Answer:
Step-by-step explanation:
This is a binomial distribution problem, where each person either has car insurance with Geico or doesn't have.
Let's denote the probability of a person having car insurance with Geico as p = 0.75, and the probability of not having car insurance with Geico as q = 0.25.
The probability of getting exactly k people out of n people who have car insurance with Geico is given by the binomial distribution formula:
P(k) = (n choose k) * p^k * q^(n-k)
where (n choose k) is the number of ways to choose k items out of n items, which is calculated by the formula:
(n choose k) = n! / (k! * (n-k)!)
where n! denotes the factorial of n.
We need to find the probability of getting at least 8 people out of 10 who have car insurance with Geico, which is the same as the probability of getting 8, 9, or 10 people who have car insurance with Geico. So, we can calculate this probability by adding the probabilities of these three cases:
P(at least 8) = P(8) + P(9) + P(10)
P(8) = (10 choose 8) * 0.75^8 * 0.25^2 = 0.002
P(9) = (10 choose 9) * 0.75^9 * 0.25^1 = 0.054
P(10) = (10 choose 10) * 0.75^10 * 0.25^0 = 0.056
Therefore, the probability of at least 8 people out of 10 having car insurance with Geico is:
P(at least 8) = P(8) + P(9) + P(10) = 0.002 + 0.054 + 0.056 = 0.112
So, the probability that at least 8 people out of 10 have car insurance with Geico is 0.112 or approximately 11.2%.
Domain is now called the ____________ which means before a change
Answer:
Step-by-step explanation:
Domain is now called the "source" which means before a change or transformation. In mathematics, the term "source" is often used to refer to the set of all possible inputs or values that can be fed into a function or transformation, before any changes or transformations take place. The set of all possible outputs or resulting values from the function or transformation is called the "range" or "codomain".
Miles is planning to spend 2/3 as many hours bicycling this week as he did last week is Miles going to spe
Miles is going to spend less than the hours that were spent last week since 2/3 is a fraction.
Is a fraction less or greater than the whole?A fraction represents a part of a whole, and is therefore always less than the whole. For example, 2/3 represents two out of three equal parts of a whole.
The implication of this is that the time that Miles would have to spend on biking in the coming week would be wo out of three equal parts of a whole time that was spent in the last week and this would be less than the time spent last week.
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farmers marked 45 cows and released them next day counted 150 ,witch 15 had marks what is the estimated population
Answer:
450
Step-by-step explanation:
I will mark you brainiest!
If JL = 30, JK = 18, and LM = 6, then the value of LN is
A) 3
B) 6
C) 9
D) 15
Answer: LN = 15
Make a proportional relationship:
[tex]\dfrac{LN}{JL}=\dfrac{LM}{KL}[/tex]
Insert the values:
[tex]\longrightarrow\dfrac{LN}{30} =\dfrac{6}{30-18}[/tex]
cross multiply:
[tex]\longrightarrow LN=\dfrac{30(6)}{12}[/tex]
Simplify:
[tex]\text{LN}= \text{15}[/tex]9x-7=-7 please answer quick
Answer:
x = 0
Step-by-step explanation:
9x - 7 = -7
Add 7 to both sides.
9x - 7 + 7 = -7 + 7
9x = 0
Divide both sides by 9.
9x/9 = 0/9
x = 0
Answer:
x=0
Step-by-step explanation:
Which of the following represents the distributive property?
A. a = b then bea
B. a(b+c)=ab+ac
C. if a = band b-c, then a = c
D. If a = b then ac- be
The expression represents the distributive property from the list of options is (b) a(b + c) = ab + ac
Which of the expression represents the distributive property?The distributive property is a mathematical property that applies to multiplication and addition or subtraction.
It states that when you multiply a number (or variable) by a sum or difference inside parentheses, you can distribute the multiplication across the terms inside the parentheses.
