When the original two-digit number is equal to the sum of the number's digits plus the product of its digits, the number is said to be special two-digit number.
We are required to describe the 2-digit special number in the provided question.
When the original two-digit number is equal to the sum of the number's digits plus the product of its digits, the number is said to be special.
Remove the first and last digits of the number, then add and multiply each digit separately. The two-digit number should then be multiplied by the sum and product of its digits, and the output should be compared to the initial value. It is a special two-digit number if they coincide; if not, it is not.
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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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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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How do you solve a polynomial on a graphing calculator?.
Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression or equation made up of variables, constants, and exponents.
Find the x-intercepts in step one.
Solve the equation to obtain the x-intercepts.
Find the y-intercepts in step two.
Put x=0 in the equation to determine the y-intercepts.
STEP 3: Determine the final action
A polynomial's final behavior and the final behavior of a leading term are identical.
STEP 4: Locate the pivotal moments
We must locate the first derivative of p in order to identify the turning point (x)
The first derivative's zeros are where the turning point's x coordinate is situated.
Substituting the aforementioned value into p will yield the y coordinate (x).
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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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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!
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What are the 3 properties of parallel lines?.
The three properties of parallel lines are transitive property of parallel lines, symmetric properties of parallel lines and properties cut by transversal.
Properties of parallel lines when cut by a transversal
Two lines when cut by a transversal line are parallel if the corresponding angles so formed are equal. Generally, the corresponding angles are in relative positions and lie along the same side of the transversal.
Two lines cut by a transversal line are said to be parallel if the alternate interior angles so formed are equal. In general, the pairs of the alternate interior are found in the inner side but lie on the opposite sides of the transversal.
Two lines cut by a transversal line are said to be parallell if the alternate exterior angles so formed are equal. In general, the pairs of alternate exterior angles are found on the outer side but lie opposite each other.
The above mentioned are 3 properties of parallel lines.
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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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One circle ha a radiu of 1/4 and another circle ha a radiu of 2. What i the ratio of the circumference of the larger circle to the circumference of the maller circle?
The ratio of the larger circle's circumference to the smaller circle's circumference is 8π : π.
Given info;
There are two circles, one with a radius of 1/4 and the other with a radius of 2.
To know the ratio of the larger circle's circumference to the smaller circle's circumference,
Let,
Circle's circumference = π * diameter
The circumference of the smaller circle = π/2
The diameter of the larger circle = 4π
Now,
The ratio of the circumference of the larger circle to the circumference of the smaller circle is,
⇒ 4π : π/2
8π : π
Hence, the ratio is 8π : π.
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Given a polynomial function f(x) = 2x2 – 3x 5 and an exponential function g(x) = 2x – 5, what key feature do f(x) and g(x) have in common? Both f(x) and g(x) have the ame domain of ([infinity], -[infinity]). Both f(x) and g(x) have the ame range of [0, -[infinity]). Both f(x) and g(x) have the ame x-intercept of (2, 0). Both f(x) and g(x) increae over the interval of [-4 , [infinity])
The key feature f(x) and g(x) have in common is both f(x) and g(x) have the same domain of ([infinity], -[infinity]). Option A is correct.
We are given the functions;
Polynomial function; f(x) = 2x² - 3x + 5
Exponential function; g(x) = 2ˣ - 5
In this question we must analyze the domain, range, x-intercepts, and changing intervals:
The domain of both functions is a set of all real numbers with both functions continuous.
The range of both functions is;
Range of f(x) = (3.875, +∞)
Range of g(x) = (-5, +∞)
The x-intercepts of both functions are;
x-intercept for f(x) is non-existent.
x-intercept for g(x) is (2.322, 0).
Thus, the key feature f(x) and g(x) have in common is both f(x) and g(x) have the same domain of ([infinity], -[infinity]). Option A is correct.
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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
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?)
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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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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) 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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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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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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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:
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 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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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:
complete the coordinate proof of the theorem.given: a b c d is a rectangle. prove: the diagonals of a b c d are congruent. art: a rectangle is graphed on a coordinate plane. the horizontal x-axis and vertical y-axis are solid. the vertex labeled as a lies on begin ordered pair 0 comma 0 end ordered pair. the vertex labeled as b lies on begin ordered pair a comma 0 end ordered pair. the vertex labeled as d lies on begin ordered pair 0 comma b end ordered pair. the vertex c is unlabeled. diagonals a c and b d are drawn by dotted lines.enter your answers in the boxes.
