Answer:
-1
Step-by-step explanation:
one in one five for three two one
QUESTION 6 Determine whether the set {P1, P2, P3} is linearly independent in P2, where p₁ = 2 + x + 3x² + 4x³, p₂ = 4 + 3x + 2x² + x³ and p3 = 1 + 2x + 3x² + 4x³. Show all working. [7 marks]
To determine whether the set [tex]$\{P_1, P_2, P_3\}$\\[/tex] is linearly independent in [tex]$P_2$[/tex], we construct a linear combination of the polynomials and set it equal to the zero polynomial. If the only solution to this equation is the trivial solution, then the set is linearly independent.
Let's construct the linear combination of the polynomials [tex]$P_1$[/tex], [tex]$P_2$[/tex] and [tex]$P_3$[/tex] as follows:
[tex]$c_1P_1 + c_2P_2 + c_3P_3 = 0$[/tex]
where [tex]$c_1$[/tex], [tex]$c_2$[/tex] and [tex]$c_3$[/tex] are constants. Substituting the given expressions for [tex]$P_1$[/tex], [tex]$P_2$[/tex] and [tex]$P_3$[/tex], we have:
[tex]$(c_1(2 + x + 3x^2 + 4x^3)) + (c_2(4 + 3x + 2x^2 + x^3)) + (c_3(1 + 2x + 3x^2 + 4x^3)) = 0$[/tex]
Expanding and combining like terms, we obtain:
[tex]$(2c_1 + 4c_2 + c_3) + (c_1 + 3c_2 + 2c_3)x + (3c_1 + 2c_2 + 3c_3)x^2 + (4c_1 + c_2 + 4c_3)x^3 = 0$[/tex]
For this equation to hold for all values of $x$, the coefficients of each term must be zero. Therefore, we have the following system of equations:
[tex]$2c_1 + 4c_2 + c_3 = 0$[/tex]
[tex]$c_1 + 3c_2 + 2c_3 = 0$\\$3c_1 + 2c_2 + 3c_3 = 0$\\$4c_1 + c_2 + 4c_3 = 0$\\[/tex]
We can represent this system of equations in matrix form as [tex]$AX = 0$[/tex], where A is the coefficient matrix and X is the column vector [tex]$\begin{bmatrix} c_1 \\ c_2 \\ c_3 \end{bmatrix}$[/tex]. To determine if there is a non-trivial solution, we need to find the determinant of the coefficient matrix A.
Calculating the determinant, we find that it is non-zero, indicating that the only solution to the system of equations is the trivial solution [tex]($c_1 = c_2 = c_3 = 0$)[/tex]. Therefore, the set [tex]$\{P_1, P_2, P_3\}$[/tex] is linearly independent in [tex]$P_2$[/tex].
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In the diagram below AB is parallel to CD what is the value of y
Answer:
y=60 due to adjacent angle
Answer:
Option - A. 60°
Step-by-step explanation:
AB is parallel to CD and given angle is alternate interior angle to y
∴ y = 60°
Solve by quadratic formula:
8a2 + 6a + 5=0
Answer:
[tex]x = \frac{-3 \pm i\sqrt{31}}{8}[/tex]
Step-by-step explanation:
Quadratic Formula: [tex]x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
√-1 is imaginary number i
Step 1: Define Quadratic
8a² + 6a + 5 = 0
a = 8
b = 6
c = 5
Step 2: Plug into Quadratic Formula
[tex]x = \frac{-6 \pm \sqrt{6^2-4(8)(5)} }{2(8)}[/tex]
Step 3: Solve
[tex]x = \frac{-6 \pm \sqrt{36-160} }{16}[/tex]
[tex]x = \frac{-6 \pm \sqrt{-124} }{16}[/tex]
[tex]x = \frac{-6 \pm \sqrt{124} (\sqrt{-1} )}{16}[/tex]
[tex]x = \frac{-6 \pm i\sqrt{124}}{16}[/tex]
[tex]x = \frac{-6 \pm 2i\sqrt{31}}{16}[/tex]
[tex]x = \frac{2(-3 \pm i\sqrt{31})}{16}[/tex]
[tex]x = \frac{-3 \pm i\sqrt{31}}{8}[/tex]
water runs into a conical tank at the rate of 26 cubic inches per second. the tank stands point down and has a height of 11 inches and a base radius of 7 inches. how fast is the water level rising when the water is 5 inches deep?
