Consider the following planes. x + y + z = 5, x + 3y + 3z = 5A) Find parametric equations for the line of intersection of the planes. B) Find the angle between the planes.
Answer:
Step-by-step explanation:
Consider the following planes. x + y + z = 5, x + 3y + 3z = 5
the parametric equations for the line of intersection of the planes are determined as follows:
From the first plane, the normal of the first plane is [tex]n_1 = (1,1,1)[/tex]
from the second plane, the normal of the second plane is [tex]n_2 = (1,3,3)[/tex]
[tex]n_1 \times n_2 = \begin {vmatrix} \left \begin{array}{ccc}i&j&k\\1&1&1\\1&3&3 \end{array}\right \end {vmatrix}[/tex]
= i(3-3) -j(3-1)+k(3-1)
= i(0) - j(2) + k(2)
= -2j +2k
Suppose z = 0
x+y + 0 = 5 ---(1)
x+3y + 3(0) = 5 (2)
subtracting by elimination
-2y = 0
y = 0/-2
y = 0
The intersection on point of the plane is (5,0,0)
The equation of plane is r (t) =(5, 0, 0) + t(0, -2, 2)
∴
(x(t), y (t), z(t) ) = (5, -2t, 2t)
B) Find the angle between the planes
The angle between the planes can be represented by the equation:
[tex]cos \theta = \dfrac{a_1a_2+b_1b_2 + c_1c_2}{\sqrt{a^2_1+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}[/tex]
[tex]cos \theta = \dfrac{1 \times 1+1\times 3 +1 \times 3}{\sqrt{1^2+1^2+1^2}\sqrt{1^2+3^2+3^2}}[/tex]
[tex]cos \theta = \dfrac{1+ 3 +3}{\sqrt{3}\sqrt{19}}[/tex]
[tex]cos \theta = \dfrac{7}{\sqrt{3}\sqrt{19}}[/tex]
[tex]\mathbf{\theta = cos ^{-1} (\dfrac{7}{\sqrt{57}})}[/tex]
What is the value of the expression when y = 2? StartFraction 2 minus y Over 4 plus y EndFraction plus StartFraction 3 (y plus 2) Over y EndFraction
Answer:
12
Step-by-step explanation:
Answer:
2.4
Step-by-step explanation:
graph h(t)=-2(t+5)^2+3, find h(-8)
Answer:
h(-8)=-15
Step-by-step explanation:
Substitute t=-8
h(-8) =-2(-8+5)^2+3
=-2(-3)^2+3
=-2(9)+3
=-18+3
=-15
h(-8) = - 15
Step-by-step explanation:h(t) = - 2(t + 5)² + 3
replace t with - 8
h(-8) = - 2(- 8 + 5)² + 3
h(-8) = - 2(-3)² + 3
h(-8) = -2×9 + 3
h(-8) = - 18 + 3
h(-8) = - 15
4(6c+5) - 2(3c - 5) = 120
Answer:
[tex]c=5[/tex]
Step-by-step explanation:
[tex]4(6c+5)-2(3c-5)=120[/tex]
Use the distributive property to expand the equation:
[tex]4(6c)+4(5)-2(3c)-2(-5)=120\\\\24c+20-6c+10=120[/tex]
Combine like terms to simplify the equation:
[tex]24c-6c+20+10=120\\\\18c+30=120[/tex]
Subtract 30 from both sides:
[tex]18c+30-30=120-30\\\\18c=90[/tex]
Isolate the variable c. Divide both sides by 18:
[tex]\frac{18c}{18}=\frac{90}{18}\\\\ c=5[/tex]
So, c is equal to 5.
:Done
Sofia invests her money in an account paying 7% interest compounded semiannually. What is the effective annual yield on this account? Enter your response as a percentage rounded to two decimal places and omit the percentage sign
Answer:
7.12
Step-by-step explanation:
The formula for the effective annual yield is given as:
i = ( 1 + r/m)^m - 1
Where
i = Effective Annual yield
r = interest rate = 7% = 0.07
m= compounding frequency = semi annually = 2
i = ( 1 + 0.07/2)² - 1
i = (1 + 0.035)² - 1
= 1.035² - 1
= 1.071225 - 1
= 0.071225
Converting to percentage
0.071225 × 100
= 7.1225%
Approximately to 2 decimal places = 7.12
Therefore, the annual effective yield = 7.12
:
a.
