Question 7 (4 points) Find and describe the intersection of the following line and plane: x-3 1: 2 1*7* = y +2= and + 1:2x+5y+32-1=0
Answers
To find the intersection of a line and a plane, we need to solve for the point where the line and plane intersect.
First, let's rewrite the plane equation in standard form:
2x + 5y - 31 = 0
Next, we need to find a point on the line. We can do this by setting y = -2 in the equation of the line:
x - 3 = 7
Solving for x, we get:
x = 10
So a point on the line is (10, -2).
Now we can substitute these values into the plane equation:
2(10) + 5(-2) - 31 = 0
Simplifying, we get:
20 - 10 - 31 = -21
So the point of intersection is (10, -2, -21).
Therefore, the intersection of the line and plane is the single point (10, -2, -21).
To find the intersection of the line and plane given, we need to rewrite the equations in a more recognizable form and then solve for the point of intersection. Here are the given equations:
Line: (x - 3)/1 = (y + 2)/2 = z/7
Plane: 1/2x + 5y + 3z - 1 = 0
First, we can express the line in parametric form by introducing a parameter t:
x = 1t + 3
y = 2t - 2
z = 7t
Now, we can substitute these expressions into the plane equation:
1/2(1t + 3) + 5(2t - 2) + 3(7t) - 1 = 0
By solving for t, we can then find the point of intersection:
1/2t + 3/2 + 10t - 10 + 21t - 1 = 0
32.5t - 7.5 = 0
t = 7.5/32.5 = 3/13
Substitute the value of t back into the parametric equations to find the point of intersection:
x = 1(3/13) + 3 = 3/13 + 3 = 42/13
y = 2(3/13) - 2 = 6/13 - 2 = 6/13 - 26/13 = -20/13
z = 7(3/13) = 21/13
The intersection point of the line and plane is (42/13, -20/13, 21/13).
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Related Questions
test the series for convergence or divergence. [infinity] ∑ e^n / n^2 n=1
Answers
The series ∑ e^n / n^2, where n starts from 1 and goes to infinity, diverges. This means that the series does not have a finite sum and keeps growing indefinitely.
To determine the convergence or divergence of the series ∑ e^n / n^2, we can use various tests. One commonly used test is the comparison test.
When we compare the given series to a known series, such as the harmonic series or geometric series, we can see that the terms of the given series do not decrease or approach zero as n increases. In fact, the exponential term e^n grows exponentially, and the denominator n^2 increases at a much slower rate.
As a result, the terms of the series do not tend to zero, and we can conclude that the series diverges. In other words, the sum of the series goes to infinity as n approaches infinity. This indicates that the series does not have a finite sum and keeps growing indefinitely.
Therefore, the series ∑ e^n / n^2 diverges.
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Expand and simplify no wrong answer or files or blank answers or reported
Answers
Answer:
-20t-18
Step-by-step explanation:
4t+6-24t-24
A hollow sphere sits snugly in a foam cube so that the sphere touches each side of the cube. Find the volume of the foam. A. 4 times the volume of the sphere B. 3 times the volume of the sphere C. 2 times the volume of the sphere D. The same as the volume of the sphere
Answers
Therefore, the correct option is C. 2 times the volume of the sphere.
The volume of the foam can be determined by subtracting the volume of the hollow sphere from the volume of the cube.
Let's denote the radius of the sphere as "r" and the side length of the cube as "s". Since the sphere touches each side of the cube, its diameter is equal to the side length of the cube, which means the radius of the sphere is half the side length of the cube (r = s/2).
The volume of the sphere is given by V_sphere = (4/3)πr^3.
Substituting r = s/2, we have V_sphere = (4/3)π(s/2)^3 = (1/6)πs^3.
The volume of the cube is given by V_cube = s^3.
The volume of the foam is the volume of the cube minus the volume of the hollow sphere:
V_foam = V_cube - V_sphere
= s^3 - (1/6)πs^3
= (6/6)s^3 - (1/6)πs^3
= (5/6)πs^3.
Comparing this with the volume of the sphere (V_sphere), we see that the volume of the foam is 5/6 times the volume of the sphere.
