The three properties of a subspace must be demonstrated for the set of all vectors orthogonal to w, indicated as w?, in order to demonstrate that it is a subspace of Rn.
What is the vector?In mathematics, objects with both magnitude and direction are called vectors. The vector's size is determined by the magnitude. It is shown as a line with an arrow, where the length of the line indicates the vector's magnitude and the arrow points in the desired direction. In addition, it goes by the names Euclidean vector, Geometric vector, Spatial vector, or just "vector."
What is the vectors are orthogonal?The term "orthogonal" in mathematics denotes a direction at a 90° angle. If two vectors are perpendicular to one another and the result of the dot product analysis is zero, then the vectors are said to be orthogonal.
a) Let u be any component of w and choose any z in w. Since z and w are orthogonal to one another, zu = 0. Now, let cz be the result of c and z for any scalar c. The equation (cz)u = c(zu) = c * 0 = 0 is known. As u was an arbitrary element of w, this demonstrates that cz is orthogonal to u and therefore cz is in w?
b) Let u be any component of w and consider z1 and z2 in w. Both z1u and z2u are known to be zero. Given that the first argument of the dot product is linear, we know that (z1 + z2)u = z1u + z2u = 0 + 0 = 0. As u was an arbitrary member of w, this demonstrates that z1 + z2 is orthogonal to u and that z1 + z2 is in w?
c) We have demonstrated that w? is closed under addition and scalar multiplication from a and b. We observe that the zero vector is obviously orthogonal to any vector in w and is thus in w? to demonstrate that it contains the zero vector. This demonstrates that w? is a subspace of Rn since it satisfies all three characteristics of a subspace.
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PLEASE HELP ASAP
Apply the square root principle to solve (x-3)² + 9 = 0.
a. x=0,6
b. x=0,-6
c. x=-3+3i, -3 -3i
d. x=3+31,3-3i
The obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
(x-3)² + 9 = 0
(x-3)²= -9
(x-3)=√-9
(x-3)=√9×√-1
(x-3)=±3i
x=3±3i
Thus, the obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.
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High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers have calculated the maximum horsepower for the engine to be 830HP. Twenty five engines are randomly selected for horsepower testing. The sample has an average maximum HP of 880 with a standard deviation of 55HP. Assume the population is normally distributed.Calculate a confidence interval for the average maximum HP for the experimental engine. Use a significance level of α=0.01. Round your answers to two decimal places.
The 99% of a confidence interval for the average maximum HP for the experimental engine. (843.0906, 916.9094)
Given,
In the question:
Given that the mean of the Population = 830HP
Given that the size of the sample 'n' = 25
Given that the mean of the sample = 880HP
Given that the sample standard deviation = 55HP
To find the confidence interval for the average maximum HP for the experimental engine.
Use a significance level of α=0.01.
Now, According to the question:
Degrees of freedom = n-1 =25 - 1 = 24
t₀.₀₀₅ = 3.3554
The 99% of a confidence interval for the average maximum HP for the experimental engine.
[tex](x -\frac{t_0_._0_0_1}{2},24\frac{S.D.}{\sqrt{n} } , x^2 +\frac{t_0_._0_0_1}{2},24\frac{S.D.}{\sqrt{n} })[/tex]
(880 - 3.3554 [tex]\frac{55}{\sqrt{25} }[/tex] , 880 + 3.3554 [tex]\frac{55}{\sqrt{25} }[/tex])
(843.0906, 916.9094)
Hence, The 99% of a confidence interval for the average maximum HP for the experimental engine. (843.0906, 916.9094)
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Choose five other iterated integrals that are equal to the given iterated integral. integral^2_0 integral^2_y integral^y_0 f(x, y, z) dz dx dy f(x, y, z) dz dy dx f(x, y, z) dz dy dx f(x, y, z) dz dy dx f(x, y, z) dz dy dx f(x, y, z) dz dy dx
By Changing the order of integral we can find five iterated integral that are equal to [tex]\int\limits^2_0 \int\limits^2_y \int\limits^y_0 {f(x,y,z)}\, dz dx dy[/tex]
Changing the order of integral means switching the dx dy order of integration into dy dx .