Which of the following statements best describes the difference between sales tax and property tax?
Sales tax is applied to items as they are purchased while property tax is applied to items
already owned
b. Sales tax is applied repeatedly while property tax is paid only once for as long as you own the
item.
Sales tax can be applied to a new speed boat while property tax cannot.
d. Sales tax is strictly meant for food and consumables while property tax is meant for non-food
items
C
Answer:
Sales tax is applied to item as they are purchased while property tax is applied to items already owned
Step-by-step explanation:
Sales tax is applied to items as they are purchased while property tax is applied to items already owned. Therefore, option A is the correct answer.
What is the sales tax?Calculating the sales tax applied to a purchase is a matter of simply multiplying the tax rate by the purchase price using the equation sales tax = purchase price × sales tax rate. Adding the sales tax to the original purchase price gives the total price paid with tax.
Property tax is a charge made on real estate that is owned by a person, a business, or another type of legal body. Property tax is most frequently a real estate ad-valorem tax, which is regarded as a regressive tax. It is computed by the local government in the area where the property is situated, and the owner is responsible for paying it.
Sales tax is applied to items as they are purchased while property tax is applied to items already owned. Therefore, option A is the correct answer.
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A report on Americans' attitudes toward teachers' pay found that 82% of the respondents to the survey upon which the report is based think that teachers don't make enough money. Which factor is most relevant when evaluating this report? A. 49% of the respondents were women. B. 78% of the respondents were married. C. 51% of the respondents were men. D. 62% of the respondents were educators.
Answer:
I think the answer is A. 49% of the respondents were women
Find the missing value of 2/5=?/15
Answer:
2/5=6/15
Step-by-step explanation:
2/5
Multiply with 3 both numerator and denominator
=>2x3/5x3
=>6/15
x = 6
Step-by-step explanation:2/5 = x/15
x = 2×15/5
x = 30/5
x = 6
Write a verbal reprsentation that could be translated to the equation 7k + 8 = 100.
Answer:
Eight more than seven times x (or x times seven) is one hundred
Answer: "The product of 7 and k plus 8 yields 100"
Step-by-step explanation: Simply translate the numbers and signs into words. "the product of 7 and k" means multiply 7 times k, which is the same as 7k. "plus 8" means addition. "yield" is the same as equal.
Give two points with integer coordinates that have a slope of 2/5 between them.
Answer:
yes
Given a 2D line e.g. (3,10) -> (8.3,16.5), how can I find any point on that line that has has whole-number coordinates?
I can easily iteratively walk along one of the axis in integer steps, seeing if the value on the other axis is integer, but this is slow for very very long lines.
A race car driver completes 30 laps and 15 minutes at a constant speed. What is the drivers speed?
Answer:
60 mph
Step-by-step explanation:
It takes two minutes to drive one mile at 30 mph. You are planning on covering two total miles. If your average speed is 60 mph, it would take two minutes to cover these two miles. So you have to go 60 mph.
Hope This Helps :)
The driver's speed is 30 miles per hour.
One mile is approximately 4 laps so 30 laps would be:
= 30 / 4
= 7.5 miles
The driver drove 7.5 miles in 15 minutes.
15 minutes in hours is:
= 15 / 60
= 0.25 hours
The speed of the driver is therefore:
= 7.5 miles / 0.25 hours
= 30 mph
The driver was therefore driving at a speed of 30 mph
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Felix signs up for a cell phone that his parents require him to pay for. His bill is $46.80. What impact will his cell phone have on his savings account over the period of a year
Answer:$561.60
Step-by-step explanation: The cost of each month is 46.80 and there is 12 months in a year so 46.80×12=561.60
For his cell phone , Felix will pay a bill of $561.60 in a year .
Felix has a bill of $46.80 per month which is paid by his parents.
We have to find out that what will be the impact on his savings account over the period of a year.
What is the cost of 10 pens , if one pen costs $10 ?
The cost of 10 pens will be 10 × 10 = $ 100.
As per the question ;
Felix is paying a bill of $ 46.80 in a month.
∵ 1 year = 12 months
So,
Felix will pay a bill in a year or 12 months is of ;
= 12 × $ 46.80
= $ 561.60
Thus , for his cell phone , Felix will pay a bill of $561.60 in a year .
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I need help with this pls ASAP
A square has the following vertices. Find the area of the square.