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Find 0% of 108:
Find 100% of 108:
Answers
Answer:
0% of 108 = 0
100% of 108 = 108
Step-by-step explanation:
0% of 108
= ( 0 / 100 ) x 108
= 0 x 108
= 0
100% of 108
= ( 100 / 100 ) x 108
= 1 x 108
= 108
Determine the pH of a 5.43 *10^-3 M Ca(OH)2 solution. Your answer should contain 3 decimal places as this corresponds to 3 significant figures when dealing with logs. pH =
Answers
To determine the pH of a solution, find the concentration of hydrogen ions (H+) and hydroxide ions (OH-) using Kw. The concentration of OH- ions is twice Ca(OH)2. Calculate the negative logarithm of H+ ions, resulting in a pH of approximately 12.37.
To determine the pH of a solution, we need to find the concentration of hydrogen ions (H+). In the case of a basic solution like Ca(OH)2, we need to first find the concentration of hydroxide ions (OH-) and then use the Kw (ion product constant for water) to find the concentration of H+ ions.
1. Ca(OH)2 dissociates into one Ca2+ ion and two OH- ions.
2. So, the concentration of OH- ions in the solution is twice the concentration of Ca(OH)2.
Concentration of OH- = 2 * 5.43 * 10^-3 M = 1.086 * 10^-2 M
Now, using the Kw value of 1.0 * 10^-14 at 25°C, we can find the concentration of H+ ions.
3. Kw = [H+][OH-]
1.0 * 10^-14 = [H+][1.086 * 10^-2]
[H+] = (1.0 * 10^-14) / (1.086 * 10^-2)
To find the pH, we need to take the negative logarithm (base 10) of the concentration of H+ ions.
4. pH = -log[H+]
pH = -log((1.0 * 10^-14) / (1.086 * 10^-2))
Calculating this expression using a calculator, the pH of the 5.43 * 10^-3 M Ca(OH)2 solution is approximately 12.37 (rounded to three decimal places).
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Which of the following is an irrational number?*
770
O 9.222...
7/2
O
7100
Answers
Answer:
I guess 09.222....
Step-by-step explanation:
the office supply vendor that delivers printer ink to companies charges a subscription fee of 230 for its services plus x dollars for each cartoon of ink. if a company paid 1364 for 18 cartoons of ink, including the subscription fee, what is the value of x?
Answers
The value of x, which represents the cost of each carton of ink is $63.
Let's break down the given information:
The subscription fee for the printer ink service is $230.
The company paid a total of $1364, which includes the subscription fee.
The company purchased 18 cartons of ink.
To find the value of x, we need to determine the cost of the ink cartridges alone, excluding the subscription fee. We can subtract the subscription fee from the total payment to get the cost of the ink:
Total payment - Subscription fee = Cost of ink cartridges
$1364 - $230 = $1134
Now, we divide the cost of the ink cartridges by the number of cartridges to find the cost per cartridge:
Cost of ink cartridges / Number of cartridges = Cost per cartridge
$1134 / 18 = $63
Therefore, the value of x, which represents the cost of each carton of ink, is $63.
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1.A recipe for salad dressing calls for three parts oil for every one part vinegar. How many tablespoons of oil are vinegar are needed to make 1/2 cup salad dressing?
Answers
Answer:
4 to 7 percent.
Step-by-step explanation:
We use the traditional oil-to-vinegar ratio: three parts oil to one part vinegar/acid, but this ratio can vary depending on your choice of vinegar/acid and personal taste. The less acidic the vinegar/acid, the less oil you need. It's all about balance!
graph the function f(x) = 1/2(2)^x on the coordinate plane.
Answers
Answer:
See below
Step-by-step explanation:
You can always plug in x's and solve for y.
1. a certain college wants to estimate the amount of time students, who live off campus, spend commuting to classes each week. a random sample of 45 off-campus students is surveyed. a) identify the population and sample for this study. b) what data is being collected? what type of data is this? c) what type of study is this?
Answers
The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.
a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.
b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.
c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.
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A negative correlation has a/an?
positive trend
decreasing trend
stable trend
increasing trend
Answers
Answer:
decreasing trend
A Ferris wheel car moves from point C to point D on the circle shown below:
Circle A is shown with points C and D on the circle and the central angle C A D marked 45 degrees. The diameter is 15 feet.
