From the given vectors, we have that:
a) The vectorial products are given as follows:
(b x a) = -3i - j + 4z.(a x c) = a x c = 1i - 2z.b) The angle between vectors a and c is of 6.84º.
How to find a vectorial product?A vectorial product between two vectors A and B is found from the determinant of a matrix, in which:
The first line is composed by the coordinates i, j and k.The second line is composed by the elements of vector a.The third line is composed by the elements of vector b.Then for the vectorial product b x a, the matrix is:
[tex]\left[\begin{array}{ccc}i&j&k\\3&-1&2\\-2&2&1\end{array}\right][/tex]
Using a calculator, the determinant, which is the vectorial product, is given by:
b x a = -3i - j + 4z.
For the vectorial product a x c, the matrix is:
[tex]\left[\begin{array}{ccc}i&j&k\\-2&2&-1\\-2&3&-1\end{array}\right][/tex]
a x c = 1i - 2z.
The angle is found as follows:
sin(θ) = |a x c|/(|a| x |c|)
The norms are given as follows:
[tex]|a \times c| = \sqrt{1^2 + (-2)^2} = \sqrt{5}[/tex]. [tex]|a| = \sqrt{(-2)^2 + (2)^2 + (-1)^2} = 3[/tex]. [tex]|c| = \sqrt{(-2)^2 + (3)^2 + (-1)^2} = \sqrt{14}[/tex].Hence:
[tex]\sin{\theta} = \frac{\sqrt{5}}{3\sqrt{14}}[/tex]
[tex]\theta = \sin^{-1}{\left(\frac{\sqrt{5}}{3\sqrt{14}}\right)}[/tex]
θ = 6.84º.
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I need help solving this
Solution:
Given:
[tex]108,105,102,...,15[/tex]This is an arithmetic sequence because it has a common difference.
From the nth term of an arithmetic sequence,
[tex]\begin{gathered} a_n=a+(n-1)d \\ a=108 \\ d=105-108=102-105=-3 \\ a_n=15 \\ \\ Hence,\text{ the number of terms in the sequence is;} \\ 15=108+(n-1)-3 \\ 15-108=-3(n-1) \\ -93=-3(n-1) \\ \frac{-93}{-3}=n-1 \\ 31=n-1 \\ 31+1=n \\ 32=n \\ n=32 \end{gathered}[/tex]The sum of an arithmetic sequence is given by;
[tex]\begin{gathered} S_n=\frac{n}{2}(a+l) \\ \\ where: \\ first\text{ term, }a=108 \\ last\text{ term, }l=15 \\ n=32 \\ \\ Hence, \\ S_n=\frac{32}{2}(108+15) \\ S_n=16(123) \\ S_n=16\times123 \\ S_n=1968 \end{gathered}[/tex]herefore, the sum oft the sequence is 1968
12.03 km = _________ m ______ cm
1km = 1000 m
12.03 km = 12.03 x 1000
12.03 km = 12030 m
1km = 100000 m
12.03 km = 12.03 x 100000
12.03 km = 1203000 cm
Graph the equation y= −4x −3
Answer: See attached.
Step-by-step explanation:
We can look at the values given in the equation to graph it.
➜ The -3 shows the line will intercept the y-axis at -3.
➜ The equation has a slope of -4, so for everyone right we move four down.
Which of the following could be an equation of g?
A) g(x)= (x-5)(x-9)
This is the answer because basically you need to find the roots of the function, since the function g intersects the x-axis at x=5 and x=9 you can conclude easily that those are the roots.
If:
x=5
g(5)=(5-5)(5-9)=0(-4)=0
and
If:
x=9
g(9)=(9-5)(9-9)=(4)(0)=0
If the area of a rectangular sign is approximately 4260 ft. and the width is approximately 60 feet what is the height of the sign
Answer:
The height is 71 feet.
Step-by-step explanation:
[tex]60h = 4260[/tex]
[tex]h = 71[/tex]
If the area of a rectangular sign is approximately 4260 square feet and the width of the sign is approximately 60 feet then, the height of the sign is approximately 71 feet.
To find the height of the given rectangular sign, let's put the given values in the formula for finding the area of a rectangle i.e.,
Area of rectangle = Height x Width
4260 = Height x 60
Solve the equation for the area of a rectangle where
Height (H) = Area of rectangle/Width
Height (H) = 4260/60
Height of the sign = 71 feet
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Which pair of complex numbers has a real-number product?
The product of (1 + 3i)(1 – 3i) is a real number.
What is a complex number?Complex Numbers in Math. Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).
