In each part, let S be the standard basis for P2. Use the results proved in Exercises 22 and 23 to find a basis for the subspace of P2 spanned by the given vectors. (a) –1 + x – 2x², 3 + 3x + 6x?, 9 (b) 1 + x, x2, 2 + 2x + 3x2 (c) 1 + x – 3x2, 2 + 2x – 6x², 3 + 3x – 9x2
Answers
Find a basis for the subspace of P2 spanned by the given vectors using the results from Exercises 22 and 23.
How we find basis basis for the subspace?
For the subspace spanned by -1 + x - 2x², 3 + 3x + 6x?, 9, a basis can be found by applying the Gram-Schmidt process to the given vectors in order. This gives the basis {1 - 2x², 3x + 1}.
For the subspace spanned by 1 + x, x², 2 + 2x + 3x², a basis can be found by applying the Gram-Schmidt process to the given vectors in order. This gives the basis {1 + x, x² - 1, 3x² + 2x + 2}.
For the subspace spanned by 1 + x - 3x², 2 + 2x - 6x², 3 + 3x - 9x², a basis can be found by applying the Gram-Schmidt process to the given vectors in order. This gives the basis {1 + x - 3x², -2x + 4x², -x + 2x²}.
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Related Questions
Use Mean value theorem to prove √6a + 3 < a + 2 for all a > 1.
Using methods other than the Mean Value Theorem will yield no marks. {Show all reasoning).
Answers
√6a + 3 < a + 2, we have proven that √6a + 3 < a + 2 for all a > 1 using the Mean Value Theorem.
To use the Mean Value Theorem to prove √6a + 3 < a + 2 for all a > 1, we first note that the function f(x) = √6x + 3 is continuous on the interval [1,a].
Next, we need to find a point c in the interval (1,a) such that the slope of the line connecting (1,f(1)) and (a,f(a)) is equal to the slope of the tangent line to f(x) at c.
The slope of the line connecting (1,f(1)) and (a,f(a)) is given by:
(f(a) - f(1)) / (a - 1) = (√6a + 3 - √9) / (a - 1) = (√6a) / (a - 1)
To find the slope of the tangent line to f(x) at c, we first find the derivative of f(x):
f'(x) = (1/2) * (6x + 3)^(-1/2) * 6 = 3 / √(6x + 3)
Then, we evaluate f'(c) to get the slope of the tangent line at c:
f'(c) = 3 / √(6c + 3)
Now, by the Mean Value Theorem, there exists a point c in (1,a) such that:
f'(c) = (√6a) / (a - 1)
Setting these two expressions for f'(c) equal to each other, we get:
3 / √(6c + 3) = (√6a) / (a - 1)
Solving for c, we get:
c = (a + 2) / 6
(Note that c is indeed in (1,a) since a > 1.)
Now, we can evaluate f(a) and f(1) and use the Mean Value Theorem to show that:
√6a + 3 - √9 < (√6a) / (a - 1) * (a - 1)
Simplifying, we get:
√6a + 3 < a + 2
as desired.
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17
Solve the inequality and graph the solution.
3(x+5) > 12
Answers
Answer:
x > -1
Step-by-step explanation:
3(x + 5) > 12
Distribute
3x + 15 > 12
Subtract 15 to both sides
3x > -3
Sivide both sides by 3
3x/3 > -3/3
x > -1
Hope this helps and pls do mark me brainliest if you can:)
what percent of 925is37
Answers
Answer:
4%
Step-by-step explanation:
to find percentage do 37 divided by 925 helps it helps :)
PLS HELP!! WILL GIVE BRAINLY!! ASAP PLS!!!!!
Answers
Answer:
The solutions are,
x=0 and x= 5
(I don't know if you have to write both of these or only one, sorry)
Step-by-step explanation:
\(x^2-3x+6=2x+6\\solving,\\x^2-3x-2x+6-6=0\\x^2-5x+0=0\\x^2-5x=0\\x(x-5)=0\\\\x=0, x-5=0\\x=0,x=5\)
So, the solutions are,
x=0 and x= 5
Suppose you are to receive an allowance each week for the next 26 weeks. Would you rather receive (a) $ 1000 per week or (b) $ .02 the first week, $ .04 the second week, $ .08 the third week, and so on for the 26 weeks? Justify your answer.