(-7,-5), (-4,-2), (-1,-5), (-4,-8)
(1 point)
O V18 square units
O 18 square units
O V6 square units
O 6 square units
Answer:
18 square units
Step-by-step explanation:
Since the shape is a square lets find the distance between two close point then square the distance to find the answer.
Lets take the point (-7,-5), (-4,-2)
Distance= √((y2-y1)²+(x2-x1)²)
Distance= √((-2--5)²+(-4--7)²)
Distance= √((-2+5)²+(-4+7)²)
Distance= √((3)²+(3)²)
Distance= √(9+9)
Distance= √18 units
Area= distance ²
area= √18²
Area= 18 square unit
HELP PLEASE! ON A TIME LIMIT.
Javi and MeriAnne competed to see who could read the most pages of their novels in a week.
According to the bar graph, how many more pages did the winner of the contest read than the loser? Show your work or explain how you got your answer.
Answer:
5
Step-by-step explanation:
First add the sum of the Javi's total page count from Monday to Friday. You get 125 pages. Next find MeriAnne using the same process. You get 120 pages. Find the difference by subtracting one from the other. 125-120=5 page difference.
Javi wins from MeriAnne by 5 pages
What is data?Data is information that has been translated into a form that is efficient for movement or processing. Relative to today's computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.
Total number of pages read by Javi
=10+20+60+20+15
=125
Total number of pages read by MeriAnne
=20+30+40+20+10
=120
So, Javi wins from MeriAnne by= 125-120= 5 pages
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Keith sold half of his comic books and then bought nine
more. He now has 20. How many did he begin with?
Answer:
22 comic books.
Step-by-step explanation:
(20 - 9) * 2 First subtract 9 from 20
11 * 2 Multiply 11 by 2
22 is the product
{6} E { {6}, {14} } true or false
Answer: true and stop deleting my answers im right im in collage
and I dont need to explain again when i already did so STOP and trust me
A SNACK THAT SMILES BACK®
The perimeter of the original rectangle is 16 feet. A small rectangle has a length of 6.2 feet and width of 1.8 feet. A larger rectangle has a length of 12.4 feet and width of blank. Not drawn to scale What is the perimeter of the enlarged rectangle? Round to the nearest tenth if necessary.
Answer:
32 ft
Step-by-step explanation:
The length of the larger rectangle is double that of the smaller one. If we assume the rectangles are similar, the perimeter will be double as well:
2·(16 ft) = 32 feet . . . . perimeter of larger rectangle
__
The width of the larger one is 2·1.8 ft = 3.6 ft.
Answer:
C) 32 feet
Step-by-step explanation:
＼(ﾟｰﾟ＼)
There are 87 first graders in after care.after 39 students are picked up, the teacher put the remaining students into 4 groups for an activity. How many students are in a group?
Answer:
There are 12 students in each group
Step-by-step explanation:
87-39= 48
48/4= 12
Hope this helped. ;)
Answer:
12 students are in a group
Step-by-step explanation:
There are 87 first graders, but 39 students are picked up. So, we have to calculate how many students are left.
87 - 39 = 48
There are 48 students left.
The teacher divided these 48 students intro 4 groups.
48 / 4 = 12
So, there are 12 students in a group.
Hope this helps ^^
The graph shows Demarco's changing distance as he ran during his workout. What does point A tell you about Demarco's speed?
Answer:
Demarco ran 2 miles in 24 minutes
Answer:
Demarco ran 2 miles in 24 minutes.
thats how it is in ttm
Andre and Morgan are both headed to Florida for vacation. Andre will drive 70 miles per hour. Morgan will drive 55 miles per hour but will leave 3 hours earlier than Andre. How many hours will Morgan have been driving before Andre catches up with her?
Answer:
14hours
Step-by-step explanation:
Since Andre and Morgan are both heading to the same location i.e Florida, they will have the same distance.
Distance = Speed × Time
For Morgan:
His speed = 55mi/hr
Let his time = x
Distance covered by Morgan = 55x
For Andre
His speed = 70mi/hr
Time = x-3 (since morgan leaves 3 hours earlier than Andre)
Distance covered = 70× (x-3) = 70(x-3)miles
Since they are driving towards the same location;
55x = 70(x-3)
55x = 70x-210
55x-70x = -210
-15x = -210
x = 210/15
x = 14
Hence Morgan will have been driving 14hours before Andre catch up
3. Determine if the equation represents y as a function of x.
9x + 3y = 12
if AM = 14y - 2 and MB = 10y + 6, find AM.