This is represented by the following formula:
a(b + c) = ab + ac
This is represented by Option (B)
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Given that cos theta= 3/10 and 3pi/2 < theta < 2pi, find the exact value of each of the following:
a) sin 2theta
b) The quadrant in which the angle theta/2 is located.
b) cos theta/2
In response to the stated question, we may state that Since [tex]\theta[/tex]is in the trigonometry fourth quadrant, [tex]\theta/2[/tex] is also in the fourth quadrant.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
a) We can use the double angle formula for sine to find sin 2theta:
[tex]sin 2\theta = 2sin \theta cos \theta\\sin^2 \theta + cos^2 \theta = 1\\sin^2 \theta + (3/10)^2 = 1\\sin^2 \theta = 1 - (9/100)\\sin \theta = \sqrt(91)/10 \\sin 2\theta = 2sin \theta cos \theta\\sin 2\theta = 2(\sqrt(91)/10)(3/10)\\sin 2\theta = 3\sqrt(91)/50[/tex]
b) To find the quadrant in which [tex]\theta/2[/tex] is located, we need to find [tex]\theta/2[/tex] first:
[tex]\theta/2 = (3\pi/2 + \theta)/2\\\theta/2 = 3\pi/4 + t\heta/2\\\theta/2 - \theta/2 = 3\pi/4\\\theta/2 = 3\pi/4\\\theta = 3\pi/2[/tex]
Since theta is in the fourth quadrant, [tex]\theta/2[/tex] is also in the fourth quadrant.
c) To find cos theta/2, we can use the half angle formula for cosine:
[tex]cos(theta/2) = \sqrt((1 + cos theta)/2)\\cos(theta/2) = \sqrt((1 + 3/10)/2)\cos(theta/2) = \sqrt(13/20)\\cos(theta/2) = \sqrt(13)/2sqrt(20)\\cos(theta/2) = \sqrt(13)/10[/tex]
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What is the sum of the infinite series:
72 - 36 + 18 - 9 +...
The calculated sum of the infinite series represented as 72 - 36 + 18 - 9 +... is 48
Calculating the sum of the infinite seriesGiven that we have the following infinite series
72 - 36 + 18 - 9 +...
In the above series, we have the following parameters
Initial value, a = 72
Common ratio, r = -36/72
When the above are evaluated, we have
Initial value, a = 72
Common ratio, r = -0.5
The sum of the infinite series is then calculated as
Sum = a/(1 - r)
When values are substituted, we have
Sum = 72/(1 + 0.5)
Evaluate
Sum = 48
Hence, the sum is 48
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Oliver spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 6900 feet.
Oliver initially measures an angle of elevation of 16° to the plane at point A. At some
later time, he measures an angle of elevation of 27° to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest tenth of a foot if necessary.
The distance the plane traveled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).
What are angles?An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians, and they are used to describe the amount of rotation or turning between two lines or planes. In a two-dimensional plane, angles are usually measured as the amount of rotation required to move one line or plane to coincide with the other line or plane.
Let's first draw a diagram to visualize the problem:
/ |
/ |
/ |P (plane)
/ |
/ |
/ | h = 6900 ft
/
/ θ2. |
/ |
/ |
B ___/θ1__ _|___ A
d
We need to find the distance the plane traveled from point A to point B, which we'll call d. We can use trigonometry to solve for d.
From point A, we have an angle of elevation of 16° to the plane. This means that the angle between the horizontal and the line from point A to the plane is 90° - 16° = 74°. Similarly, from point B, we have an angle of elevation of 27° to the plane, so the angle between the horizontal and the line from point B to the plane is 90° - 27° = 63°.
Let's use the tangent function to solve for d:
x = h / tan(74°) = 19906.5 ft
d - x = h / tan(63°) = 23205.2 ft
So,
d = x + h / tan(63°) ≈ 43111.7 ft ≈ 8.15 miles.
Therefore, the distance the plane travelled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).
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1Which equation best describes the line of best fit?
⚠️please explain how bc i have a test tmr and im so confusedd!*
The best linear equation that describe given graph is y=2.5x-35 i.e. C.
What is a linear equation ?