Answers
Option (b) will result in a significantly higher total amount received compared to option (a) of $1000 per week.
In this scenario, I would prefer option (b) to receive $0.02 the first week, $0.04 the second week, and so on for the 26 weeks.
1. The amount doubles each week, so by the end of the 26 weeks, the amount will be much higher than $1000 per week.
2. To calculate the total amount received in option (b), we can use the formula for the sum of a geometric series:
S = a(1 - r^n) / (1 - r), where a is the initial term, r is the common ratio, and n is the number of terms.
3. In this case, a = 0.02, r = 2, and n = 26.
Plugging these values into the formula, we find that the total amount received is $0.02(1 - 2^26) / (1 - 2) = $0.02(1 - 67,108,864) / (-1) = $1,342,177.28.
In conclusion, option (b) will result in a significantly higher total amount received compared to option (a) of $1000 per week.
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(3c)° 42° 111°
Find the value of C in the figure
Answers
9 is the value of C.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The three given angles are (3c)° 42° 111°
We need to find the value of C.
The figure might be a triangle because there are three angles.
From angle sum property , the sum of three angles of triangle is 180 degrees.
3c+42+111=180
3c+153=180
Substitute 153 from both sides
3c=27
Divide both sides by 3
c=9
Hence, the value of c is 9.
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RATIONAL EXPONENTS pls help what do i do??
Answers
Answer:
x = 3
Step-by-step explanation:
\(26=-1+(27x)^{\frac{3}{4}}\)\(\implies 26+1=27^{\frac{3}{4}} x^{\frac{3}{4}}\)\(\implies 27\div 27^{\frac{3}{4}} =x^{\frac{3}{4}}\)\(\implies 27^{1-\frac{3}{4}} =x^{\frac{3}{4}}\)\(\implies 27^{\frac{4-3}{4}} =x^{\frac{3}{4}}\)\(\implies 27^{\frac{1}{\cancel 4}} =x^{\frac{3}{\cancel 4}}\)\(\implies 27 =x^{3}\)\(\implies 27^{\frac{1}{3}} =x\)\(\implies (3^3)^{\frac{1}{3}} =x\)\(\implies x = 3\)Answer:
x = 3Step-by-step explanation:
\(26=-1+\left( 27x\right)^{\frac{3}{4} }\)
\(\Longleftrightarrow 27=\left( 27x\right)^{\frac{3}{4} }\)
\(\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =\left[ \left( 27x\right)^{\frac{3}{4} } \right]^{\frac{4}{3} }\)
\(\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =\left( 27x\right)^{\frac{3}{4} \times \frac{4}{3} }\)
\(\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =27x\)
\(\Longleftrightarrow x=\frac{27^{\frac{4}{3} } }{27}\)
\(\Longleftrightarrow x=27^{\frac{4}{3} -1}\)
\(\Longleftrightarrow x=27^{\frac{1}{3} }\)
\(\Longleftrightarrow x=\sqrt[3]{27}\)
\(\Longleftrightarrow x=3\)
analysis is a form of horizontal analysis that can reveal patterns in data across periods. it is computed by taking the (analysis period amount/base period amount) x 100.multiple choice question.ratiotrendmodified horizontal
Answers
The type of analysis described in the statement is ratio analysis.
Ratio analysis is a tool used to evaluate the financial performance of a company by comparing different financial ratios over time or between companies. It involves calculating different ratios such as liquidity ratios, profitability ratios, and solvency ratios and comparing them across different periods to identify trends or patterns in the data. The ratio analysis formula mentioned in the statement is used to calculate the percentage change in a ratio between two periods, with the base period amount serving as the denominator.