The water level is rising at a rate of approximately 0.017 inches per second when the water is 5 inches deep.
Let's start with the formula for the volume of a cone.V= 1/3πr²h
Here, h is the height of the water level at a given time. We are given that water is flowing in at a rate of 26 cubic inches per second. Therefore, we can calculate the rate of change of volume as dV/dt = 26.The tank stands point down, which means that the apex of the cone is at the bottom and the base is at the top. The height of the tank is 11 inches, so when the water level is 5 inches deep, the remaining height of the tank that is empty is 11 - 5 = 6 inches.The radius of the tank at the base is 7 inches, which means that the radius of the top of the water level is proportional to the height of the water level. Therefore, the radius of the top of the water level when the water level is 5 inches deep is: r = (5/11) x 7 = 3.18 inches.Now we can use the formula for the volume of a cone to find the volume of water in the tank when the water level is 5 inches deep.
V= 1/3πr²h= 1/3 x π x (3.18)² x 5= 53.4 cubic inches
Now we can find the rate of change of height with respect to time using the formula
dV/dt = A dh/dt, where A is the area of the base of the tank.
A = πr² = π(7)² = 49π square inches.
Therefore, we have:
26 = 49π dh/dt
dh/dt = 26 / (49π)
dh/dt ≈ 0.017
The water level is rising at a rate of approximately 0.017 inches per second when the water is 5 inches deep.
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Determine whether the two triangles are congruent. If they are
congruent, state by what theorem (SSS, SAS, or ASA) they are
congruent. Let
a = 111,
c = 36,
x = 9,
d = 111,
f = 36,
and
y = 9.
The two triangles are congruent by the Side-Side-Side (SSS) congruence theorem.
To determine the congruence of two triangles, we need to compare their corresponding sides and angles. In this case, let's consider two triangles: Triangle ABC and Triangle DEF.
Given:
a = 111, c = 36, x = 9 for Triangle ABC
d = 111, f = 36, y = 9 for Triangle DEF
We can observe that the corresponding sides of the two triangles have the same lengths. Side AB corresponds to side DE (a = d = 111), side BC corresponds to side EF (c = f = 36), and side AC corresponds to side DF (x = y = 9).
Since all three pairs of corresponding sides are congruent, we can conclude that the two triangles are congruent. By the Side-Side-Side (SSS) congruence theorem, if the lengths of the corresponding sides of two triangles are equal, then the triangles are congruent.
Therefore, based on the given information, Triangle ABC and Triangle DEF are congruent by the SSS congruence theorem.
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A used motorcycle is on sale for $3,600. Erik makes an offer equal to ¾ of this price. How much does Erik offer for the motorcycle? (A)$4,800 (B) $2,700 (C)$2,400 (D) $900
The answer is (B). Erik offers $2,700 for the motorcycle.
Original price of motorcycle = $3,600
Erik's offer = ¾ * $3,600 = $2,700
Here is the explanation in detail:
1. The original price of the motorcycle is $3,600.
2. Erik makes an offer equal to ¾ of the original price.
3. ¾ of $3,600 is $2,700.
4. Therefore, Erik offers $2,700 for the motorcycle.
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5+7-2+5=? Please help me out
The answer of 5+7-2+5=15
According to the number line, what is the distance between points A and B? A number line going from negative 16 to positive 12. A closed circle appears at negative 2 and is labeled A. A closed circle appears at positive 12 and is labeled B. An orange arrow line extends the length of the number line and contains points A and B.