A linear equation is a mathematical equation that, when plotted on a graph, represents a straight line. It is an equation of the following form:
y = mx + b
where y = dependent variable, x = independent variable, m= slope of the line, and b = y-intercept (the point where the line crosses the y-axis).
Now,
Lets take a point on the given graph that is on line (50,90)
then the equation of line should give the same values.
So,
For A, y=0.4x-35
y=0.4*50-35
y=-15 Hence, It does not follow.
For B, y= y=0.4x-70
y=0.4*50-70
y=-50 Hence, It does not follow.
For C, y= y=2.5x-35
y=2.5*50-35
y=125-35
y=90
Hence, It does follow the given point.
Therefore, The best linear equation that describe given graph is y=2.5x-35
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Solve the given third-order differential equation by variation of parameters.
y''' + y' = cot(x)
Answer: To solve the third-order differential equation y''' + y' = cot(x) by variation of parameters, we first need to find the solution to the associated homogeneous equation, which is:
y''' + y' = 0
The characteristic equation is r^3 + r = 0, which can be factored as r(r^2 + 1) = 0. This gives us the roots r = 0, r = i, and r = -i. Therefore, the general solution to the homogeneous equation is:
y_h = c1 + c2 cos(x) + c3 sin(x)
To find a particular solution to the non-homogeneous equation using variation of parameters, we assume that the solution has the form:
y_p = u1(x) + u2(x) cos(x) + u3(x) sin(x)
where u1, u2, and u3 are functions to be determined.
We can find the derivatives of y_p:
y'_p = u1'(x) + u2'(x) cos(x) - u2(x) sin(x) + u3'(x) sin(x) + u3(x) cos(x)
y''_p = u1''(x) + u2''(x) cos(x) - 2u2'(x) sin(x) - u2(x) cos(x) + u3''(x) sin(x) + 2u3'(x) cos(x) - u3(x) sin(x)
y'''_p = u1'''(x) + u2'''(x) cos(x) - 3u2''(x) sin(x) - 3u2'(x) cos(x) - u2(x) sin(x) + u3'''(x) sin(x) + 3u3''(x) cos(x) - 3u3'(x) sin(x)
Substituting these derivatives into the non-homogeneous equation, we get:
u1'''(x) + u2'''(x) cos(x) - 3u2''(x) sin(x) - 3u2'(x) cos(x) - u2(x) sin(x) + u3'''(x) sin(x) + 3u3''(x) cos(x) - 3u3'(x) sin(x) + u1'(x) + u2'(x) cos(x) - u2(x) sin(x) + u3'(x) sin(x) + u3(x) cos(x) = cot(x)
Grouping the terms with the same functions together, we get:
u1'''(x) + u1'(x) = 0
u2'''(x) cos(x) - 3u2''(x) sin(x) - u2(x) sin(x) + u2'(x) cos(x) + u2'(x) cos(x) = cot(x) cos(x)
u3'''(x) sin(x) + 3u3''(x) cos(x) - 3u3'(x) sin(x) + u3'(x) sin(x) + u3(x) cos(x) = cot(x) sin(x)
The first equation is a first-order differential equation, which can be solved by integrating both sides:
u1'(x) + u1(x) = c1
where c1 is a constant of integration. The solution to this equation is:
u1(x) = c1 + c2 e^(-x)
where c2 is another constant of integration.
Step-by-step explanation:
if walter eats 12 cookies, which represents 25% of the bag how many cookies where in the bag before any was eaten
Answer:
48 cookies were in the bag.
Step-by-step explanation:
It said 12 was 25%, so you want to multiply it by 4 to get 100% and 100% of the bag was 48 cookies.
what type of shape is the box of cremora ?
What is the fractional equivalent of 3.15?