According to the question ,
The given integral is
=> [tex]\int\limits^2_0 \int\limits^2_y \int\limits^y_0 {f(x,y,z)}\, dz dx dy[/tex]
where;
the region is bounded by 0 ≤ z ≤ y, y≤ x ≤ 2, 0 ≤ y ≤ 2
(a) Changing the order of integral from dzdxdy to dzdydx
When y= 0 => x = y
and y = 2 => x = 2
[tex]\int\limits^2_0\int\limits^x_0 \int\limits^y_0 {f(x, y ,z )} \, dz dy dx[/tex]
(b) Now , changing the order of integral from dzdxdy to dxdzdy
When x = 0 => z = 0
x = 2 => z = y
[tex]\int\limits^2_0\int\limits^y_0 \int\limits^2_y {f(x, y ,z )} \, dx dz dy[/tex]
(c) Now ,Changing the order of integral from dzdxdy to dxdydz
[tex]\int\limits^2_0\int\limits^2_z \int\limits^2_y {f(x, y ,z )} \, dxdydz[/tex]
(d) Now ,Changing the order of integral from dzdxdy to dydzdx
[tex]\int\limits^2_0\int\limits^x_0 \int\limits^x_z {f(x, y ,z )} \, dydzdx[/tex]
(e) Now ,Changing the order of integral from dzdxdy to dydxdxz
[tex]\int\limits^2_0\int\limits^2_0 \int\limits^x_0 {f(x, y ,z )} \, dydxdz[/tex]
Are the five iterated integral that are equal to the integral [tex]\int\limits^2_0 \int\limits^2_y \int\limits^y_0 {f(x,y,z)}\, dz dx dy[/tex].
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(1 point) If p(x) and (x) are arbitrary polynomials of degree at most 2, then the mapping
=p(-1)q(-1) + p(070) +p(3)q(3) defines an inner product in P3- Use this inner product to find
||P||||9||, and the angle between p(x) and (x) for p(x) = 2x2 + 6 and 7(x) = 4x2 - 4x. < p, >= ||pl= ||ql| = A = radians.
If p(x) and q(x) are arbitrary polynomials of degree at most 2 then
||p||||q|| = 26([tex]\sqrt{640}[/tex]) and angle between p(x) and q(x) is 0.233.
Given that
<p,q> = p(-1)q(-1) + p(0) q(0) + p(3)q(3)
and p(x) = 2x²+ 6 , q(x)= 4x²-4x
then the values of p and q at x = -1,0,3 are given as;
x = -1,
p(-1) = 2(-1)² + 6 = 8 , q(-1) = 4(-1)² - 4(-1) = 8
x = 0,
p(0) = 2(0)² + 6 = 6 , q(0) = 4(0)² - 4(0) = 0
x = 3,
p(3) = 2(3)² + 6 = 24 , q(3) = 4(3)²- 4(3) = 24.
<p,q> = p(-1)q(-1) + p(0)q(0) + p(3)q(3)
= (8)(8) + (6)(0) + 24(24)
= 64 + 0 + 576
<p,q> = 640
Now we have to find ||p|| ||q||, for this we'll find ||p|| and ||q||
||p|| = [tex]\sqrt{ < p,p > }[/tex]
= [tex]\sqrt{8(8) + 6(6) + 24(24)}[/tex]
= [tex]\sqrt{676}[/tex]
||p|| = 26
and
||q|| = [tex]\sqrt{ < q,q > }[/tex]
=[tex]\sqrt{8(8) + 0(0) + 24(24)}[/tex]
||q|| =[tex]\sqrt{640}[/tex]
∴||p||||q|| = 26([tex]\sqrt{640\\[/tex])
Now we have to find angle between p(x) and q(x),
∴ α = cos⁻¹[tex]\frac{ < p,q > }{||p||||q||}[/tex]
= cos ⁻¹ [tex]\frac{640}{26(\sqrt{640}) }[/tex]
= cos ⁻¹ [tex]\frac{4\sqrt{10} }{13}[/tex]
α = 13.34°
In radian
α = 0.233.