We know that,
[tex]i^{2} = -1[/tex]
case A) [tex](1+3i)(6i)[/tex]
applying distributive property
[tex]6i+18i^{2}[/tex]
[tex]6i-18[/tex]
This is not a real number.
case B) (1+3i) (2-3i)
applying distributive property
[tex]2-3i+6i-9i^{2}[/tex]
[tex]11+3i[/tex]
This is also not a real number.
case C) [tex](1+3i) (1-3i)[/tex]
applying difference of square
[tex]1-9i^{2}[/tex]
1+9 = 10
This is a real number.
case D) [tex](1+3i) (3i)[/tex]
applying distributive property
[tex]3i+9i^{2}[/tex]
[tex]3i-9[/tex]
This is not a real number.
Hence, The product of (1 + 3i)(1 – 3i) is a real number
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I opened a grocery account at my bank with $150. Every week thereafter, I withdraw $55 from the account to pay for groceries.
If x is the number of weeks I've had the account, then y is the amount in the account.
Find an equation of a line in the form y = mx + b that describes my grocery account balance.
y=
If he opened a grocery account at my bank with $150 and every week thereafter he withdraw $55 from the account to pay for groceries, then the equation of the line in the form y = mx+b that describes the grocery account balance is y = -55x+150
The balance in the bank account = $150
The amount he withdraw from the account for groceries = $55
Consider the number of week he had the account as x
y is the amount in the account
Then the equation will be
y = 150-55x
Rearrange the term and make the equation in the form y = mx+b
y = -55x+150
Hence, If he opened a grocery account at my bank with $150 and every week thereafter he withdraw $55 from the account to pay for groceries, then the equation of the line in the form y = mx+b that describes the grocery account balance is y = -55x+150
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Write the following inequality in s
19x + y ≤ -11
Write your answer with y first, fo
fractions, and improper fractions
The inequality in slope intercept form is –y≥19x+11
What is slope intercept?
Slope intercept form is defined as the graph of linear equation y=mx+b where m and b as the y-intercept.
What is inequality?
Inequality is an equation that is used to show the non equal comparison of two or more numbers and variables.
Given inequality is 19x+y≤-11
To solve this inequality in y form, we will subtract 19x from both side, we get
y≤-11-19x
Now, we will take minus sign common,
-y≥19x+11
Hence, the required answer.
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which of the given values are in the interval (-3,1]?
The values coming in the interval (-3,1] are -2, -1, 0, and 1.
What is defined as the term interval notations?An interval is represented on a number line using interval notation. In all other sayings, it is a method of writing real number line subsets. An interval is made up of numbers that fall between two specific data set.Intervals can be categorized according to the numbers in the set.Interval Open: The endpoints of a inequality are not included in this type of interval.Interval Closure; The endpoints of a inequality are included in this type of interval.Interval with Half-Open Doors: This interval contains only one of inequality's endpoints.The given interval notation is;
(-3,1], it is the case of half open half close.
-3 comes with the open interval, it means its value will not be included in the interval.
1 is with the closed interval, it means its value will be included in the interval.
Thus, the values lying between the interval (-3, 1] are -2, -1, 0, and 1.
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Find domain and range
polynomial degree 3 root of multiplicity 2 at x=1 root of multiplicity 1 at x=-2 y-intercept is y =-1.6
By using the definition of a polynomial in product form is described by y = - 0.8 · (x - 1)² · (x + 2)
How to determine a least degree polynomial
According to algebra, polynomials are products of binomials of the form x - r, where r is a root of the polynomial. The product form of polynomials is described by the following formula:
p(x) = a · Π (x - r), for i = {1, 2, 3, n}, where n is the grade of the polynomial and a is the lead coefficient.
If we know that y(0) = - 1.6, r₁ = r₂ = 1 and r₃ = - 2, then the equation of the polynomial is:
- 1.6 = a · (0 - 1)² · (0 + 2)
- 1.6 = a · (- 1)² · 2
- 1.6 = 2 · a
a = - 0.8
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maths question to purely maths tutor
answer is here
some drawing:
cool
∉343
[tex]\sqrt[422\sin 242]{e}2424\begin{cases}x=24 \\ y=24242f(x)=\begin{cases}4242 \\ 4242 \\ 424224\lim _{n\to\infty}2424244224\end{cases}\end{cases}[/tex]Answer: Need a math question
Step-by-step explanation: x3+y3+z3= ?
You are offered two different furniture sales jobs. The Furniture Barn offers you a job that pays straight commission of 5% of the sales. The Furniture Warehouse offers you a job that pays a salary of $350 per week plus 1% of the sales. How much would you have to sell in a week in order for the job at The Furniture Barn to pay as well as the job at The Furniture Warehouse? Round the answer to the nearest cent.
A = amount of sales
so hmmm The Furniture Barn gives only 5% of "A" then, that means
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of A}}{\left( \cfrac{5}{100} \right)A}\implies 0.05A[/tex]
whilst The Furniture Warehouse gives you 350 bucks per week and only 1% of "A", well, that means you gross pay there will 350 + 0.01A.
hmmm how much will "A" be for both offers to pay the same amount?
