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]
Write an equation in slope-intercept form (y = mx + b).
A vertical line passing through (1, -4).
Answer:
x=1
Step-by-step explanation:
Anytime there is a vertical line, the y value becomes infinite as the line goes on forever. The only restriction on the line is on the x value of your coordinate. The same goes for a horizontal line, only the x value would become infinite and the y value would be constant.
Vertical Line: (x,∞)
Horizontal Line: (∞,y)
Consider the graphs of f (x) = x cubed and of g (x) = StartFraction 1 Over x cubed EndFraction. Are the composite functions commutative? Why or why not?
Answer:
c
Step-by-step explanation:
They are not commutative because the domains of f(x) and g(x) are different.
The functions [tex]f(x) = x^{3}[/tex] and [tex]g(x) = \frac{1}{x^{3} }[/tex] are not commutative because domains of f(x) and g (x) are different.
Here,
The functions are [tex]f(x) = x^{3}[/tex] and [tex]g(x) = \frac{1}{x^{3} }[/tex] and graph of the function are shown in figure.
We have to check the function are composite or not.
What is Domain of function?
The domain of a function is the set of all possible inputs for the function.
Now,
Domain of function [tex]f(x) = x^{3}[/tex] is ( -∞, ∞).
And, Domain of function [tex]g(x) = \frac{1}{x^{3} }[/tex] is ( -∞,0 ) U ( 0, ∞).
Hence, the domain of the functions are different so they are not commutative.
So, The functions [tex]f(x) = x^{3}[/tex] and [tex]g(x) = \frac{1}{x^{3} }[/tex] are not commutative because domains of f(x) and g (x) are different.
Learn more about the Domain of function visit:
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What value of q makes the equation true? -8=32-5q
List several figures other than rectangles that tessellate the plane using translations
Answer:
A
Step-by-step explanation:
Solve the equation.
5x + 8 - 3x = -10
x = -9
X = -1
x = 1
X = 9
Cand
Its the Right Answer on the Test. Hopes This Helps.
Thank You
I need help with 25. 26. And 27 plz I don’t know how
Answer:
25. 8ft
26. 3m
27. 7cm
Step-by-step explanation:
Because it says each is an area of a sqare the square root will give you the side length
ERROR ANALYSIS In Exercises 39 and 40, describe and
correct the error in solving the equation.
identical
shown.
one of th
39.
X
-0.8 + r= 12.6
r= 12.6 +(-0.8)
r= 11.8
40.
X
m
= -4
3•(-5= 3•(-4)
a. W
m= -12
on
b. Th
Answer:
39. r = 13.4
40. m = 12
Step-by-step explanation:
39. Given the equation, [tex] -0.8 + r = 12.6 [/tex], to solve for r, the following are the correct steps to take to arrive at the solution:
[tex] -0.8 + r = 12.6 [/tex] (given)
Add 0.8 to both sides of the equation (addition property of equality)
[tex] -0.8 + r + 0.8 = 12.6 + 0.8 [/tex] (this is where the error occurred.)
[tex] r = 13.4 [/tex]
40. The correct steps to take in solving the equation, [tex] -\frac{m}{3} = -4 [/tex] is as follows:
[tex] -\frac{m}{3} = -4 [/tex] (given)
Multiply both sides by 3 (multiplication property of equality)
[tex] 3*-\frac{m}{3} = 3*(-4) [/tex]
[tex] -m = -12 [/tex] (this is where the error occurred. This is what we should have at this line/step)
[tex] m = 12 [/tex] (dividing both sides by -1)
The percentage of first year college males who will claim no religious affiliation in 2030 is approximately ___%
Answer:
34.5%
Step-by-step explanation:
If we assume the relationship is approximately linear with time, we can use technology to draw a line of best fit through the given data. Extrapolating to the year 2030 predicts the value to be 34.5%.
In 2030, we might expect about 34.5% of male first-year college students to claim no religious affiliation.
_____
Additional comment
When it comes to religion, many factors are in play. The assumption we have made has no justification whatever, except that it provides a method for answering the question. (It also predicts the percentage to be 0 in 1963, which we believe to be unrealistic.) An exponential fit is better (r^2 = 0.97), and it predicts about 46.0%.
for each equation below, find y if x=3
Evaluate x^2 + 2x + 3
for x = 4
Steps to solve:
x^2 + 2x + 3 when x = 4
~Substitute
4^2 + 2(4) + 3
~Simplify
16 + 8 + 3
~Add
24 + 3
~Add
27
Best of Luck!