Answer:
Below
Step-by-step explanation:
3.15 can be read as 3 and 15 hundredths = 3 15/100 = 3 3/20
Answer: 63/20
Step-by-step explanation:
Can anyone show how to solve these two questions. Thank you!
according the given question the exact value of given expression is [tex]$\cos\frac{x}{2} = -\sqrt{\frac{1}{2(1 - \left(-\frac{160}{81}\right)^2)}} = -\sqrt{\frac{81^2}{2(81^2 - 160^2)}} = \boxed{-\frac{81\sqrt{239}}{319}}$[/tex]
First, we need to find [tex]$\sin x$[/tex] using the identity[tex]$\cos^2x + \sin^2x = 1$:$\sin^2x = 1 - \cos^2x = 1 - \left(-\frac{4}{5}\right)^2 = \frac{9}{25}$[/tex]
Since [tex]$\frac{\pi}{2} < x < \pi$[/tex], we know that [tex]$\frac{\pi}{4} < \frac{x}{2} < \frac{\pi}{2}$[/tex]. Therefore, we can use the
identity [tex]$\tan\frac{x}{2} = \frac{\sin x}{1 + \cos x}$[/tex]:
[tex]$\tan\frac{x}{2} = \frac{\sqrt{\frac{9}{25}}}{1 - \frac{4}{5}} = \frac{\frac{3}{5}}{\frac{1}{5}} = \boxed{3}$[/tex]
[tex]If $\tan x = \frac{40}{9}$ and $\pi < x < \frac{3\pi}{2}$, find $\cos\frac{x}{2}$.[/tex]
First, we need to find [tex]$\sin x$[/tex] using the identity [tex]$\tan^2x + 1 = \sec^2x$[/tex]:
[tex]$\sin x = \frac{\tan x}{\sec x} = \frac{\frac{40}{9}}{-\frac{9}{40}} = -\frac{160}{81}$[/tex]
[tex]Since $\pi < x < \frac{3\pi}{2}$, we know that $\frac{\pi}{2} < \frac{x}{2} < \frac{3\pi}{4}$[/tex]. Therefore, we can use the identity [tex]$\cos\frac{x}{2} = \pm\sqrt{\frac{1 + \cos x}{2}}$[/tex]:
[tex]$\cos\frac{x}{2} = -\sqrt{\frac{1 + \cos x}{2}} = -\sqrt{\frac{1 + \frac{\cos^2x}{\sin^2x}}{2}} = -\sqrt{\frac{\sin^2x + \cos^2x}{2\sin^2x}} = -\sqrt{\frac{1}{2(1 - \sin^2x)}}$[/tex]
Plugging in [tex]$\sin x = -\frac{160}{81}$[/tex] , we get:
[tex]$\cos\frac{x}{2} = -\sqrt{\frac{1}{2(1 - \left(-\frac{160}{81}\right)^2)}} = -\sqrt{\frac{81^2}{2(81^2 - 160^2)}} = \boxed{-\frac{81\sqrt{239}}{319}}$[/tex]
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Your grandfather invested a lump sum 18 years ago at 5% interest. Today, he gave you the proceeds of that investment, which amounted to R6 649,93 in total. How much did your grandfather originally invest?
The lumpsum amount invested in 18 years ago for the given value Future value and interest is = Rs 2763,18.3268
What about lumpsum?
In mathematics, a lump sum refers to a single, fixed amount of money or quantity of something that is paid or received all at once, rather than being paid or received in installments or over a period of time.
The term "lump sum" can be used in various mathematical contexts, such as in finance, where it can refer to a single payment or investment, or in statistics, where it can refer to a single value or data point.
Define future value:
In mathematics, future value (FV) refers to the value of an investment or cash flow at a specified date in the future, assuming a certain rate of return.
The future value of an investment is the amount of money that an investor would expect to have at a specified date in the future if they were to invest a certain amount of money today, and if that investment earns a certain rate of return over time.
⇒ The formula for calculating the future value of an investment is:
[tex]FV = PV x (1 + r)^n[/tex]
According to the given information:
Interest Rate = 5%
Time Period = 18 years
Future Value = Rs 6649,93.