[tex]\stackrel{Furniture~Barn}{0.05A}~~ = ~~\stackrel{Furniture~Warehouse}{350 + 0.01A} \\\\\\ 0.04A=350\implies A=\cfrac{350}{0.04}\implies \boxed{A=8750}[/tex]
Please help I have no idea
PLS ANSWER THIS MATH PROBLEM!!
Answer:
See picture
Step-by-step explanation:
I’m confused on this and don’t know what to do
Answer:29
Step-by-step explanation:
3(3)^3+2(4)-6
3(9)+8-6
27+8-6
27+2
29
Question 1 Describe the error in writing an equation of the line that passes through the point (3, 4) and is parallel to the line y = 2x+1. Responses The x- and y-coordinates are substituted for the wrong variables. The , x, - and , y, -coordinates are substituted for the wrong variables. The y-intercept b should be solved for instead of the slope m. The , y-intercept b should be solved for instead of the slope m, . To find m, standard form must be used instead of slope-intercept form. To find , m, standard form must be used instead of slope-intercept form. Once the new slope is found, the new y-intercept must also be found. Once the new slope is found, the new , y, -intercept must also be found. Question 2 Correct the error. The line y = is parallel to the line y = 2x+1 and passes through the point (3,4).
An error in writing an equation of the line is to use 1 as the y intercept, or to use the negative inverse of the slope which gives you a perpendicular line, not a parallel line
How to write a Line in slope Intercept form?
For a line to be parallel, it means that the line must have the same slope, but a different y-intercept because If it has the same y intercept, it means that it is the same line.
Now, we are told that the line passes through the point (3, 4) and is parallel to the line y = 2x +1. Thus;
The slope; m = 2
The coefficient of the x term, when the equation is solved for y is;
y = mx + c is the standard equation in slope intercept form with c as the y intercept
Plug in the coordinate point to solve for c;
4 = 2(3) + c
c = 4 - 6
c = -2
Thus, we conclude that the parallel line through the given point is gotten as; y = 2x - 2
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help a sister out with a polynomial and quadratic functions question
Answer:
when you multiply the exponents, you add the numbers
so it'll now be y^5
Find the surface area of the sphere.r= 4 cmFormulas for SpheresS.A. = 4tr2v = frer S.A. = [?] cm2Round to the nearest tenth.Enter
The radius of sphere is r = 4 cm.
Substitute the value in the formula to determine the surface area of sphere.
[tex]\begin{gathered} SA=4\pi\cdot(4)^2 \\ =64\pi \\ =201.061 \\ \approx201.1 \end{gathered}[/tex]So answer is S.A = 201.1
A set of 25 two digit numbers are listed below 10,17,19.22,24,28,32,39,42,44,44,46,51,54,57,60,64,66,71,74,77,79,84,93,97,98
How can I get what is the probability of the sum of the number's digits is odd?
The probability that the sum of the number's digit is odd is 1/5.
What is the probability?
Probability is used to determine how likely it is that a random event would happen.
An odd number is a number that is not perfectly divisible by 2. Examples of odd numbers include 1, 3, 5.
Sum of the number's digits:
1 + 0 = 1 (odd number)
1 + 7 = 8
1 + 9 = 10
2 + 2 = 4
2 + 4 = 6
2 + 8 = 10
3 + 2 = 5 (odd number)
3+ 9 = 12
4 + 2 = 6
4+ 4 = 8
4 + 4 = 8
4 + 6 = 10
5 + 1 = 6
5 + 4 = 9 (odd number)
5 + 7 = 12
6 + 0 = 6
6 + 4 = 10
6 + 6 = 12
7 + 1 = 8
7 + 4 = 11 (odd number)
7 + 7 = 14
7 + 9 = 16
8 + 4 = 12
9 + 3 = 12
9 + 7 = 16
9 + 8 = 17 (odd number)
The probability that the sum of the digits is odd = number of odd digits / total number
5 / 25 = 1/5
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Zeke learned that he could make another
$2,000 a year if he became fluent in Spanish.
If he intends to learn the language and work another 10 years at that job, how much is learning Spanish worth to him?
If Zeke learned that he could earn another $2000 a year if he become fluent in Spanish and he intended to learn the language and work another 10 years at that job, then the amount is learning Spanish worth to him is $20000
The extra amount he could make if he learn Spanish = $2000
The number of years he works = 10 years
To find the extra amount, we have to use multiplication
The extra amount he could make if he learn Spanish = The extra amount he could make if he learn Spanish × The number of years he works
Substitute the values in the equation
= 2000×10
Multiply it
= $20000
Hence, if Zeke learned that he could make another $2000 a year if he become fluent in Spanish and he intended to learn the language and work another 10 years at that job, then the amount is learning Spanish worth to him is $20000
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In a 30-60-90 triangle, how many sides do you need to know in order to determine the remaining sides?