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In a bubble sort, on each pass through the list that must be sorted, you can stop making pair comparisons _____. A. one comparison later B. one comparison sooner C. two comparison sooner D. two comparison later
Answers
Answer:
In a bubble sort, on each pass through the list that must be sorted, the largest value "bubbles" to the end of the list. Therefore, after each pass, the end of the list is guaranteed to be sorted. This means that we can stop making pair comparisons one comparison sooner, which is option B.
Step-by-step explanation:
Bubble sort works by repeatedly comparing and swapping adjacent elements in the list if they are in the wrong order. During each pass through the list, the largest unsorted element "bubbles up" to its correct position. As a result, after the first pass, the largest element is in its correct position, after the second pass, the two largest elements are in their correct positions, and so on.
Therefore, with each subsequent pass, you can stop making pair comparisons one comparison sooner because the elements at the end of the list are already sorted.
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Here is a system of linear equations: 2x + y = 6 3x - y = 9
What is the solution to the system of equations shown?
Answers
Answer: C
Step-by-step explanation:
Because i said so
Simplify the expression (6^4)^2.What is the simplified form of this expression?
Answers
Answer:
6^8Step-by-step explanation:
Use of formula (a^b)^c = a^(bc)Simplify
(6^4)^2 = 6^(4*2) = 6^8Answer:
brainliest plsssssss
Step-by-step explanation:
(6^4)^2
=(6^4)^2
=(6^4) x (6^4)
=(6 x 6 x 6 x 6) x (6 x 6 x 6 x 6)
=6 x 6 x 6 x 6 x 6 x 6 x 6 x 6
=68
=1679616
A farmer needs to plant 180 tomato plants. He can plant 9 plants every 15 minutes.
a) What percentage of the planting will be complete after 75 minutes?
It will be
% complete.
b) How many minutes will it take to finish 90% of the planting?
It will take ____ minutes.
Answers
Answer:
52.94%
270 minutes
Step-by-step explanation:
1. 9 plants - 15 minutes
x plants - 75 minutes
Cross multiply
15x = 75 x 9
15x = 675
Divide both sides by 15
x = 675/15
x = 45 plants
45/85 x 100
= 52.94%
2. 90% of 180
= 90/100 x 180
= 162 plants
9 plants - 15 minutes
162 plants - x minutes
Cross multiply
9x = 162 x 15
9x = 2430
Divide both sides by 9
x = 2430/9
x = 270 minutes or 4 hours 30 minutes.
Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. the first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.
1. Write an equation for each tank representing the total amount of water in gallons in the tank, y, in terms of the number of hours, x, that the tank drains
2. what is the solution to this system of equations.
3. suppose Aiko starts draining the tanks at the same time. When will both tanks have the same amount of water? How much water is in each tank at that time
Answers
The answers to each part is mentioned above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.
( 1 ) -Equation for tank {1} -
y = 175 - 25x
Equation for tank {2} -
y = 200 - 30x
( 2 ) -For the solution we can write -
175 - 25x = 200 - 30x
- 25x + 30x = 200 - 175
5x = 25
x = 5
and
y = 200 - 150
y = 50
( 3 ) -For the same amount of water we can write -
175 - 25x = 200 - 30x
- 25x + 30x = 200 - 175
5x = 25
x = 5 hours
In tank (1), there is : 175 - 25 x 5 = 50 gallons
In tank (2), there is : 200 - 30 x 5 = 50 gallons
Therefore, the answers to each part is mentioned above.
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I need help on this question thanks
Answers
Answer:
length of arc YPX=πrtheta /180
given radius =8m
= π(8)(360-90)/180=π(8)(270)/180=12πm
What is the rate of change for this function? 29. y = 5
Answers
Correct answer is (0,5)
6 16 Next → Pretest: Scientific Notation Drag the tiles to the correct boxes to complete the pairs.. Particle Mass (grams) proton 1.6726 × 10-24 The table gives the masses of the three fundamental particles of an atom. Match each combination of particles with its total mass. Round E factors to four decimal places. 10-24 neutron 1.6749 × electron 9.108 × 10-28 two protons and one neutron one electron, one proton, and one neutron Mass 0-24 grams two electrons and one proton one proton and two neutrons Submit Test Particles F
Answers
We can drag the particles in mass/grams measurement to the corresponding descriptions as follows:
1. 1.6744 × 10⁻²⁴: Two electrons and 0ne proton
2. 5.021 × 10⁻²⁴: Two protons and one neutron
3. 5.0224 × 10⁻²⁴: One proton and two neutrons
4. 3.3484 × 10⁻²⁴: One electron, one proton, and one neutron
How to match the particlesTo match the measurements to the descriptions first note that one neutron is 1.6749 × 10⁻²⁴. One proton is equal to 1.6726 × 10⁻²⁴ and one electron is equal to 9.108 × 10⁻²⁸.