Using the concept of TVM calculation we have that,
Present value = [tex]\frac{Future Value}{(1+r)^{t} }[/tex]
So, the Present Value = [tex]\frac{664993}{(1+0.05)^{18} } = 2763,18.3268[/tex]
Hence, the Lumpsum Amount is Rs 2763,18.3268
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Help! See image below
In the polygon, using sum of exterior angles the value of x = 37°
What is a polygon?A polygon is a shape that has 3 or more sides.
Given the polygon which is a hexagon to find the value of x, we note that the angles are all exterior angles. We know that the sum of the exterior angles of a polygon is 360°.
So, we have the equation as
x + 2x + (x - 1) + 3x + (x + 18) + (x + 10) = 360°
Collecting like terms, we have that
x + 2x + x + 3x + x + x - 1 + 18 + 10 = 360°
9x + 27° = 360°
Subtracting 27° from both sides of the equation, we have that
9x + 27° - 27° = 360° - 27°
9x + 0 = 333°
9x = 333°
Dividing both sides by 9, we have that
x = 333°/9
x = 37°
So, the value of x = 37°
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Find the value of angle ZOX
using the image below
Answer: 64°
Step-by-step explanation:
Had this problem and got it right
add me
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The value οf the variable y is 9 when k is -3 in the given question.
What is variable?In mathematics and statistics, a variable is a quantity οr a characteristic that can take οn different values οr attributes. Variables can be classified as either quantitative οr categοrical, depending οn the type οf data they represent.
A quantitative variable is a variable that represents a numerical measurement οr quantity. Examples οf quantitative variables include height, weight, temperature, and incοme.
A categοrical variable is a variable that represents a grοup οr categοry. Examples οf categοrical variables include gender, race, and type οf car.
Given: y=k x
where, x= -3 and k= -3
we can find the value of y by multiplying k with x,
so, y=k x
now, putting values as follows:
we get, y = -3 × -3
= 9
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Lara grows apples in her orchard and sells them at the weekly farmer's market. Each week, she sells the apples for a different price and records the number of apples sold. The scatter plict below
shows the price of one apple and the number of apples that were sold. A line of best fit for these data points, the equation y=-z+32, is also shown on the plot
Apples Number of Apples Sold
solve this please! i've been trying for a while but i cant get it
The three-dimensional object in the figure has a surface area of 52 square yards.
What does surface area dimension mean?Surface area is the two-dimensional measure or area of a three-dimensional space's boundary, just as perimeter is the one-dimensional measure or length of a two-dimensional area's boundary.
The object's rectangular base has a length of 4 yards and a width of 3 yards, as seen in the figure. As a result, the base's area is:
Area of base = length x width = 4 x 3 = 12 square yards
Area of a triangular face = (1/2) x base x height = (1/2) x 4 x 5 = 10 square yards
Since the object has four triangular faces, the total area of the four triangular faces is:
Total area of triangular faces = 4 x 10 = 40 square yards
We add the base's area to the sum of the four triangle sides to determine the object's surface area:
Surface area = Area of base + Total area of triangular faces
Surface area = 12 + 40 = 52 square yards
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PLEASE HELP ME!! Suppose babies bom after a gestation period of 32 to 35 weeks have a mean weight of 2700 grams and a standard deviation of 800 grams while babies bom after a gestation period of 40 weeks have a mean weight of 3200 grams and a standard deviation of 480 grams. If a 32-week gestation period baby weighs 2575 grams and a 40-week gestation period baby weighs 3075 grams, find the corresponding z-scores. Which baby weighs less relative to the gestation period?
Find the corresponding scores. Which baby weighs relatively less? Select the correct choice below and fill in the answer boxes to complete your choice.
(Round to two decimal places as needed)
A The baby bom in week 32 weighs relatively less since its z-score, ___ is larger than the
z-score of ___ for the baby born in week 40.
B The baby bom in week 40 weighs relatively less since its score, ____, is larger than the z-score of ____ for the baby born in week 32.
C. The baby born in week 40 weighs relatively less since its z-score ____, is smaller than the z-score of, ____ for the baby bom in week 32.
The baby born in week 40 weighs relatively less since its z-score -0.26, is smaller than the z-score of -0.16 for the baby born in week 32.