Answer:
220
Step-by-step explanation:
RoBoCo Costume Inc plans to launch a major campaign to sell Robby the Robot costumes for Halloween. The price-demand equation for Robby costumes is
x = 160 - p
The demand x is the number of Robby costumes in thousands) that can be sold at a price p dollars.
a. How many costumes can be sold at a price of $140?
b. What price should be charged if the demand is 120,000 Robby costumes?
$
c. If the price increases by $1.00, by how much does the demand decrease?
Answer:
x = 20,000
p = $40
If the price increase by $1, the demand will decrease by 1000
Step-by-step explanation:
Given:
x = 160 - p
x = number of Robby costumes demanded in thousands
p = price in dollars.
a. How many costumes can be sold at a price of $140?
x = 160 - p
x = 160 - 140
= 20
x = 20,000
20 thousand costumes can be sold at a price of $140
b. What price should be charged if the demand is 120,000 Robby costumes?
x is in thousand
p is in dollars
x = 160 - p
x + p = 160
120 + p = 160
p = 160-120
= 40
p = $40
c. If the price increases by $1.00, by how much does the demand decrease?
x = 160 - p
= 160 - 141
= 19
x= 19,000
If the price increase by $1, the demand will decrease by 1000
HELP PLEASE!!!
The following graph shows farm sector production in billions of dollars from 1994–2003. One line shows the yearly production and the other shows the average over the time span. According to the graph, in which 3 years were the values of farm sector production closest to the average for the 10 years shown?
A): 1994, 1996, 1998
B): 1996, 1998, 2000
C): 1998, 2000, 2002
D): 2000, 2002, 2004
Answer:
C): 1998, 2000, 2002
Explanation:
You can find the answer by looking at which part of the line graph intersects the line where it says 1994-2003 average. As you can see, the years 1998, 2000, and 2002 are meeting up with the average of 1994-2003.
Answer: C) 1998, 2000, 2002 !!
Step-by-step explanation:
Express the given quantity in terms of the indicated variable.
The area (in ft) of a rectangle that is eight times as long as it is wide;
w = width of the rectangle (in ft)
ft2
X
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Answer:
X = 8W²Step-by-step explanation:
Area of a rectangle is expressed as Length * Width
X = L*W where X is the area of the rectangle in fe²
If the triangle is eight times as long as it is wide, then L = 8W
Substitute L = 8W into the formula for calculating the area of a triangle, we will have;
X = L*W
X = (8W)*W
X = 8W²
The expression X in terms of W is therefore X = 8W²
Select the relationship that does represent a function.
Answer:
Picture number 3 is the answer
Step-by-step explanation:
A function is a relation in which each element in the domain is paired with exactly one element in the range not 2.
Picture number one has a range left with no domain so it's not a function
Picture number 2 is showing an element in the domain which paired 2 elements in the range so it's not a function
Picture 3 is correct because each element in the domain macthes one element in the range.
Picture 4 is wrong because it's showing elements in the domain that matches 2 elements in the range. Hope it makes sense.
The required relationship that represents a function is given by 3rd image. Option C is correct.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
The first image has a range with no domain, hence it is not a function. In 2nd image depicts an element in the domain that paired two elements in the range, indicating that it is not a function. In 3rd image, it is valid because each element in the domain corresponds to one element in the range. In picture 4, it is incorrect since it depicts domain components that match two range elements.
Thus, the required relationship that represents a function is given by 3rd image. Option C is correct.
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Twice a number is at most 36.
Answer:
18?
Step-by-step explanation:
Write the equation of the line graphed below.
Answer:
y=2x +3
Step-by-step explanation:
The slope hits the points (-1,2) and (0,2). If you count how many units are right and up, then that's your slope. In this case, the distance between those two points are 1 right and 2 up which is the same thing as 2. The y-intercept is 3 since the slope crosses the y-axis there.
which equation can be represented by the number line
Answer:
B
Step-by-step explanation:
The arrow is going left four units. Since it's going left, we know that we are adding a negative number and since it's going left 4 units, we know that we are adding -4 in our equation. This narrows it down to options B and D. However, the arrow usually represents the second number being added, hence, the answer is B.