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) prove that the absolute value of the integral is less than or equal to the integral of the absolute valu
By using the concept of integration, it can be proved that
The absolute value of the integral is less than or equal to the integral of the absolute value.
What is integration?
Integration is the process of adding of different individual parts into a whole.
Integration is the reverse of differentiation.
Integration is used to find the area under curve
Let [tex]f^+(x)[/tex] = max{f(x), 0} and [tex]f^-(x)[/tex] = -min{f(x) , 0}
[tex]f^+(x) + f^-(x) = \frac{1}{2}[f(x) + 0 + |f(x) - 0| - f(x) - 0+|f(x) -0|] = |f(x)|\\ f^+(x) - f^-(x) = \frac{1}{2}[f(x) + 0 + |f(x) - 0| + f(x) + 0-|f(x) -0|] = f(x)\\[/tex]
[tex]|\int^a_bf| = |\int^a_bf^+ -\int^a_b f^-| \leq \int^a_bf^+ + \int^a_bf^- = \int^a_b (f^+ + f^-) = \int^a_b|f|[/tex]
So [tex]|\int^a_bf|\leq\int^a_b|f|[/tex]
So, the absolute value of the integral is less than or equal to the integral of the absolute value.
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Write an equivalent expression for 8(1/2y - 7)
4y - 56 is the equivalent expression for 8(1/2y - 7)
How to write equivalent expressions?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).
Given: 8(1/2y - 7)
In order to write an equivalent expression, clear the parenthesis:
8(1/2y - 7) = 8(1/2y ) - 8(7)
= 4y - 56
Therefore, the equivalent expression for 8(1/2y - 7) is 4y - 56
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jenny has a box of candies with different flavors. she will randomly choose one piece of candy. the probability that she chooses a strawberry-flavored piece is 611. what are the odds against her choosing a strawberry-flavored piece? 116
The odds against her choosing a strawberry-flavored piece is 5/11.
What is the probability?Probability is the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The odds against her choosing a strawberry-flavored piece = 1 - probability that she chooses a strawberry-flavored piece
The odds against her choosing a strawberry-flavored piece = 1 - 6/11
The odds against her choosing a strawberry-flavored piece = 5/11
Here is the complete question:
jenny has a box of candies with different flavors. she will randomly choose one piece of candy. the probability that she chooses a strawberry-flavored piece is 6/11. what are the odds against her choosing a strawberry-flavored piece?
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Can someone help me find the inverse of this matrix please?