How to solveTo find the z-score, we use the formula:
z = (x - μ) / σ
where x is the individual value, μ is the mean, and σ is the standard deviation.
For the 32-week gestation period baby (weight = 2575 grams):
μ = 2700 grams (mean weight)σ = 800 grams (standard deviation)z = (2575 - 2700) / 800 = -125 / 800 = -0.15625For the 40-week gestation period baby (weight = 3075 grams):
μ = 3200 grams (mean weight)σ = 480 grams (standard deviation)z = (3075 - 3200) / 480 = -125 / 480 = -0.26042Now, we round the z-scores to two decimal places:
z-score for the 32-week baby: -0.16z-score for the 40-week baby: -0.26Since the z-score for the 40-week baby (-0.26) is smaller than the z-score for the 32-week baby (-0.16), the correct answer is:
C. The baby born in week 40 weighs relatively less since its z-score -0.26, is smaller than the z-score of -0.16 for the baby born in week 32.
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The data shows the number of video streaming hours for10 household in New Hampshire during the month of January and July last year. Which of the following best describes the data?
Please let me know which one is the answer, 100 points! Thank you
Answer: brainliest ?
The correct answer is: The data is dependent, because the hours of video streaming in January and July occurred in the same households.
This is because the data collected is related to the same households and not different people. The same households were monitored during both January and July, which means that any changes in the video streaming hours during those months are likely due to factors within those households, such as changes in habits, routines, or available free time.
If the data were independent, then it would mean that the hours of video streaming in January and July were not related or influenced by any factors from the other month. For example, if the data were collected from two completely different sets of households, then it would be considered independent because there would be no connection or influence between the households in January and July. However, this is not the case in the given scenario, so the correct answer is that the data is dependent.
Step-by-step explanation:
hope its help <:
Find the value of X. Round to the nearest tenth
Answer:i don't know the answer
Step-by-step explanation: i don't konw
PLEAS HELP!!!
Find the volume of the pyramid. Write your answer as a fraction or mixed number.
The volume of the triangular pyramid is 26 2/3 yd³
How to determine the volumeThe formula for calculating the volume of a triangular pyramid is expressed with the equation
A = 1/3bh
Such that the parameters in the equation are;
A is the area of the triangular pyramid.b is the base area of the triangular pyramid.h is the height of the pyramid.The base area of the pyramid is;
Area = 1/2 × 4 × 5
Multiply the values
Base area =20/2
Base area = 10 yd
Substitute the value
Volume = 1/3 × 10 × 8
Multiply the values
Volume = 80/3
Divide the values
Volume = 26 2/3 yd³
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Help me.. Please asap
The vector equations of L₂ when expressed as Cartesian equations are
y = 0
x = (z ± √(z² - 4(z-2))) / 2
z = [(4 - ((x-1)/(-z))²) ± √((4 - ((x-1)/(-z))²)² + 64)] / 8
What is the vector equation of the line L₂To find the vector equation of the line L₂, we need to find a vector that is perpendicular to L₁ and passes through the point (1,0,2). Let's start by finding the vector equation of L₁.
Let P(x,y,z) be a point on L₁. Then the vector equation of L₁ is given by:
r₁ = P + t * d₁
where d₁ is the direction vector of L₁ and t is a scalar parameter.
Since L₂ is perpendicular to L₁, its direction vector must be perpendicular to d₁. Thus, we can find a vector that is perpendicular to d₁ by taking the cross product of d₁ with any non-zero vector that is not parallel to d₁. Let's choose the vector (0,1,0):
v = d₁ x (0,1,0) = (-z,0,x)
Note that we can choose any non-zero vector that is not parallel to d₁, and we will still get a vector that is perpendicular to d₁.
Now we have a point on L₂ (1,0,2) and a direction vector (v), so we can write the vector equation of L₂:
r₂ = (1,0,2) + s * v
where s is a scalar parameter.