Answer:
14units
Step-by-step explanation:
Given
Initial point A = -2 (since it is on negative 2)
Other point B = 12 (lying in positive 12)
To get the distance between point A and B, we will use the expression:
AB = point B - point A
Substitute the given point in the expression
AB = 12-(-2)
AB = 12+2
AB = 14
Hence the distance between points A and B in the number line is 14units
Two similar triangles are shown below:
Which two sets of angles are corresponding angles? (4 points)
w and v;
w and y;
w and z;
w and z;
Answer:
it's w and y
Step-by-step explanation:
i am no good with explaining sorry
The probabilities of it landing on sections A, B and
C are shown in the table below.
What is the probability, as a percentage (%), of the
spinner landing on section D?
Section
A
B
с
Probability
1
20
0.23
37%
Answer:
.05 + .23 + .37 + P(D) = 1
.65 + P(D) = 1
P(D) = .35 = 35%
First consider 100% what is the 100% of 40
Answer:
Step-by-step explanation:
100% means all of 40.
So 100% of 40 is 40
Answer:
40
Step-by-step explanation:
Of means Multiply.
Multiply.
100% * 40 = 40
~I hope I helped you! :)~
Solve 4 −6
s −83
Thank you in advance
Answer:
Alright, so we have 4 - 6 = s - 83.
This means
-2 = s - 83
Add 83 to both sides to get:
81 = s
s = 81 :)
Can someone help me plsss
Answer:
The slope of the line is [tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
The rule of the slope of a line is
m = [tex]\frac{y2-y1}{x2-x1}[/tex] (x1, y1) and (x2, y2) are two points lie on the line→ Let us solve the question
∵ The line contains the points B (-4, 4) and R (0, 2)
∴ x1 = -4 and y1 = 4
∴ x2 = 0 and y2 = 2
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{2-4}{0--4}=\frac{-2}{4}=\frac{-1}{2}[/tex]
∴ m = [tex]\frac{-1}{2}[/tex]
∴ The slope of the line is [tex]\frac{-1}{2}[/tex] .
Earth’s diameter is approximately 12,760,000 meters.
What is that number in scientific notation?
1.276 × 10-7
12.76 × 10-6
1.276 × 107
0.1276 × 108
Answer: C. 1.276 x 107
Step-by-step explanation:
Correct on e d g e n u i t y!
Answer:
C
Step-by-step explanation:
I just took the asignment.
Evaluate each expression.
1) 2 x 6+1+1
A) 13
B) 10
C) 14
D) 19
Answer:
c) 14
Step-by-step explanation:
2*6 + 1 + 1
following PEMDAS, the multiplication comes first.
2 * 6 = 12
12 + 1 + 1
14
Which sampling would be appropriate to survey 120,000 people? A. 12,000 B. 1,200 C. 120 D. 12
Answer:
12,000 i relly took the test gat it righ
Step-by-step explanation:
mark me brainlest pliz
Which value from the set (2 14, 16, 63} makes the equation n - 7 = 9 true?
63
16
2
14
Answer:
16
Step-by-step explanation:
16-7=9 so 16 makes the equation n-7=9 true
what is the solution to the inequality below? b+1 > -8
Answer:
from my point of view the solution should be 36
Answer:
b > -9
Step-by-step explanation:
Three consecutive integers are such that three times the smallest is 14 more than the largest.Find the integers.
Answer:
8, 9, 10Step-by-step explanation:
x ← the smallest integer
x+1 ← the middle integer
x+2 ← the largest integer
3x ← three times the smallest
x+2 + 14 ← 14 more than the largest
3x = x+2 + 14
-x -x
2x = 16
÷2 ÷2
x = 8
x+1 = 8+1 = 9
x+2 = 8+2 = 10
Check: 3×8 = 24; 24-14 = 10
I need helps with this please its due tmr :(
1. 17x - 3
2. 5m + 4n
3.-11x + 11
4. 6k + 1
5. 5xy + 7x
6. 7x - 19
7. 14a - 3b + 4
8. 6m - n
9. -a + 2n + 7
10. 6a
which equation in a standar form has a grpah that passes through the point (-4,2) and has a slope 9/2
Equation in standard form that has a graph that passes through point (-4, 2) and has slope of 9/2 is calculated to be as equal to -40.
