as 1 hundred is
\boxed{ \ 10 \times 1 \ hundred \rightarrow \boxed{ \ 10 \ hundreds \ } \ }
Furthermore, 10 hundreds have the same meaning as 1 multiplies 10 hundreds which can produce 1 thousand.
\boxed{ \ 1 \times 10 \ hundred \rightarrow \boxed{ \ 1 \ thousand \ } \ }
Quick steps
Part-1
\boxed{ \ 10 \times 1 \ hundred = X \ hundred \ }
\boxed{ \ 10 \ hundred = X \ hundred \ }
Thus, \boxed{\boxed{ \ X = 10 \ }}
Part-2
\boxed{ \ 10 \times 1 \ hundred = Y \ thousand \ }
\boxed{ \ 10 \times 100 = Y \ thousand \ }
\boxed{ \ 1,000 = Y \ thousand \ }
\boxed{ \ 1 \ thousand = Y \ thousand \ }
Thus, \boxed{\boxed{ \ Y = 1 \ }}
- - - - - - -
Conclusions
10 times as many as 1 hundred is _10_ hundreds or _1_ thousand.
Learn more
9 ten thousands divided by 10 (in unit form) brainly.com/question/4786449
How do you write 770,070 in expanded form? brainly.com/question/4725342
100 is ¹/₁₀ of what? brainly.com/question/96535
Keywords: 10 times as many as 1 hundreds, hundreds, thousands, place value, operations, multiply, equal, blank, quick steps
√-25/√9 please solve
Answers
Step-by-step explanation:
The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.
Let's break down the expression step by step:
√(-25) / √9
The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.
√(-1) is equal to "i," and the square root of 25 is 5.
So, the expression becomes:
i * 5 / √9
The square root of 9 is 3.
Now, we can simplify further:
i * 5 / 3
Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.
Find the nth Maclaurin polynomial for the function. f(x) = sec(x), n = 2 P_2(x) =
Answers
Answer:
\(\mathbf{P_2(x) = 1+\dfrac{x^2}{2}}\)
Step-by-step explanation:
Given that:
f(x) = sec (x) , n = 2
Where are to find P_2(x)
Suppose ; f(x) = sec (x) , n = 2
then
\(f(0) = sec (0) = 1\)
\(f'(x) = sec (x)* tan (x)|_{x=0} = 0\)
\(f''(x) = sec (x)*tan ^2(x)+ sec (x) * sec^2(x)\)
\(f''(x) = sec (x)*tan ^2(x)|_{x=0} + sec^3(x)\)
\(f''(x) = 0 + sec^3(0)\)
\(f''(x) = 1\)
\(f(x) = f(0) + \dfrac{f'(0)x}{1!}+ \dfrac{f''(0)x^2}{2!}+ \dfrac{f'''(0)x^3}{3!}+...\)
\(f(x) = 1 + \dfrac{0}{1!}x+ \dfrac{x^2}{2!}+...\)
\(f(x) = 1 + \dfrac{x^2}{2}+...\)
since order n =2
\(\mathbf{P_2(x) = 1+\dfrac{x^2}{2}}\)
Judy uses 9.7 pints of blue paint and white paint to paint her bedroom walls.3/5
of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Answers
Answer:
3.88 Pints
Step-by-step explanation:
First we need to find the amount of blue paint that was used. We can do that by multiplying 9.7 by 0.60 since that is 3/5 in decimal form
\(9.7*0.60=5.82\)
Now we know how much blue paint was used, now we just need to find how much white paint was used. We can do that by subtracting our amount of blue paint from the total amount of paint used
\(9.7-5.82=3.88\)
thus, 3.88 is the amount of white paint used
What is the value of x? Enter your answer in the box. ___ units
Answers
Answer:
x = 28
Step-by-step explanation:
Consider the two triangles ΔAPR and ΔCDR
We see that AP ║ CD
Therefore m∠PAR = m∠CR, m∠APR= m∠CDR
Angle ∠R is common to both triangles
So the triangles are similar
Therefore the ratios of the sides must be the same ratio
\(\dfrac{AR}{CR} = \dfrac{PR}{DR}\\\\\)
AR = x + 10
CR = x
PR = 42 + 15 = 57
DR = 42
PR = 42 + 15 = 57
Plugging in the values for these sides:
\(\dfrac{x + 10}{x} = \dfrac{57}{42}\\\)
Cross-multiplying we get
\(42(x + 10) = 57x\\\\42x + 420 = 57x\\\\420 = 57x - 42x = 15x\\\\15x = 420\\\\x = 420/15\\\\= 28\)
Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
A. √2:2
B. √√3:√√3
C. √5:3
D. 1 √3
□ E. 1: √2
O F. 2:3
SUBMIT
Answers
Answer: E
Step-by-step explanation:
n =64
x bar = 65.1
σ = 24
h₀: μ = 60
hₐ: μ ≠ 60
The test statistic equals ____
A. -1.70
B. 1.70
C. 0.3904
D. 0.0446
Answers
Answer:
B. 1.70
Step-by-step explanation:
Given:
\(n=64\)\(\overline{x}=65.1\)\(\sigma=24\)\(\textsf{h}_0:\mu=60\)\(\textsf{h}_1:\mu\neq 60\)\(\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \overline{X} \sim \left(\mu,\dfrac{\sigma^2}{n}\right) \implies Z=\dfrac{\overline{X}-\mu}{\sigma / \sqrt{n}} \sim \textsf{N}(0,1)\)
\(\textsf{then test statistic is}: \quad z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}\)
Substituting the given values into the formula to find the test statistic z:
\(\begin{aligned}\implies z &=\dfrac{65.1-60}{24 / \sqrt{64}}\\\\&=\dfrac{5.1}{3}\\\\&=\dfrac{17}{10}\\\\&=1.7\end{aligned}\)
find the missing angle
Answers
Answer:
? = 77°
Step-by-step explanation:
the 3 angles in a triangle sum to 180° , that is
? + 35° + 68° = 180°
? + 103° = 180° ( subtract 103° from both sides )
? = 77°
Answer:77
Step-by-step explanation:
180-103=77
carpet is sold in square yards how much carpet would a person need to buy for a rectangle that has dimensions of 10 yards by 18 feet
Answers
A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
How to determine the amount of carpet needed for a rectangular room?