The inverse of the 4 × 4 matrix, [tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0\\ 0& 0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}[/tex] found using an online matrix tool is presented as follows;
[tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0\\ 0& 0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}^{-1}=\begin{bmatrix}\dfrac{1}{a} & 0& 0 &0 \\\\ 0& \dfrac{1}{b} & 0 & 0\\\\0 &0 &\dfrac{1}{c} & \\\\0 &0 &0 &\dfrac{1}{d} \\\end{bmatrix}[/tex]
What is the inverse of a matrix?The inverse, A⁻¹ of a matrix, A, can be found using the formula;
[tex]A^{-1}=\dfrac{adj \, A}{det\, A}[/tex]
The adjugate of the specified matrix, [tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}[/tex] is found using an online tool as follows;
[tex]adj\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}=\begin{bmatrix}b\cdot c\cdot d &0 &0 &0 \\ 0& a\cdot c \cdot d& 0& 0 \\ 0&0 &a\cdot b\cdot d &0 \\ 0& 0& 0& a\cdot b\cdot c\\\end{bmatrix}[/tex]
The value of the determinant of the matrix found using an online calculator is presented as follows;
[tex]det\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix} = a\cdot b \cdot c\cdot d[/tex]
The inverse of the matrix in the question is therefore;
[tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}^{-1}=\dfrac{\begin{bmatrix}b\cdot c\cdot d &0 &0 &0 \\ 0& a\cdot c \cdot d& 0& 0 \\ 0&0 &a\cdot b\cdot d &0 \\ 0& 0& 0& a\cdot b\cdot c\\\end{bmatrix}}{a\cdot b\cdot c \cdot d} = \begin{bmatrix}\dfrac{1}{a} &0 &0 &0 \\ \\0& \dfrac{1}{b} & 0& 0 \\ \\0&0 &\dfrac{1}{c} &0 \\\\ 0& 0& 0& \dfrac{1}{b} \\\end{bmatrix}[/tex]
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I really need help to get this done, please.
The area of the shaded portion of the inscribed hexagon is; 3.395 ft²
How to find the area of a hexagon?We are given;
Diameter of circle = 5 ft
Thus;
radius; r = 5/2 = 2.5 ft
Now, the long diagonal of the hexagon is given as 5ft and we know that if the side of the hexagon is a, then;
a = d/2
where d is the length of the long diagonal
Formula for area of hexagon is;
A = (3/2) * √3 * a²
Thus;
A = (3/2) * √3 * 2.5²
A = 16.24 ft²
Area of circle is gotten from the formula;
A = πr²
A = π * 2.5²
A = 19.635 ft²
Thus;
Area of shaded portion = 19.635 ft² - 16.24 ft² = 3.395 ft²
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Using compound interest formula [tex]A = p(1 +\frac{r}{n} )^{nt}[/tex] , the the amount after 5 years is $15,095.39
How to find the amount Eric owes for 6 years?The total amount a college student has in a saving account if 13000 dollars was invested and earned 3% compounded quarterly for 5 years can be calculated as follows:
Therefore, it is compounded quarterly which means 4 times.
[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]
where
p = principalr = rate t = timen = number of time compoundedTherefore,
p = 13000 dollars
t = 5 years
n = 4
r = 3% = 0.03
Therefore,
[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]
[tex]A = 13000(1+ \frac{0.03}{4} )^{(4)(5)}[/tex]
A = 13,000.00(1 + 0.0075)²⁰
A = $15,095.39
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a batter hits the ball and runs toward first base at a speed of 28 ft/s. at what rate (in ft/s) does the distance between the runner and second base change when the runner has run 20 ft? (round your answer to two decimal places.)
The rate at which the distance between the runner and second base changes is 28.71 ft/s.
Given, a batter hits the ball and runs toward first base at a speed of 28 ft/s. we have to find the rate (in ft/s) at which the distance between the runner and second base change when the runner has run 20 ft.
As, distance = speed × time
d = st
On differentiating both the sides
d' = s't + s
d' = 20/28 + 28
d' = 0.71 + 28
d' = 28.71
Hence, the rate at which the distance between the runner and second base changes is 28.71 ft/s.
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Write down the value of the 6 in the number 263.7
Answer:
60
Step-by-step explanation:
the 6 is in the tens place so it is worth 60
Hopes this helps please mark brainliest
Answer: 60
Step-by-step explanation: the value of 263.7 is; 60 pls mark brainly i really need it pls i neeed it its important to me bc i have a gammy who just passed away last week
problem 4.37 (a) apply to (equation 4.175), and confirm that you get . (b) apply to (equation 4.176), and confirm that you get zero. (c) show that and (equation 4.175) are eigenstates of , with the appropriate eigenvalue
a) √2 t |1, -1>
b ) t√0 |0, 1>=0
c) 2t² |1, -1> are the eigenstates of S² with the appropriate eigen value.
