a) Dot product: recall that
i • i = j • j = k • k = 1
i • j = i • k = j • k = 0
Then
a • b = (i + 2j - 7k) • (5i - 2j + 4k)
a • b = 5 (i • i) - 4 (j • j) - 28 (k • k)
a • b = 5 - 4 - 28
a • b = -27
b) Cross product: recall that
i × i = j × j = k × k = 0
i × j = -(j × i) = k
j × k = -(k × j) = i
k × i = -(i × k) = j
Then
a × b = (i + 2j - 7k) × (5i - 2j + 4k)
a × b = -2 (i × j) + 4 (i × k) + 10 (j × i) + 8 (j × k) - 35 (k × i) + 14 (k × j)
a × b = -12 (i × j) - 6 (j × k) - 39 (k × i)
a × b = -6i - 39j - 12k
c) Recall the dot product identity
x • y = ||x|| ||y|| cos(θ)
We have
||a × b|| = √((-6)² + (-39)² + (-12)²) = 9√21
Then the direction cosines α, β, γ of a × b are
(a × b) • i = ||a × b|| ||i|| cos(α)
⇒ cos(α) = -6/(9√21) = -2/(3√21)
(a × b) • j = ||a × b|| ||j|| cos(β)
⇒ cos(β) = -39/(9√21)
(a × b) • k = ||a × b|| ||k|| cos(γ)
⇒ cos(γ) = -12/(9√21) = -4/(3√21)
d) a × b is perpendicular to both a and b, so we can get a unit vector by scaling this down by its magnitude. This is the same as the vector of direction cosines:
(a × b)/||a × b|| = (-6i - 39j - 12k)/(9√21)
(a × b)/||a × b|| = -2/(3√21) i - 39/(9√21) k - 4/(3√21) k
Loan payments of $4000 due 200 days ago and $6000 due 63 days ago are to be replaced
by a payment of$5000 today and the balance 92 days from today. If money is worth 8.3%
and the agreed focal date is 92 days from today, what is the size of the final payment?
The size of the final payment is $5378.08
What is the size of the final payment?P1 = One loan payment = $4000
P2 = Second loan payment = $6000
P3 = Payment = $5000
Let P4 = Second payment
n1 = 200 days
n2 = 63 days
n3 = 92 days
r = Interest rate = 8.3%
[P1 * (1+ (r * n1 /365))] + [P2 * (1+ (r * n2 /365))] = P3 + [P4 / (1+(r*n3/365)]
[$4000 * (1+(8.3%*200/365)] + [$6000 * (1+(8.3%*63/365)] = $5000 + [P4 / (1+(8.3%*92/365))]
[$4000 * 1.04547945] + [$6000 * 1.01432603] = $5000 + [P4 / 1.02092055]
$4181.9178 + $6085.95618 = $5000 + [P4/1.02092055]
P4/1.02092055 = $5267.87398
P4 = $5378.080801
Therefore, the size of the final payment is $5378.08
Learn more about loans on:
https://brainly.com/question/26011426
#SPJ1
Which expression is equivalent to the given expression?
2n−6
A −2(n−3)
B 6−2n
C −4n
D 2(n−3)
The perimeter of any rectangle in which the length is 4 more than twice the width is P = 6 w + 8 , where w is the width. Which formula can be used to find the width given the perimeter? Multiple choice question. cross out A) w = P − 4 3 cross out B) w = 1 6 P − 8 cross out C) w = − P + 8 6 cross out D) w = P − 8 6
Answer: option D
Step-by-step explanation:
Given equation:
P = 6 w + 8 [eq1]
l=2w+4 [where l is length]
using eq1 we have:
6w=P-8
w=(P-8)/6
hence option D
learn more about perimeter here:
https://brainly.com/question/28499208
#SPJ9
How do I find out the check amount before the tip when the total amount was $55 with a 10% tip
Answer:$49.50
Step-by-step explanation:
First you have to find what 10% of 55 is. So if you times 10% by 55 you come out with $5.5. So after that you must subtract 5.5 from 55 which comes out to $49.50.
Which is the least whole number that rounds to 2000 when rounded to the nearest hundred
The required number is 2001.
To solve this problem we need to know the concept of rounding off.
Rounding off a number means making the value of number equal to the nearest tens place.
When we round off 45 we will get 50; when we round off 44 we get 40.