What is the arc length the car traveled, to the nearest hundredth?
5.89 feet
6.23 feet
7.46 feet
8.15 feet
Answers
Answer:
5.89 feet.
Step-by-step explanation:
I just took the test :)
The arc length the car traveled, to the nearest hundredth is 5.88 feet, the correct option is A.
What is a Circle?A circle is a round-shaped figure with all points lie in the same plane, the distance between all the points on the circle and the center of the circle is equal.
The line that passes through the center of the circle and has end point on the circumference is called the diameter, the radius is half the measure of the diameter.
A Ferris wheel car moves from point C to point D on the circle.
Circle A is shown with points C and D on the circle and the central angle C A D marked 45 degrees.
The diameter is 15 feet.
The arc length is determined by using the formula
L = ( \(\rm \theta\)/ 360) * 2 π r
L = ( 45 / 360) * 2 * 3.14 * r
r = diameter / 2
r = 15/2 = 7.5 ft
L = ( 45 / 360) * 2 * 3.14 * 7.5)
L = 5.8875 ft
L = 5.89 feet.
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2b x b
is this answer only 2b ^ 2 or is there any other answer without using exponentiation
Answers
The answer to the expression 2b x b is simply 2b^2. Exponentiation is a mathematical operation that raises a number to a power, and in this case, b is raised to the power of 2.
Alternatively, if exponentiation is not allowed, the answer to the expression is simply 2b * b, which can be simplified to 2b^2 as well.
So, the answer to the expression 2b x b is 2b^2, regardless of whether or not exponentiation is used.
The expression 2b x b represents the product of two scalars, 2 and b, multiplied by a scalar b.
The expression could represent a variety of quantities in mathematics and science, including the area of a rectangle, the volume of a cube, or the kinetic energy of an object, among others.
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Use the picture below to answer Problems 1 and 2.
1. Describe a sequence of translations that would map Figure H onto Figure K.
2. Describe a sequence of translations that would map Figure ) onto itself.
Answers
Answer: 1. Describe a sequence of translations that would map Figure H onto Figure K.
⃗⃗⃗⃗⃗⃗
Translate Figure H along vector , and then
⃗⃗⃗⃗⃗⃗ translate the image along vector .
⃗⃗⃗⃗⃗⃗
Translate Figure H along vector , and then
⃗⃗⃗⃗⃗⃗ translate the image along vector .
2. Describe a sequence of translations that would map Figure J onto itself.
⃗⃗⃗⃗⃗⃗
Translate Figure J along vector , and then
⃗⃗⃗⃗⃗⃗ translate the image along vector .
⃗⃗⃗⃗⃗⃗
Translate Figure J along vector , and then
⃗⃗⃗⃗⃗⃗ translate the image along vector .
Step-by-step explanation:
PLEASEEEEEE HELPPPPPPPP I’ll MAKE YOU BRAINLY
When viewed from the side, the frame of a ball-return net
angles with the ground.
forms a pair of supplementary
Find m/BCE and mZECD.
Answers
Answer:
BCE= 115 ECD=65
Step-by-step explanation:
(5x+10)+(3x+2)=180
8x+12=180
8x=168
x=21
5(21)+10=115
3(21)+2=65
Answer:
<BCE=115°
<ECD=65°
And their sum is 180°
Step-by-step explanation:
< BCE + <ECD =180° ( Being sum of supplementary angle which is formed in the given diagram is 180°)
(5x + 10)° + (3x + 2)°= 180°
5x + 10 + 3x + 2 = 180°
5x + 3x + 10 +2 = 180°
8x + 12= 180°
8x = 180°-12°
8x = 168
x= 168/8
x=21°
Now,
<BCE = 5x+10
= 5*21+10
=105+10
=115
<ECD
= 3x+2
= 3*21+2
=65
A triangle has side lengths 4.47 cm, 4 cm, and 4.47 cm. The angles measures are 64°, 64°, and 52°. What type of triangle is this triangle? Acute isosceles obtuse scalene acute scalene obtuse isosceles
Answers
Answer:
The type of triangle is this triangle is the acute isosceles triangle
Step-by-step explanation:
They are all less than 90 degrees and two of the sides are the same and two of the angles are the same
Answer:
The type of triangle is this triangle is the acute isosceles triangle
Step-by-step explanation:
bro get smart stop cheating
If the ticket was $36 and she bought it at original price and marked it up 10% and resold the ticket .how much did he resell the ticket for?