How much discount is received on an item with a marked price of Rs 500 if the discount rate is 3%? * Rs 50 Rs 15 Rs 25 Rs 5
Answer:
Rs.15
Step-by-step explanation:
3% = 3/100 × 500 = 15
Solve the inequality 6t>t+6. Enter your answer as an inequality with just t on the left side. For example, if the inequality in the problem were true for all negative t, then you'd enter "t =3".
Answer: t > 6/5
In decimal form, this would be t > 1.2
==============================================
Work Shown:
6t > t+6
6t-t > t+6-t ...... subtracting t from both sides
5t > 6
5t/5 > 6/5 .... dividing both sides by 5
t > 6/5
t > 1.2
Order the following numbers from least to greatest
Answer:
Step-by-step explanation:
Change all numbers to their decimal form.
37.5 % = 37.5 / 100 = 0.375
1/3 = 0.3333
0.3 = 0.3
40% = 40/100 = 0.4
3/5 = 0.6
Order
0.3
0.33333
0.375
0.4
0.6
The length of a rectangle is twice the width. The area is 72 yd^2. Find the length and the width.
Answer:
The length is 12yd and the width is 6yd.
Step-by-step explanation:
an airplane is traveling at 400 miles per hour. which equation can be used to find the total distance the plane will travel in h hours.
Answer:
y=400h
Where y is distance and h is time.
Match these non-parametric statistical tests with their parametric counterpart by putting the corresponding letter on the line.
_____ Friedman test
_____ Kruskal-Wallis H test
_____ Mann-Whitney U test
_____ Wilcoxon Signed-Ranks T test
A. Paired-sample t-test.
B. Independent-sample t-test.
C. One-way ANOVA, independent samples.
D. One-way ANOVA, repeated measures.
Answer:
A. Paired-sample t-test. --- Wilcoxon Signed-Ranks T testB. Independent-sample t-test. --- Mann-Whitney U testC. One-way ANOVA, independent samples. --- Kruskal-Wallis H testD. One-way ANOVA, repeated measures. --- Friedman testStep-by-step explanation:
The nonparametric statistics is a branch of statistics, that seeks out the population distribution that is either being distributed freely or specifically. Wilcoxon Signed-Ranks T-test is a hypothesis test used to compare the two or pre related columns that can be matched and maybe a repeated measure on a single sample.The Mann-Whitney U test is a null hypothesis and states the probability of a random sample of X and Y from the population is greater than the X and that Y is greater than X.Kruskal-Wallis H test is a test of one variance analysis and tests that sample originates from the same distribution.The Friedman test is used to find treatment across multiple tested attempts. It involves the ranking of the rows and then considering the values of the column.If x=.5, what is the numerical value of 20x ?
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PLZ HELP ASPPP PLZ WILL GIVE YOU BRAINLIST
Answer:
x=(-9)
PQ=2
PR=3
Step-by-step explanation:
How many one-thirds are in one-sixth?
there are (1/6)/(1/3) one-third in one sixth
Step-by-step explanation:
that means
no. of one-third is 1/2
Answer:
there are 2 one third in one sixth
-3(x+n)=x To solve for x
Answer:
x = -3n/4
Step-by-step explanation:
If KL = x + 4, LM = 2, and KM = 5x − 3, what is KL?
Step-by-step explanation:
then put x valule into KL equation
Geometry. Answer the question in the photo.
Answer:
5
Step-by-step explanation:
Since, A, B, C, D are collinear.