So, if a number has 5 at its unit place then it will be rounded off to the tens place which is ahead of 5 and if a number is less than 5 then it is rounded off to the tens place before that number.
Here it is asked to find the least whole number that rounds off to 2000 when rounded off to nearest hundred which will be 2001.
To learn more about rounding off visit the link:
https://brainly.com/question/13391706
#SPJ9
Lizzy had #500, John has #50
FIFI will have #700.Who has more money amongst the three.
Answer:
John
Step-by-step explanation:
it says Lizzy had which means we don’t know how much she has now. It says Fifi will have so we don’t know how much they have right now. But it says John has so we know what he has so therefore he has the most as of right now
A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in years. The equation
p=0.007y^2-0.003y+122
gives a person's blood pressure, p,at the age y year
A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 41 years.
The systolic pressure, to the nearest tenth of a millimeter, for a person of age 41 years is; 133.6 mm Hg
How to solve problems using quadratic equations?We are given the equation that gives a person's blood pressure, p at the age y year is;
p = 0.007y² - 0.003y + 122
To find the systolic pressure for a person of age 41 years, just plug in y = 41 into the given quadratic equation to get;
p(41) = 0.007(41)² - 0.003(41) + 122
p(41) = 11.767 - 0.123 + 122
p(41) = 133.6
Thus, the systolic pressure, to the nearest tenth of a millimeter, for a person of age 41 years is; 133.6
Read more about Quadratic Equations at; https://brainly.com/question/1214333
#SPJ1
What is the midpoint of the line segment from p1 to p2 is (-4,1). If P1 =(-4,5) what is p2??
According to a recent study, the number of prisoners in a prison decreased by 312 inmates over a one-year period. If the decrease was the
same for each of the 12 months, write the monthly decrease as a quotient of integers and find the monthly decrease.
The expression to find the monthly decrease in prisoners is.
(Do not simplify.)
The number of inmates in the prison decreased by inmates per month.
(Simplify your answer.)
Over a year, a prison's population dropped by 312 inmates. We know that 1 Year = 12 Months.
Additionally, considering that each of the 12 months declined at the same rate.
the Monthly decrease in members = 312 / 12 = 26
Therefore, the expression used to calculate the monthly drop in prisoner population = Number of prisoners decreased per year / Number of months
Note: If the monthly drop rate is the same, the aforementioned equation is correct ( for all months in that year)
A similar problem where this expression is explained, is mentioned below:
https://brainly.com/question/12188151
#SPJ1
help i need answer to this math question???
The solution of the geometrical system is (x, y) = (2.5, 48.5).
What are the missing values associated with a geometrical system?In this question we have a picture representing two lines and a semirray that brings out two formulae for supplementary angles, these are shown below:
(x + 10) + 30 + (3 · y + 2) = 180
x + 3 · y = 148 (1)
30 + (3 · y + 2) + (5 · x - 10) = 180
5 · x + 3 · y = 158 (2)
And now we resolve the entire system of linear equations by substitution:
By (1):
x = 148 - 3 · y
(1) in (2):
5 · (148 - 3 · y) + 3 · y = 158
740 - 15 · y + 3 · y = 158
12 · y = 582
y = 48.5
By (1):
x = 148 - 3 · 48.5
x = 2.5
The solution of the geometrical system is (x, y) = (2.5, 48.5).
To learn on systems of linear equations: https://brainly.com/question/20379472
#SPJ1
If you have the function f(x) = 5^x - 5 then find the value of f(t)
The value of the function is [tex]5^t-5[/tex] .
A function is defined as a expression containing one or more variables.
A function, in technical terms, is a mechanism to connect a collection of inputs to a set of outputs.
A function of a single variable (say x) is defined mathematically as g(x).
Let us consider a function of a variable x such that it is defined as:
g(x)=x+1
Here the output are calculated for all values of x . At x=1 the value of the function is denoted as g(1)=1+1=2.
Mathematically to calculate the value of the function f(x) for any particular value of x we substitute the value of x into the value of f(x).
Now the given function is given as:
[tex]f(x)=5^x-5[/tex]
Therefore at x=t,
[tex]f(t)=5^t-5[/tex]
To learn more about a function:
https://brainly.com/question/5975436
#SPJ9
I need help with math ngl
Answer:
Oldest to newest:
10^-35, 10 ^-10, 0
Step-by-step explanation:
Scientific notation
To figure out the power of 10 think "how many places do I move the decimal point?"