What is meant by eigen value?In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it. The associated eigenvalue, generally indicated by lambda, is the factor by which the eigenvector is scaled.
Eigenvalues and eigenvectors play an important role in the analysis of linear transformations. The prefix eigen- comes from the German word eigen, which means "property," "characteristic," or "own."
a) S- |1,0>= t√(1+0)(1-0+1) |1, 0-1>
=t√2 |1, -1>
=√2 t |1, -1>
∴S±(s, m>=t√(s±m)(s±m+1) |s, m±1>
b) S₊ |0, 0>= t√(0-0)(0+0+1) |0, +1>
=t√0 |0, 1>=0
S₋ |0, 0>=t√(0+0)(0-0+1_) |0. -1>
c) S² |1, 1>= 1(1+1)t² |1, 1>
=2t² |1, -1>
∴ S² |s, m>=s(s+1)t² |s, m>
Hence, |1, -1> and |1, -1> are eigen function of S² with eigen value 2t²s.
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What are the factors of the polynomial P x x3 5x2 2x 8?.
By usinf Divison method and Prime Factorization, the factors of the polynomial are x=1,2,2
Short explanation of what polynomials are?A polynomial is an expression made up of variables, constants, and exponents that is combined using mathematical operations such as addition, subtraction, multiplication, and division.
cubic polynomial = x³ - 5x² + 8x - 4
suppose x = 1 ,
x - 1 = 0
So, one of the factor = (x - 1)
Now,
By Division method
x³ - 5x² + 8x - 4 = Dividend
x - 1 = Divisor
x² - 4x + 4 = Quotient
Now for x² - 4x + 4
x² - 2x- 2x + 4
(x-2)(x-2)
x=2,2
so, factors are x=1,2,2
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what is after googolplex
Answer: A googolplexian
Step-by-step explanation: A googolplexian is a number with a googol of zeros after it.
hope this helps!
please give brainliest!
1. Determine which property is demonstrated below:
OG=NQ and GE=UY,
so OG +GE=NQ +UY
O subtraction property
distribution property
substitution property
O addition property
O None of these are correct.
4
Hence, the property is based on addition property,
OG=NQ and GE=UY,
so OG +GE=NQ +UY.
What is addition property?
When the same amount is added to both sides of an equation, the equation does not change, according to the addition property of equality. A = B remains valid even if a number x is added to both sides of the equation. It can be mathematically stated as A + x = B + x.
As demonstrated below
OG=NQ and GE=UY,
so OG +GE=NQ +UY
So this property leads to addition property.
So the correct option regarding this,
Addition property.
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A factory produced 475812 pen of one kind and 651652 pen of another kind. All the pen are mixed thoroughly and packed equally in 296 boxe. How many pen are packed in a box
The total number of pens packed in a box is 3809 pens.
What is an arithmetic operation?
The branch of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. Addition, subtraction, multiplication, and division are fundamental mathematical operations.
Given, A factory produced 475812 pens of one kind
And 651652 pens of another kind.
So, total pens = 475812 + 651652 = 1127464 pens
Total number of boxes = 296 boxes
Now,
Total number of pens packed in a single box = 1127464/296
= 3809 pens per box
Hence, the total number of pens packed in a box is 3809 pens.
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A political researcher takes a survey of 300 randomly selected registered voters in atlanta, and each person was asked who they plan on voting for in the 2020 mayoral election. 101 said they plan on voting for candidate a, 184 said they plan on voting for candidate b, and 15 were unsure or plan to vote for another candidate. In question 8, the political researcher estimated p, the population proportion of all registered voters in atlanta who plan to vote for candidate a, with a 95% confidence interval. The researcher now wants to estimate p with a margin of error of 3%. What is the minimum sample size needed?.
The minimum sample size needed is 93.