To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.
The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),
18 feet ÷ 3 feet/yard = 6 yards
So the dimensions of the room in yards are 10 yards by 6 yards.
To find the total area of the room, we need to multiply the length and width,
10 yards × 6 yards = 60 square yards
Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
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At a meeting, there were 18 men and 24 women. What is the ratio of men to women at the meeting?
Answers
Answer:
18:24
Step-by-step explanation:
There is 18 men and they are at the beginning of the problem so the 18 men go first then the 24 Women.
Lena took out a $9000 loan for 7 months and was charged simple interest. The total interest she paid on the loan was $336.
Answers
The loan given has a rate of 0.53%
Simple InterestSimple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same, unlike compound interest where we add the interest of previous years principal to calculate the interest of the next year.
The formula of simple interest is given as;
S.I = P(1 + RT)
S.I = Simple interestP = principalR = rateT = timeSubstituting the values into the formula;
(9000 + 336) = 9000(1 + r * 7)
9336 = 9000 + 63000r
Collecting like terms
336 = 63000r
r = 0.0053
r = 0.0053 * 100
r = 0.53%
The rate on the loan is 0.53%
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H(p)=p/5 + 15
What is the independent variable in this function
Answers
In the given function H(p) = p/5 + 15, the independent variable is "p" ,
The independent variable in this function is denoted by "p." The independent variable can also be referred to as the input variable, which means that it is the value that is inputted into the function to produce an output. In this specific function, "p" represents the price of a good or service.
It is important to distinguish between the independent and dependent variables in a function. The dependent variable is denoted by "H(p)" in this case, and it is the output of the function. The value of the dependent variable is determined by the independent variable. In this function, "H(p)" represents the total cost of the good or service, which is dependent on the price "p." p is the input variable representing the price of the good or service.
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PLEASE HELP ASAP!!
I'd really appreciate the help on this.. Thanks in advance.
In order to answer the questions below you will need the
speed of light: c = 299 792.458 km/s. Use proper unit conversion if necessary and answer with the correct number of significant digits. The questions can be solved using the speed – distance – time relation.
For the questions below, provide a complete solution with explanation.
1. How long does it take light to travel from
a. the Moon to the Earth? (Data: Earth-Moon distance = 384,000 km)
b. the Sun to the Earth? (Data: Earth-Sun distance = 149,600,000 km)
2. Suppose you wanted to reach Alpha Centauri in 100 years.
How fast would you have to go in km/hr? (Data: Sun-Alpha Centauri distance = 4.37 light years)
Answers
Answer:
Step-by-step explanation:
Oof, this question is long.
Alr,
1.
a) Time = Distance/ speed = 384000/299792.458 = 1.28 seconds
b) Time = Distance/speed = 149600000/299792.458 = 499.0 or 8.317 minutes.
2.
If the distance 4.37 light years, if we travel at the speed of light, we can reach there in 4.37 years.
so, Speed = Distance/time
Speed = 4.37 light years/100 years
Speed = 0.0437 light year/year
So, the speed would be 0.0437 x speed of light. or 13100 or 1.31 x 10⁴.
Find the least common denominator. Then express each fraction using the least common denominator. 1/9 and 2/15
Answers
Answer:
10/90,12/90
Step-by-step explanation:
least common denominator is 90
Find the indicated probability. Round your answer to 6 decimal places when necessary.Two "fair" coin are tossed. Let A be the event of number of heads equal 1 and B be the event of getting tails for the second coin.Find the probability that either A or B occurs
Answers
Answer:
\(P(A\text{ U B) = }\frac{3}{4}\)Explanation:
Here, we want to find the probaility that either of two events occur
When we toss two coins at the same time, the possible results are:
\(HT\text{ HH TH TT}\)So, the first event is that we have a head only
We can see this in two out of the four and that makes its probability 2/4 = 1/2
The second event talks about getting tails in the second toss
We can see this in HT and TT too
The probability is 2/4 = 1/2
So, the probability that either occurs is the sum of the two which we have as follows:
\(P(A\text{ U B) = P(A) + P(B) - P(A n B)}\)Now, the probability of P(A n B) is the intersection of the two sets
The intersection means that we have situations where we have one head, and we have tails in the second event
This situation arise in HT (one head and second coin tail)
The probability of this is 1/4 (1 out of 4)
Finally, we compute the probability of either or as follows:
\(P(A\text{ UB) = }\frac{1}{2}+\frac{1}{2}-\frac{1}{4}\text{ = }\frac{3}{4}\)