When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.
When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.
Are you confident that you can round 7.396 to the nearest hundredth
Answer:
7.4
Step-by-step explanation:
When the decimal in any place is more than 0.5, round up.
Please help i dont understand
Answer :
1) If x = 6
Substitute 6 for x in the expression.
a) 5x-9
5(6)-9
30-9
21
b) 2x-7
2(6) -7
12-7
5
c) 8x+5
8(6)+5
48+5
53
d) 4(x+3)
4(6+3)
4(9)
36
e) x²-(-4)
6²-(-4)
36+4
40
f) 3x²+1
3(6²)+1
3(36) +1
108+1
109
2) Solve
a) 54 = 3x
Divide both sides by 3.
54/3 = 3x/3
x = 18
b) x-9 = -3
Add 9 to both sides.
x-9+9 = -3+9
x = 6
c) x/7 = 140
Express the 140 over 1 and cross multiply.
x/7 = 140/1
x = 140×7
x = 980
d) x/8 = 72
Express the 72 over 1 and cross multiply.
x/8 =72/1
x = 72×8
x = 576
A bookcase is to have 4 shelves including the top as pictured below.
The width is to be 12 feet less than 3 times the height. Find the width and the height if the carpenter
expects to use 22 feet of lumber to make it.
Width:
feet
Height:
feet
Answer:
The width is 3 feet and the height is 6 feet.
Step-by-step explanation:
A bowl weighs 11/40 pound.
a. Express this weight as a decimal.
b. Explain how you can find the decimal by thinking of the denominator as a 4 and using mental math.
Answer: 0.275
Step-by-step explanation:
a. To express 11/40 as a decimal, you need to divide 11 by 40. (Steps shown in image)
b. Sorry, I can't figure out the answer to this. I don't recommend making the denominator a 4 as the numerator would become 1.1.
help me out
Simplify the
expression: 4^2 + 8 ÷2.
a. 12
b. 20
c. 8
d. 16
Market research was undertaken to determine whether an ad campaign was successful for the software company. 15 men and 75 women were asked if they had seen the company’s latest TV advertisement. Altogether, 2 5 of the people said ‘yes’. 6 15 of the men said ‘yes’. What percentage of women said ‘no’ out of the total survey population?
50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Market research was undertaken to determine whether an ad campaign was successful for the software company.
Total number of people = 15 + 75 = 90
The number of people who said yes = (2/5)90 = 36
The number of people who said no = 90 - 36 = 54
The number of men said yes = (6/15)x15 = 6
The number of men said No = 15 - 6 = 9
The number of women who said no = 54 - 9 = 45
Percentage = (45/90)x100
The percentage of women who said ‘no’ out of the total survey population:
= 50%
Thus, 50% of women who said ‘no’ out of the total survey population if 15 men and 75 women were asked if they had seen the company’s latest TV advertisement.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ1
5(x+4) =1/2(12) (2X-6) STEPS TO SOLVE
hi
5(x+4) =1/2 *(12)* (2X-6)
5x+20 = 6 * ( 2x-6)
5x+20 = 12x-36
5x-12x = -36-20
-7x = -56
x = -56/-7
x = 8
Xaivier played video games for 1 hour and 45 minutes before he went to bed. If he went to bed at 9:00 pm,what time did he start playing video games
Answer:7:15 pm
Step-by-step explanation:
We know he went to bed at 9:00 PM and spent 1 hr and 45 minutes playing games. Start by subtracting one hour away, so we get 8:00 PM. subtract 45 minutes from that and he would have started playing at 7:15 PM.
10-0.5(12+8b)+b
pls help if you can!
Answer: 4-3b
Step-by-step explanation:
10-0.5(12+8b)+b First, distribute -0.5 into 12 and 8b
10-6-4b+b Then combine like terms
4-3b Done!
Which diagram shows two figures intersecting at exactly four points?
Answer:
The rightmost figure
Step-by-step explanation:
That is the only figure where there are 4 points of intersection. It is a rhombus inscribed in a square
Identify the errors made in finding the inverse of
y = x- + 12x.
x = y2+ 12x
y?=x-12x
y2=-11x
y=V-11x, for x 2 0
Describe the three errors.