[tex] \implies A - B - C - D \\
\therefore \: AD = (AB + BC) + CD \\ \therefore \: 18 = AC + CD.. (\because AB + BC =AC) \\ \therefore \: 18 = 8 + CD \\ \therefore \: 18 - 8 = CD \\ \therefore \: 10 = CD \\ \\ \because \: BC + CD = BD \\ BC = BD - CD \\ BC = 15 - 10 \\ BC = 5 \\ [/tex]
what is 765,903 rounded to nearest hundred thousand
Answer:
800,000
Step-by-step explanation:
The numbers are above 5 making it round up not down
my noob has 36 apples he puts 29 in a bag how much he has now
Answer: He has 7 at the moment, technically, if he still has the bag, he still has all 36
Step-by-step explanation:
Answer:
he has noob 7
Step-by-step explanation:
.At a certain animal shelter, the ratio of puppies to adult dogs is 7 to 4. This week there are a total of55 dogs in the shelter. How many puppies are in the shelter this week? How many adult dogs are in the shelter this week
Answer:
There are 35 adult dogs and 20 puppies
Step-by-step explanation:
Represent the puppies with P and the Adult dogs with A
Given
[tex]A : P = 7 : 4[/tex]
Dogs = 55
Required
Determine A and P
First, we need to sum the ratios;
[tex]Total = A + P[/tex]
[tex]Total = 7 + 4[/tex]
[tex]Total = 11[/tex]
Adult Dogs is then calculated as follows;
[tex]A = \frac{A\ Ratio}{Total} * Dogs[/tex]
[tex]A = \frac{7}{11} * 55[/tex]
[tex]A = \frac{385}{11}[/tex]
[tex]A = 35[/tex]
Puppies is calculated by subtracting the number of adult dogs from the total
[tex]P = Dogs - Adult\ Dogs[/tex]
[tex]P = 55 - 35[/tex]
[tex]P = 20[/tex]
Hence;
There are 35 adult dogs and 20 puppies
on Tuesday, the Soto salad restaurant served 6 1/2 cups of Italian salad dressing. if the restaurant serves 1/2 cups of dressing with each salad, how many salads where ordered?
Answer:
11
Step-by-step explanation:
In a particularclass of 22 students, 10 are men. What fraction of the students in the class are
women?
Answer: 6/11
Work Shown:
22 people total, 10 men, so 22-10 = 12 women are in the class.
12/22 = (2*6)/(2*11) = 6/11 is the fraction of women in the class
Answer:
I'm pretty sure the answer they want is 12/22 or 6/11 students are women although some people are not men or women which technically makes the question impossible to solve.
You invest $2000 in a bank account. Find the amount of simple interest you earn in two years for an annual interest rate of 5.5%. Use the formula for simple interest I = p · r · t, where I is the interest, p is the principal, r is the annual interest rate, and t is the time in years.
Answer:
$220 is the amount of simple interest you will earn
Step-by-step explanation:
I = p * r * t
Principle = $2000
Rate = 5.5% (you need to change this to a decimal by dividing by 100) or
0.055
Time = 2 years
I = 2000 * 0.055 * 2
I = $220
Use the general slicing method to find the volume of the solid whose base is the triangle with vertices (0,0), (7,0), and (0,7) and whose cross sections perpendicular to the base and parallel to the y-axis are semicircles.
(need exact answer in terms of pi).
Answer:
The answer is "[tex]\bold{\frac{343 \ \pi}{24} \ \text{cubic units}}[/tex]"
Step-by-step explanation:
The volume of the mass whose cross-sectional area has been perpendicular is usually sliced by the method The cross-section, which is based to parallel to y-axis;
[tex]V = \int_{a}^{b} A (x)dx[/tex]
The semi-circular segment of the strong and seems to be perpendicular to foundation and
Y-axis parallel.
Its cross-section does have a diameter of: [tex](7-x)[/tex].
It also transverse radius is: [tex]\frac{1}{2}(7-x)[/tex].
The semi-circular segment area is,
[tex]Formula: \\\\ A(x)=\frac{1}{2} \times \pi \times r^2[/tex]
[tex]=\frac{1}{2} \times \pi \times (\frac{(7-x)}{2})^2\\\\=\frac{1}{2} \times \pi \times (\frac{(7-x)^2}{4})\\\\=\frac{1}{8}\pi(7-x)^2\\[/tex]
when
[tex]0 \leq \ x \ \leq 7[/tex]
Calculating the volume from the solid accordingly:
[tex]V= \int_{0}^{7}\frac{1}{8} \times\pi \times (7-x)^2 dx[/tex]
[tex]= \frac{1}{8} \pi \int_{0}^{7}(7-x)^2 dx \\\\= \frac{1}{8} \pi [\frac{(7-3)^3}{-3}]_{0}^{7}\\\\= \frac{\pi}{24} \times [7^3-0]\\\\= \frac{\pi}{24} \times 343\\\\= \frac{343 \pi}{24} \\[/tex]
There are 18 men on 2 baseball teams. 2/3 of them brought their sons to watch them play. How many brought their son?