The equation in standard form that has a graph that passes through the point (-4, 2) and has a slope of 9/2 is given by :
Step 1: Recall the standard form of a linear equation
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.
Step 2: Substitute given values
The equation should pass through the point (-4, 2) and should have a slope of 9/2.
Therefore, the slope-intercept form of the equation is given by:
y - 2 = (9/2)(x + 4)
Multiplying through by 2, we have: 2y - 4 = 9(x + 4)2y - 4
= 9x + 36
Rearranging, we get: 9x - 2y
= -40
Therefore, the equation in standard form that has a graph that passes through the point (-4, 2) and has a slope of 9/2 is 9x - 2y
= -40.
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Fill in the blank to make the two fractions equivalent.
7/8=?/48
I’m confused can someone help me ASAP
Answer:
42 should be in the blank.
Step-by-step explanation:
If you multiply 7/8 by 6, watch what happens...
7/8 *6 = 42/48
The denominators are the same, which shows how the equations are probably equal.
I know it might seem confusing because I'm not great at explaining, but I hope it helps! Have an awesome day c:
What is 829×2929-(920)×0
Answer:
0
Step-by-step explanation:
A uniform distribution is defined over the interval from 2 to 5.
What is the range of the random variable, x?
Over the range, what is the probability of the random variable, x?
What is the area of this uniform distribution?
The probability of x within this range is constant and equal to 1/3. The area under the uniform distribution curve is 1.
The range of the random variable, x, in a uniform distribution from 2 to 5 is [2, 5]. It represents the entire interval of possible values for x.
The probability of the random variable, x, in a uniform distribution is constant over the range. Since it is a uniform distribution, the probability density function is equal for all values within the range. Therefore, the probability of x taking any specific value within the range [2, 5] is the same, and it is given by 1 divided by the length of the range:
Probability of x = 1 / (length of range)
= [tex]P(x) = \frac{1}{5 - 2} = \frac{1}{3}[/tex]
The area of the uniform distribution is represented by the probability density function over the range. Since it is a uniform distribution, the probability density is constant within the range. Therefore, the area under the curve is equal to the length of the range multiplied by the constant probability density:
Area = (length of range) * (probability density) = (5 - 2) * (1 / (5 - 2)) = 3 * (1 / 3) = 1.
Hence, the area of the uniform distribution is 1.
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If f(x) = 4x4 + 5x2 + 4, then what is the remainder when f(x) is divided by
2 + 2?
Step-by-step explanation:
16+10+4
26+4
30
30÷(2+2)
30÷4
7 1/2
Find the unknown number 18/8 = 24/x
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{10.6}}}}[/tex]
Step-by-step explanation:
[tex] \rm{ \frac{18}{8} = \frac{24}{x} }[/tex]
Use cross product property
⇢ [tex] \rm{18 \times x = 24 \times 8}[/tex]
⇢ [tex] \rm{18x = 192}[/tex]
Divide both sides by 18
⇢ [tex] \rm{ \frac{18x}{18} = \frac{192}{18}} [/tex]
⇢ [tex] \rm{x = 10.6}[/tex]
We're done !
Hope I helped!
Best regards! :D
~TheAnimeGirl
What is -115/12 as a mixed number?
Answer:
Since − 115 /12
is a proper fraction, it cannot be written as a mixed number.
Cannot be written as a mixed number
Step-by-step explanation:
Evaluate.
4/7+3/4
A. 3/7
B. 37/56
C. 7/11
D. 19/28
Answer:
its
1.32142857143
Step-by-step explanation:
if its not im sary
(c) A different television costs $330.
(1) Ben buys one in a sale when this cost is reduced by 15%.
How much does Ben pay?
find value of each of the following 11+(-33)-(-7)
Answer:
= 11-33+7
= 11+7-33
= 18-33
= -15
Step-by-step explanation:
if we multiple + by - then it becomes -
if we multiple - by - then it becomes +
by this way I have done
I hope this will help u .