The following mistakes were made in the solution of the inverse function:
There is an incorrect swap between the variables y and x.The ± sign should be included in the square root.The domain of the function is incorrect because the radicand can only have a real value if x is less than 0.What are inverse functions?The original value for which the function's output was provided is returned by the inverse function.F and G are inverse in terms of functions, with f(g(x)) = g(f(x)) = x.The initial value is returned by a function that is its inverse. The inverse of f is then g(y) = (y-5)/2 = x. (x).Therefore, the first error is caused by the incorrect variable swap.
The correct expression is:
x = y² + 12yThe following error is:
y = √-11xThe correct expression:
y = ± √-11xFinally, the domain is incorrect.
Because if x is 0 or positive, y = -11x has no true value.As a result, the following errors were made in the inverse function solution:
There is an incorrect swap between the variables y and x.The ± sign should be included in the square root.The domain of the function is incorrect because the radicand can only have a real value if x is less than 0.Know more about inverse functions here:
https://brainly.com/question/3831584
#SPJ9
The correct question is given below:
Identify the errors made in finding the inverse of y = x2 + 12x.
Describe the three errors.
use addition properties and strategies to find the sum 13 + 26 + 54=
Answer:
93
Step-by-step explanation:
13 + 26 = 39
39 + 54 = 93
Maureen knows the domain of f(x) is the set of positive real numbers if she graphs f(x) on the coordinate plane what must be true about the graph
The correct option is C, if f(x) has a domain only with positive values, the graph will be on the first and fourth quadrant.
What must be true about the graph?We know that the domain of f(x) is only the set of positive real numbers. Now remember that the domain of a function is the set of the inputs of that function (the inputs are on the horizontal axis).
Then the graph of f(x) will only be on the positive side of the horizontal axis. We know that the two quadrants that are on that region are the first quadrant and the fourth quadrant.
Then if f(x) has a domain only with positive values, the graph will be on the first and fourth quadrant, this means that the correct option is C.
If you want to learn more about domains:
https://brainly.com/question/1770447
#SPJ1
10.
An airplane has economy and first class seating.
There are s seats in each row in economy.
There are t seats in each row in first class.
There are 9 rows in first class and 24 rows in economy.
Write down an expression, in terms of s and t, for the number of seats on the
airplane.
The expression, in terms of s and t, for the number of seats on the airplane is given by 24 s + 9 t.
We are given that there are 2 types of seating in an airplane which are economy and first class seating.
Also,
We are given that:
There are s seats in economy in each row and there are t seats in first class in each row.
Now, there are 24 rows in economy class seating.
So, number of seats in economy class = 24 × s = 24 s
And, there are 9 rows in first class seating.
So, number of seats in first class = 9 × t = 9 t
The total number of seats then will be = 24 s + 9 t
Therefore the expression, in terms of s and t, for the number of seats on the airplane is given by 24 s + 9 t.
Learn more about expression here:
https://brainly.com/question/723406
#SPJ9
The ratio 4:5 is equivalent to
(i) 80%
(ii) 60%
(iii) 40%
(iv) 20%
If u ans i will give 40 points and mark brainlyest
Answer:
(i)
Step-by-step explanation:
express the ratio as a fraction, that is
4 : 5 = [tex]\frac{4}{5}[/tex]
to convert the fraction to a percentage multiply it by 100%
[tex]\frac{4}{5}[/tex] × 100% = 4 × 20% = 80%
what is? 9x-x-2=3(2x-3)+ax
Three rational numbers between 1/3 and 1/5
Three rational numbers between
1/3 and 1/5 are 4/15, 3/10, and 7/30
Given:The two numbers are 1/3 and 1/5
To find:The rational number between two numbers
Solution:Now, to find the rational number, add the numbers and divide their sum by 2.
(i) First rational number between
1/3, 1/5 = 1/3+1/5=8/5
Divide 18/5 by 2------> 8/15 x 1/2= 8/30= 4/15
The series becomes, 1/3, 4/15, 1/5
(ii) Second rational number
= 4/15+1/5 = 7/15
Divide
7/15 by 2 ------> 7/15 x 1/2 = 7/30
Hope this helps!
Choose the best answer.
Use the conditional statement to answer the question.
If an angle measures 43 degrees, then the angle is acute.
Choose the best answer.
The statement is false, but the inverse is true.
Both the statement and its inverse are false.
Both the statement and its inverse are true.
The statement is true, but the inverse is false.
Answer:
D
Step-by-step explanation:
Acute angle are angles less than 90°.And 43° is less than 90° and the inverse is not less than 90°.