Given:
A political researcher takes a survey of 300 randomly selected registered voters in atlanta, and each person was asked who they plan on voting for in the 2020 mayoral election. 101 said they plan on voting for candidate a, 184 said they plan on voting for candidate b, and 15 were unsure or plan to vote for another candidate. In question 8, the political researcher estimated p, the population proportion of all registered voters in atlanta who plan to vote for candidate a, with a 95% confidence interval. The researcher now wants to estimate p with a margin of error of 3%.
here
n = 101
p = 0.5
e = 5%=0.05
z score at 95% = 1.96
[tex]n'=\frac{n}{1+\frac{z^2*p(1-p)}{e^2} }[/tex]
On submitting and solving using calculator
n = 93
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one half ÷ 3 = ___. 6 one and one-half two-thirds one-sixth (ANSWER ASAP 100 POINT!!!)
Answer:
1/6
Step-by-step explanation:
1/2 *1/3=1/6
identify the expression as a numerical expression or a variable expression. for a variable expression, name the variable. 9 10 it is a variable expression, and 9 and 10 are the variables. it is a numerical expression. it is a variable expression, and is the variable. it is a variable expression, and there is no variable.
This expression (9+10) is a numerical expression. And this is not a variable expression.
An expression made up only of numbers and operations is termed as numerical expression. While an expression written with a variable in it, is termed as variable expression. But this Both expression, that is a numerical expression and a variable expression can include powers. For example, from the given question 9 + 10 is a numerical expression, 9 and 10 are not variables. And in the expression, for example: 9a + 10b is a variable expression in which 9a and 10b are variable terms.
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Complete question- Identify the expression as a numerical expression or a variable expression. For a variable expression, name the variable.
9 + 10
A) It is a variable expression, and + is the variable.
B) It is a variable expression, and there is no variable.
C) It is a variable expression, and 9 and 10 are the variables.
D) It is a numerical expression.
Answer:
This expression (9+10) is a numerical expression. And this is not a variable expression.
Step-by-step explanation:
Use the appropriate compound-angle formula to express the following as a single trigonometric function, and then determine
the exact value of the expression.
sin π/2 cos π/4 - cos π/2 sin π/4
Answer:
[tex]\frac{1}{\sqrt{2}}[/tex]
Step-by-step explanation:
The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed. A certain ferry boat uses $100 worth of fuel per hour when cruising at 10 miles per hour. Apart from fuel, the cost of running this ferry (labor, maintenance, and so on) is$675 per hour. At what speed should it travel so as to minimize the cost per mile traveled?
The cost is minimum per mile traveled "V = 15 mph".
Given,
In the question:
The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed. A certain ferry boat uses $100 worth of fuel per hour when cruising at 10 miles per hour.
and, the cost of running this ferry is $675.
To find the speed should it travel so as to minimize the cost per mile traveled.
Now, According to the question:
C(V) ∝ V³
then,
C(V) = KV³
When, C = 100 and V = 10
then, 100 = k[tex](10)^3[/tex]
=> k = 1/10
∴ [C(V) = [tex]\frac{V^3}{10}[/tex]]
As we know,
Total cost per hour,
[tex]C_1[/tex] = [tex]\frac{V^3}{10}[/tex] + 675
Cost per mile = C/V
Now,
C₂ = [tex]\frac{\frac{V^3}{10}+675 }{V}[/tex]
=> [tex]\frac{V^2}{10} +\frac{675}{V}[/tex]
Then we'll need to discover their derivative as well as set that to zero (0) to minimize it.
[tex]C_2'[/tex],
=> [tex]\frac{2V}{10} - \frac{675}{V^2}[/tex] = 0
=> [tex]\frac{V}{5}[/tex] = [tex]\frac{675}{V^2}[/tex]
On applying cross-multiplication, we get
[tex]V^3[/tex] = 3375
V = 15
So that the cost is minimum at "V = 15 mph".
Hence, The cost is minimum per mile traveled "V = 15 mph".