Since the lengths of both diagonals are given by the square root of the sum of the squares of their coordinates, they have the same length. Therefore, the diagonals of a b c d are congruent.
What are congruency?Triangles with the same size, form, and arrangement are said to be congruent. This indicates that all three of the triangle' side lengths are congruent, or equal in size. Congruent triangles can be rotated or reversed, yet their congruence remains constant.
The Side-Side-Side (SSS) Congruence Postulate argues that if three sides of one triangle are identical in length to the corresponding sides of another triangle, the halves of are congruent.
If two angles and a side of one triangle are congruent to the corresponding angles and sides of another triangle, then the two triangles are congruent. As an alternative, one can apply the Angle-Side-Angle (ASA) Congruence Postulate.
How to solve?
The distance formula is given by d = √((x2 - x1)^2 + (y2 - y1)^2), where d is the distance between the two points, (x1, y1) and (x2, y2).
To find the length of diagonal a c, we plug in the coordinates of points a and c into the distance formula: d = √((c - 0)^2 + (d - 0)^2) = √(c^2 + d^2)
To find the length of diagonal b d, we plug in the coordinates of points b and d into the distance formula: d = √((a - 0)^2 + (b - 0)^2) = √(a^2 + b^2)
Since the lengths of both diagonals are given by the square root of the sum of the squares of their coordinates, they have the same length. Therefore, the diagonals of a b c d are congruent.
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Line segment wx is the radius of circle x, and line segment zy is the radius of circle y. Points w, x, c, y, and z are all on line segment wz. What is the area of circle c, which passes though points w and z?.
The area of circle c, which passes though points w and z is 324[tex]\pi[/tex].
Point D here is the midpoint of the outer circle that we aim to find the area of. Here, the circle C has a diameter of WZ and radii of WC and CZ
We know that YZ = YD = 10 cm is as measured
Let DC be denoted by [tex]x[/tex] and CY be denoted by [tex]10-x[/tex].
The radius of the outer circle can be written as [tex]8+8+x[/tex] or [tex]10+10-x[/tex] which we can equate by following to find the value of [tex]x[/tex]
By equating both sides we get
⇒ 8+8+x = 10+10-x
⇒ 16+x = 20-x
⇒ 2x = 4
⇒ x = 2
Putting the value of x =2 in 8+8+x we get 18 as a radius.
Thus, area of circle =[tex]\pi 18^{2}[/tex] = 324[tex]\pi[/tex]
Hence, the area of circle c, which passes though points w and z is 324[tex]\pi[/tex].
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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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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
If the nth term of a number sequence is 5n? - 2n,
find the first 3 terms and the 10th term.
The first three terms are 3,16,39 and the 10th term is 480.
What is Arithmetic progression?
The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.tₙ = 5n² - 2nnow,
t₁ = 5(1)² - 2(1)
t₁ = 5 - 2
t₁ = 3
t₂ = 5(2)² - 2(2)
t₂ = 5(4) - 4
t₂ = 16
d = t₂ - t₁
d = 16 - 3
d = 13
t₃ = 5(3)² - 2(3)
t₃ = 45 - 6
t₃ = 39
t₁₀ = 5(10)² - 2(10)
= 500 - 20
t₁₀ = 480
Hence, the first three terms are 3,16,39 and the 10th term is 480.
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use the given data to find the equation of the regression line. round the final values to three significant digits, if necessary. managers rate employees according to job performance and attitude. the results for several randomly selected employees are given below.
The results for several randomly selected employees are given below [tex]Y = 11.7 + 1.02x.[/tex]
Below, we will discover the road equation, dissociation for each the management's conduct and fulfillment.
Here, attitudes are the reaction variable even as overall performance appears to be the predictor as mindset is fulfillment dependant.If Y shows the mindset even as X pertains to workers' overall performance.Let's describe the information like: [tex]y = a + bx + e[/tex]Now we get the estimates of e through the least quadratic method, – i.e., through decreasing the quantity of segments.S= sum e [tex]i^{2}[/tex] = [tex]sum (y_ - a - b x x)/ ^ 2[/tex]limit S to gain the estimates of a and b as:hat b = sum(y i - overline y )(x i - overline x ) sum(x i - overline x )^ 2hat a = overline y - hat b overline xSo,a = [tex]11.7b = 1.02[/tex] Y = [tex]11.7 + 1.02x[/tex].Read more about regression line:
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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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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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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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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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