Answers
You purchase a car for $18,500. The tax rate is 9% and you make a $2,000 down payment. How much is your principal?
Show steps please
Answers
Answer:
15,000
Step-by-step explanation:
with regard to a​ regression-based forecast, the standard error of the estimate gives a measure of:______.
Answers
With regard to a regression-based forecast, the standard error of the estimate gives a measure of option (C) the variability around the regression line
The standard error of the estimate in a regression-based forecast is a measure of the variability of the actual data points around the predicted values of the regression line.
It tells us how much the actual data points are likely to deviate from the predicted values, and provides a measure of the accuracy of the forecast. It is not related to the time required to derive the forecast equation, the maximum error of the forecast, or the time period for which the forecast is valid.
Therefore, the correct option is (C) The variability around the regression line.
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The give question is incomplete, the complete question is:
With regard to a regression-based forecast, the standard error of the estimate gives a measure of:
A. the time required to derive the forecast equation.
B. the maximum error of the forecast.
C. the variability around the regression line.
D. the time period for which the forecast is valid.
If two coplanar lines are cut by _________ so that a pair of alternate interior angles are _,_____ then the two lines are parallel.
Answers
If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are equal then the two lines are parallel.
The four sets of opposing angles that each have their own vertex point, are on different sides of the transversal and are both either internal or exterior are called alternate angles.
In geometry, a transversal line is one that cuts across the plane in two places. It does so at two spots where two lines meet. Many right angles are produced when two transverse lines meet. There are four types of similar angles: matching, alternative interior, alternate exterior, and co-interior.
In geometry, two lines are considered parallel if and only if all pairs of alternative interior angles in any transversal are equal.
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The decimal 4.6 is the same as what fraction?
Answers
Answer:
46/10 or 23/5
Step-by-step explanation:
Answer:
46/10
Step-by-step explanation:
I got it right on imagine math
The value of the test statistic for the test H0: μ = 3.8, Ha : μ > 3 with n = 52, x⎯⎯ = 4.2 and s = 1.9 is
Answers
The value of the test statistic for the test is 1.52
How to determine the value of the test statistic for the test?From the question, we have the following parameters that can be used in our computation:
H0: μ = 3.8, Ha : μ > 3 with n = 52, x⎯⎯ = 4.2 and s = 1.9
The above parameters mean that
Sample mean = 3.8Number of samples = 52x = 4.2Standard deviation = 1.9The value of the test statistic for the test is calculated as
\(t = \frac{x - \mu_0}{s/\sqrt n}\)
Substitute the known values in the above equation
\(t = \frac{4.2 - 3.8}{1.9/\sqrt {52}}\)
Evaluate the equation
t = 1.52
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h is inversely proportional to p
p os directly proportional to the square root of t
Answers
Answer:
h ∝ \(\frac{1}{p}\)
p ∝ \(\sqrt{t}\)
Step-by-step explanation:
h is inversely proportional to p would be:
h ∝ \(\frac{1}{p}\)
Or, in terms of the constant, it would be:
h = \(\frac{k}{p}\)
p is directly proportional to the square root of t would be:
p ∝ \(\sqrt{t}\)
Or, terms of the constant, it would be:
p = k\(\sqrt{t}\)
PLEASE HELPP THANKS SIS XOXO Solve each absublute value inequality. 5=|x|+3
Answers
Answer:
−1 < x < 4
Hoped this helped ⊂◉‿◉つ
Answer:
x = ±2
Step-by-step explanation:
Move the 3 to the left side of the equation by subtracting it. This way, you get:
2=|x|.
Because x is an absolute value, that means the value of x can be negative or positive. That is why there is a "±" symbol beside the 2 in the answer.
What is the angle of depression from the start of a 3-foot-highaccess ramp that ends at a point20 feet away along the ground?