To obtain the right combinations, we have to add up the particles to arrive at the constituents. So, for the figure;
1.6744 × 10⁻²⁴, we would
Add 2 electrons and one proton
= 2(9.108 × 10⁻²⁸) + 1.6726 × 10⁻²⁴
= 1.6744 × 10⁻²⁴
The same applies to the other combinations.
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Directions: Using trig functions, find the value of each variable. Write your final answer
in the blank. Show your work and round answers to the nearest tenth.
(First problem)
Answers
x = 5.4
\(\bold{EXPLANATIONS:}\)
Helpppp ASAP
X+6/13=2
Answers
To prepare for a bake-Off, Sebastian used 830 grams of flour each day for 4 weeks. How many kilograms did Sebastian use in those 4 weeks?
1 q = 0.001 kg
Answers
If 830 grams = 1 day.
23.24 kilograms = 4 weeks.
23.24 kilograms were used by Sebastian in those 4 weeks.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 3x = 4 is an equation.
We have,
830 grams is used each day.
830 grams = 1 day ___(1)
1 week = 7 days
Multiply 4 on both sides.
4 weeks = 28 days ___(2)
From (1) and (2) we get,
4 weeks = 28 days
4 weeks = 28 x 1 day
4 weeks = 28 x 830 grams
4 weeks = 23240 grams ____(3)
1000 grams = 1 kg
Multiply both sides by 23240/1000.
23240 grams = 23.24 kilograms _____(4)
From (3) and 94) we get,
4 weeks = 23.24 kilograms
Thus,
23.24 kilograms were used by Sebastian in those 4 weeks.
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Find 4+(−1 2/3). Write your answer as a fraction in simplest form.
Answers
Answer:
\(\frac{7}{3}\)
I hope this helps!
Answer:
2 1/3
Step-by-step explanation:
What is the slope of the line?
A: 2/5
B: -2/5
C: 1/3
D: 5/2
Answers
Multiply and simplify if possible. (2sqrt3x -2)(3sqrt3x +5)
show work
Answers
The expression is simplified to give 2(9x + 2√3x - 5)
How to determine the valueFirst, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms
From the information given, we have that;
(2√3x - 2)(3√3x + 5)
expand the bracket, we get;
6√9x² + 5(2√3x) - 6√3x - 10
Find the square root factor
6(3x) + 10√3x - 6√3x - 10
collect the like terms, we have;
18x + 4√3x - 10
Factorize the expression, we have;
2(9x + 2√3x - 5)
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Q \( 5: 7(=2+2+3) \) points For each of the following languages over \( \{a, b\} \), give a relaxed or strict regular grammar to generate it. a) The set of strings that either contain bbaa or contain
Answers
To generate the set of strings that either contain "bbaa" or contain an even number of "b"s, we can provide a strict regular grammar and a relaxed regular grammar as follows:
1. Strict Regular Grammar:
S -> aS | bS | T
T -> bU | aT | bbaa
U -> aU | bU | bb
The non-terminal S generates all strings that contain either "a" or "b". The non-terminal T generates strings that contain "bbaa". The non-terminal U generates strings with an even number of "b"s. By introducing additional non-terminals and productions, we ensure that the grammar strictly generates the desired set of strings.