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Rank each pendulum on the basis of the initial gravitational potential energy (before being released) of the pendulum-Earth system, Rank from largest to smallest To rank items as equivalent, overlap them. o 12 h=60 cm m - 1 kg o h = 60 cm m - 2 kg o h - 30 cm m - 2 kg o h15 cm m = 8 kg o h - 30 cm m-4 kg o h - 45 cm m-3 kg
The energy that an object has as a result of being in a gravitational field is known as gravitational potential energy. It may be expressed as,
U = mgh
Where, m is the object's mass, g is its gravitational field, and h is its height.
The body has a weight of 2 kg and a height of 60 cm. the gravitational potential energy is as follows:
U₁ = 60× 2×g
U₁ = 120kg
The body has a weight of 1 kg and a height of 60 cm. the gravitational potential energy is as follows:
U₂ = 60× 1×g
U₂ = 60g
A body that weighs 4 kg and measures 30 cm in height. the gravitational potential energy is as follows,
U₃ = 4 ×30× g
U₃ = 120g
A body that weighs 3 kg and measures 45 cm in height. the gravitational potential energy is as follows,
U₄ = 3×45×g
U₄ = 135g
The body has a weight of 2 kg and a height of 30 cm. the gravitational potential energy is as follows,
U₅= 2×30× g
U₅ = 60g
A body that weighs 8 kg and measures 15 cm in height. the gravitational potential energy is as follows,
U₆ = 8 ×15×g
U₆ = 120g
Consequently, the initial gravitational potential energy of the specified pendulum has the following rank:
The initial gravitational potential energy is greatest .From the 1, 3, and 6 are rated second and have the same beginning gravitational potential energy.The initial gravitational field in Figures 2 and 5 is identical.To know more about gravitational potential energy
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What is the purpose of making a geological timeline Quora?.
Geological timeline is based on the presence of fossils on the rocks of various sequences, and also the classification of rock types and the correlation of rocks of different locations.
The purpose that geological timeline serve and reason scientist do make it, is portray the history of the Earth.
A geological timeline can be regarded as a system which gives the relationship between geological strata as well as events based on chronological time.This helps the scientist in studying events as well as frequency of events to Know if there are chances of recurrence of that particular event.Examples of this event could be eclipse of sun that usually occur at some point in time.The geologic time scale also helps in portraying the history of the Earth such as rocks and fossils.Therefore, geologic time scale serves as events as regards Earth history.
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The classification of rock types, the correlation of rocks from diverse locations, and the presence of fossils on the rocks of distinct sequences are all used to create the geological timeline.
What is a Geological timeline?Geological timelines have a purpose, and scientists create them in order to depict Earth's history.
(A) The relationship between geological strata and events based on chronological time can be shown using a geological timeline.
(B) The scientist can use this information to investigate events and their frequency and determine whether there is a possibility that a specific event will occur again.
(C) A sun eclipse, which often happens at some point in time, could serve as an illustration of this occurrence.
(D) Rocks and fossils that depict Earth's past can be found thanks to the geologic time scale.
(E) As a result, the geologic time scale provides information about historical events on Earth.
Therefore, the classification of rock types, the correlation of rocks from diverse locations, and the presence of fossils on the rocks of distinct sequences are all used to create the geological timeline.
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I, III, and IV
I, II, and III
I and IV
All four quadrants
The quadrants that give the solution of the inequality y ≤ ²/₃x - 4 is; I, III, and IV
What is the solution to the given inequality?We are given the inequality as;
y ≤ ²/₃x - 4
Let us draft some coordinates before plotting the graph;
When x = 0;
y ≤ ²/₃(0) - 4
y ≤ -4
When x = 1;
y ≤ ²/₃(1) - 4
y ≤ -3¹/₃
When x = 2;
y ≤ ²/₃(2) - 4
y ≤ -2 ²/₃
when x = -1;
y ≤ ²/₃(-1) - 4
y ≤ -4²/₃
From the attached graph Inequality, it is clear that the shaded area which represents the quadrants that possess the solution to the inequality that;
Quadrants I, III, and IV
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Now, find the y-intercept for the parabola
defined by this same equation:
y=x²-x-12
Separate the values with a comma.