Answers
the angle of depression from the start of the 3-foot-high access ramp to the end point 20 feet away along the ground is approximately 8.13 degrees.
The angle of depression is the angle formed between a horizontal line (such as the ground) and the line of sight from an observer's eye to a point below.
Given:
Height of the access ramp (opposite side): 3 feet
Distance from the start of the ramp to the end point along the ground (adjacent side): 20 feet
To find the angle of depression, we can use trigonometry. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
Tangent(angle) = opposite / adjacent
In this case, the opposite side is the height of the ramp (3 feet) and the adjacent side is the distance along the ground (20 feet).
Tangent(angle) = 3 / 20
To find the angle itself, we need to take the inverse tangent (also known as arctan) of the above ratio.
angle = arctan(3 / 20)
Using a calculator, we can find the approximate value of the angle:
angle ≈ 8.13 degrees (rounded to two decimal places)
Therefore, the angle of depression from the start of the 3-foot-high access ramp to the end point 20 feet away along the ground is approximately 8.13 degrees.
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Help! I'll give you the brainiest!!!
Answers
Answer:
Are you sure this is not a hacking trick?
Step-by-step explanation:
Answer:
a four-sided figure.
Regular shapes have sides that are all equal and interior (inside) angles that are all equal. Irregular shapes have sides and angles of any length and size.
Step-by-step explanation:
Suppose you have a deck of 52 cards. Let:
A: draw a 7
B: draw a diamond
Find the probability of A U B and write as a fraction
Answers
Answer:
16/52
Step-by-step explanation:
A U B= A + B - A ∩ B
A= 4/52
B= 13/52
A∩B= 1/52 (it's 1/52 because there is only one 7 of diamonds in the deck)
4/52+13/52-1/52= 16/52
What is the greatest common factor 3x^4, 15x^3 ,21x^2
Answers
Answer: 3x^2
Step-by-step explanation: Find the greatest common factor for the numerical part. For 3, 15, and 21 the greatest common factor is 3. Find the GCF for the variable part which is x^2. Multiply 3 and x^2 to get 3x^2.
The Indianapolis Colts played the Chicago Bears in the 2007 Super Bowl. Determine whether the stated conclusion is valid based on the given information. If not, Write invalid. Explain your reasoning.
Given: The Super Bowl winner has the highest score at the end of the game. The Colts had a score of 29 and the Bears had a score of 17 .
Conclusion: The Colts won the Super Bowl.
Answers
The stated conclusion is valid. The Colts won the Super Bowl based on the given information.
According to the given information, the Colts had a score of 29 and the Bears had a score of 17. The conclusion states that the Colts won the Super Bowl. Since the Super Bowl winner is determined by having the highest score at the end of the game, and the Colts had a higher score than the Bears, it can be concluded that the Colts won the Super Bowl.
The Colts' score of 29 is greater than the Bears' score of 17, indicating that the Colts outperformed the Bears in terms of points scored during the game. Therefore, based on this information, we can validly conclude that the Colts won the Super Bowl.
It's important to note that additional information about the game, such as the specific rules and regulations, the duration of the game, and any other relevant factors, are not provided. However, based solely on the given information that the Colts had a score of 29 and the Bears had a score of 17, we can confidently conclude that the Colts were the winners of the 2007 Super Bowl.
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(−2 3/2)^2
KHAN ACADEMY (EXPONENTS WITH NEGATIVE FRACTIONAL BASE)
Answers
The values of the given expression having exponent with negative fractional base i.e. \(-2^{(3/2)^2}\\\) is evaluated out to be 16/9.
First, we need to simplify the expression inside the parentheses using the rule that says "exponents with negative fractional base can be rewritten as a fraction with positive numerator."
\(-2^{(3/2)^2}\) = (-2)² × (2/3)²
Now, we can simplify the expression further by solving the exponent of (-2)² and (2/3)²:
(-2)² × (2/3)² = 4 × 4/9 = 16/9
Therefore, the value of the given expression \(-2^{(3/2)^2}\\\) is 16/9.
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The question is :
What is the value of the expression \(-2^{(3/2)^2}\) ?