2. Relaxed Regular Grammar:
S -> aS | bS | T
T -> aT | bT | bbaa | ε
The non-terminal S generates all strings that contain either "a" or "b". The non-terminal T generates strings that contain "bbaa" directly or allows for an empty string (ε) to be generated. This relaxed grammar allows for more flexibility, as it allows the generation of strings that don't necessarily contain an even number of "b"s but still fulfill the condition of containing "bbaa" or allowing an empty string.
These regular grammars can generate the desired set of strings based on the given conditions.
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x²-4
If g(x)= then determine the value of g (f (5)). Sh
>
10
Show how you arrived at your answer.
Answers
A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.
What is a function?
In mathematics, a function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is called the domain of the function and the set Y is called the codomain of the function.
The earliest known approach to the concept of functions can be traced back to the work of Persian mathematicians Al-Birni and Sharaf al-Din al-Tusi. Functions were originally an idealization of how one variable depends on another. For example, planetary positions are functions of time. Historically, this concept was refined in calculus in the late 17th century, and by the 19th century the functions considered were differentiable (i.e. they had a high degree of regularity). The concept of functions was formalized in set theory at the end of the 19th century, greatly expanding the scope of the concept.
A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.
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Which of the following is an example of the associative property of multiplicaition?
1. 7 • (3 + 5) = 21 + 35
2. 7 • (3 • 5) = 7 • (5 • 3)
3. 7 • (3 • 5) = (7 • 3) • 5
4. 7 • ⅐ = 1
Answers
The example of the associative property of multiplication is 7 • (3 • 5) = (7 • 3) • 5
How to determine the example of the associative property of multiplication?The associative property of multiplication states that
(a * b) * c = a * (b * c)
Using the above equation as a guide, we have the following equation
7 • (3 • 5) = (7 • 3) • 5
The above equation is the option (3) of the associative property of multiplication
Hence, the example of the associative property of multiplication is 7 • (3 • 5) = (7 • 3) • 5
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Qd=95−4P
Qs=5+P
a. What is Qd if P=5 ? b. What is P if Qs=20 ? β=9 c. If Qd=Qs, solve for P.
Answers
P = 90 is the solution for the given equation.
Given: Qd=95−4
PQs=5+P
To find Qd if P=5:
Put P = 5 in the equation
Qd=95−4P
Qd = 95 - 4 x 5
Qd = 75
So, Qd = 75.
To find P if Qs = 20:
Put Qs = 20 in the equation
Qs = 5 + PP
= Qs - 5P
= 20 - 5P
= 15
So, P = 15.
To solve Qd=Qs, substitute Qd and Qs with their respective values.
Qd = Qs
95 - 4P = 5 + P
Subtract P from both sides.
95 - 4P - P = 5
Add 4P to both sides.
95 - P = 5
Subtract 95 from both sides.
- P = - 90
Divide both sides by - 1.
P = 90
Thus, P = 90 is the solution for the given equation.
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The price of a phone is AED 600. It is discounted by 18%. You also have a 7% discount voucher on the
sale price.
How much will you pay for this phone?
Answers
Answer:
You will pay $457.56.
Step-by-step explanation:
600 x .18 = 108 This is the amount taken off
600 - 108 = 492 Now we will take 7% off of 492
492 x .07 = 34.44
492 - 34.44 = 457.56
Find the area of each object. Round each answer to the nearest tenth, if necessary.
Answers
Answer The small triangles each have an area of 12m^2 and the big rectangle had an area of 80m^2. This would mean that the combined area is 104m^2
Step-by-step explanation: The rectangle shape can be found by multiplying 8 by 10 to get 80m^2. The two triangles can be found by multiplying 4 (half of 8) by 6 and then dividing it by two. This would mean that the small triangles each have an area of 12.
.5.1 The height AB (hint: Theorem of Pythagoras)
Answers
Answer: give me the context please
Step-by-step explanation:
Reason 1. M∠A + m∠B + m∠C = 1. 2. 28° + x − 4° + = 180° 2. Substitution 3. X = 3. Algebra
Answers
Answer:
156°
Step-by-step explanation:
Reason 1.
M∠A + m∠B + m∠C = 1.
2.
28° + x − 4° + = 180°
We collect like terms
x = 180° + 4° - 28°
x = 156°