A. 1
B. 2
C. 0
D. 3
Answer:
Step-by-step explanation:
d
Simplify fully 24a^2 + 8a
Answer:
8a(3a + 1)
Step-by-step explanation:
24a² + 8a
8a(3a + 1)
I hope this helps!
Which of the following statements is true?
A. The diagonals of a quadrilateral are always congruent.
B. The diagonals of a parallelogram always bisect each other.
C. The diagonals of a rectangle are always perpendicular to each other.
D. The diagonals of a rhombus are always congruent and perpendicular to each other.
A linear function passes through the points (-3.14) and (2,-1). What is the rate of change of the function?
Responses
-13
−17/3
-3
−3/17
The rate of change of the linear function is the third option that is -3.
It is given in the question that the linear function passes through the points (-3,14) and (2,-1).
We have to find the rate of change of the function.
We know that,
The rate of change of a linear function is the slope of the function.
Slope of a line
The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’.
Hence, slope of a line that passes through the points (-3,14) and (2,-1) is
(-1-14)/(2-(-3)) = -15/5 = -3.
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A 14 (3/4) inch board is cut from a 34 (1/4) inch board. The saw cut takes (3/8) inch. How much of the 34 (1/4) inch board is left after cutting
(Type an integer, fraction, or mixed)
Integer - 19 (1/8)inch board would be left after cutting from 34(1/4) inch board
What is an Integer ?
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. When expressed in mathematical terms,
34 (1/4) inch board = 137/4 ----(1)
Cut piece = 14 3/4 = 59/4 ----(2)
saw cut 3/8 = 3/8 --------(3)
To calculate the board which is left after cutting will be
= 137 / 4 - 59 / 4 - 3/8
= 137 - 59 / 4 - 3 / 8
= 39 / 2 - 3 / 8
= 312 - 6 / 8
= 306 / 16
= 153 / 8
or, = 19 (1/8)inch
Hence, 19(1/8)inch board will be left after cutting
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Scale Word Problems (L1)
Oct 09, 9:51:30 AM
Watch help video
A scale drawing of a rectangur park had a scale of 1 cm = 100 m.
4.1 cm
Answer:
11.9 cm-
What is the actual area of the park in meters squared?
m²
Submit Answer
The actual area of the park when a scale drawing of the park had a scale of 1 cm = 100 m is 4879m².
How to calculate the area?From the information, the scale drawing of a rectangur park had a scale of 1 cm = 100 m.
It should be noted that the dimensions are given as 4.1 cm and 11.9cm. The area of the scale will be:
= 4.1 × 11.9
= 48.79cm²
Therefore, the actual area of the park will be:
= 48.79 × 100
= 4879m²
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USING PROPERTIES Find the product. Write your answer as a fraction in simplest form. $\left[-\frac{2}{3}\ \ \cdot\left(-\frac{5}{7}\right)\right]\cdot\ \left(-\frac{9}{4}\right)=$
By algebra properties, the rational expression [(- 2 / 3) · (- 5 / 7)] · (- 9 / 4) is equivalent to the following rational expression in simplest form: - 15 / 14.
How to simplify the product of three fractions
In this problem we find a product of three rational numbers, which we must simplify by using algebra properties, especially those of related to rational numbers:
[(- 2 / 3) · (- 5 / 7)] · (- 9 / 4) Given
[(2 / 3) · (5 / 7)] · (- 9 / 4) (- a) · (- b) = a · b
(10 / 21) · (- 9 / 4) Multiplication of fractions
- [(10 / 21) · (9 / 4)] (- a) · b = - a · b
- 90 / 84 Multiplication of fractions
- 45 / 42 Simplification of fractions
- 15 / 14 Simplification of fraction / Result
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At a factory, there are 40 new cars produced every 8 hours. How many cars can be produced in a 40-hour week?
Answer:
200
Step-by-step explanation:
Multiplying by 5, we get 200 cars can be produced in 40 hours.
Two numbers are respectively twenty percent and ten percent more than a third number. How
much percent is the first number more than the second?
The first number is 8.33 percent more than the second number.
Let m be the first number, n be the second number and p be the third number.
Two numbers are respectively twenty percent and ten percent more than a third number.
m = (100 + 20)% of p
m = 120 percent of p
m = 120 % of p
m = (120 / 100) × p
m = 1.2 p
And the second number would be,
n = (100 + 10)% of p
n = 110 percent of p
n = (110 / 100) × p
n = 1.1 p
We need to find by how much number the first number more than the second.
Consider the difference,
1.2 p - 1.1p = 0.1 p
So the required percentage noting but the difference is what percent of the first number.
(0.1 p / 1.2 p) × 100 = 8.33%
Therefore, the first number is 8.33 percent more than the second number.
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