The y-intercept of the given parabola is y = -12.
What is the y-intercept for the parabola?
A graph's y-intercept is the point at which the graph crosses the y -axis. (Because a function must pass the vertical line test, it can only have one y-intercept.) The y-intercept is frequently referred to simply as the y -value.
On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.
The given equation of the parabola is
y = x² - x - 12
To find the y-intercept of the given parabola we have to put x = 0 in the above equation, we get
y = (0)² - 0 - 12
y = -12
Hence, the y-intercept of the given parabola is y = -12.
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Which is an example of system of linear inequalities?.
Example of linear inequalities; y ≤ x – 1 and y < –2x + 1
A combination of linear inequality equations with the same variables is referred to as a system of linear inequalities.
There are five inequality symbols used to represent equations of inequality.
These are less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠). Inequalities are used to compare numbers and determine the range or ranges of values that satisfy the conditions of a given variable.
Example of linear inequalities;
Graph the following system of linear inequalities:
y ≤ x – 1 and y < –2x + 1
Graph the first inequality y ≤ x − 1.
We will draw a solid border and shade below the line due to the "less than or equal to" mark.
On the same x-y axis, graph the second inequality, y -2x + 1.
In this instance, the less-than symbol will cause our boundaries to be dashed or dotted. Under the border, cast a shade.
As a result, the darker-colored zone extending indefinitely downward is the solution to this inequality problem, as seen below.
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A. $4
B.$5
C.$6
D.$7
if u do this thank u sm ily
Answer: The answer is $6.00.
Step-by-step explanation: 25+5=30 then, 36-30=6.00
(I don't know if it makes sense to you, but the answer is $6.00)
(Also, can I get brainly for this?)
if a hypothesis is not supported after analysis of experimental data, should the experiment be deemed a failure? why or why not?
If your data contradict your hypothesis, it is by no means a failure.
What is experimental data ?Data that can be measured or gathered using some benchmark objectives, according to your experimental needs. According to the needs of your experiment, the data produced using this method should either be qualitative or quantitative.
Information not obtained through the random selection of study participants or as part of a controlled experiment. In social science research, non-experimental data are frequently employed, especially when collecting experimental data would be prohibitively expensive or immoral. Non-experimental data require more analysis and interpretation than experimental data since the researcher cannot control which people are placed in the treatment and control groups. Nonexperimental data examples include administrative files, test results, and survey data. As well, they are referred to as observational data.
If your data contradict your hypothesis, it is by no means a failure; in fact, it could be more intriguing since you might discover a fresh way to view the facts. In science, it's usual for theories to be wrong, and new investigations frequently begin as a result.
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Suppose we are making a 95% confidence interval for the population mean from a sample of size 15. What number of degrees of freedom should we use?.
The number of degrees of freedom we should use is 14 for makin95% confidence interval.
Degrees of freedom of an estimate is the number of independent pieces of information that went into calculating the estimate. It’s not quite the same as the number of items in the sample. In order to get the df for the estimate, you have to subtract 1 from the number of items.
Degree of freedom of sample size of n : n -1
When we don't have any idea about population standard deviation,
and also, the sample size is less than 30 .
We use t-distribution to calculated the statistics.
According to the question,
We are making a 95% confidence interval
The sample is 15 (<30) . So , we have to adjust and use a t-value instead of a Z score in order to account for the smaller sample size and using the sample SD.
Note that the t-value depends on the degrees of freedom (df) as a reflection of sample size. When using the t-distribution to compute a confidence interval, df = n-1.
So , making 95% confidence interval for population mean from sample size 15 , we need degree of freedom of 14
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