To express the Cartesian equations of L₂, we can write the vector equation as a set of three parametric equations:
x = 1 - sz
y = 0
z = 2 + sx
We can eliminate the parameter s by solving for it in two of the equations and substituting into the third equation:
s = (x - 1) / (-z)
s = (z - 2) / x
Setting these two expressions equal to each other and solving for x, we get:
[tex]x^2 - zx + z - 2 = 0[/tex]
This is a quadratic equation in x, so we can solve for x using the quadratic formula:
[tex]x = (z \± \sqrt{(z^2 - 4(z-2)})) / 2[/tex]
Substituting this expression for x into one of the parametric equations, we get:
y = 0
And substituting the expressions for x and s into the other parametric equation, we get:
[tex]z = 2 + [(z \± \sqrt{(z^2 - 4(z-2)})) / 2] * [(1 - sz) / (-z)][/tex]
Simplifying this equation, we get:
[tex]4z^2 - (4 - s^2)z - 4 = 0[/tex]
Again, this is a quadratic equation in z, so we can solve for z using the quadratic formula:
[tex]z = [(4 - s^2) \± \sqrt((4 - s^2)^2 + 64)] / 8[/tex]
z = [(4 - s²) ± √((4 - s²)² + 64)] / 8
Finally, we can substitute these expressions for x and z into one of the parametric equations to get:
[tex]y = 0\\x = (z \± \sqrt{(z^2 - 4(z-2)})) / 2\\z = [(4 - ((x-1)/(-z))^2) \± \sqrt{((4 - ((x-1)/(-z))^2)^2} + 64)] / 8[/tex]
These are the Cartesian equations of L₂.
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1. Find the unknown side lengths of the given right triangle.
The unknown side lengths of the given right triangle ∆LJK where LJ 30° and JK 5 are LJ = 6, and JK = 4.
What is triangle?Triangle is a three-sided polygon with three angles. It is one of the basic shapes in geometry. A triangle has three sides and three angles, usually measured in degrees. The angles always add up to 180°. Triangles can be classified according to the lengths of their sides or the sizes of their angles. Types of triangles include right, acute, obtuse, scalene, isosceles, and equilateral. Triangles are also used to form more complex shapes in geometry, such as polygons and circles.
To find the unknown side lengths of a right triangle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that the square of the hypotenuse (the longest side of a triangle) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is JK and the other two sides are LJ and JK.
We can use the Pythagorean Theorem to find the unknown side length of JK. We know that the angle LJ is 30°, so we can use the sine rule to calculate the length of side LJ. The sine rule states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal for all three sides. Therefore, we can calculate the length of LJ by dividing the sine of 30° (0.5) by the length of the opposite side (JK).
We can now use the Pythagorean Theorem to calculate the length of side JK. We know that the length of LJ is 6, and the length of JK is 5. We can plug these values into the equation a2 + b2 = c2, where a is the length of LJ (6), b is the length of JK (5), and c is the hypotenuse (JK). This yields the equation 36 + b2 = c2, which simplifies to b2 = c2 - 36. Since we know that c2 = 52, we can solve for b2 by subtracting 36 from 52, which gives us 16. The square root of 16 is 4, so the length of JK is 4.
Therefore, the unknown side lengths of the given right triangle ∆LJK where LJ 30° and JK 5 are LJ = 6, and JK = 4.
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Someone please help me answer this question
The two statements that are both true are as follows: line
AC is perpendicular to line HB and line AC is parallel to FG. That is option A.
What is a perpendicular line?A perpendicular line is defined as the line that forms angle 90° where it meets with another line in a plane.
A line is said to be parallel to each other when they do not intercept as they are both on the same plane.
From the given diagram, line AC is perpendicular to line HB because they form angle 90° at the point of intersection.
Also, line AC is parallel to FG, because they can never intersect till infinity.
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What is 12 to the second power
Answer:
Step-by-step explanation:
12 to the second power (or 12 squared) is equal to 144.
Mathematically, it can be represented as:
12^2 = 12 x 12 = 144
Which of the following equations will reduce the graph shown below
The equation y = -1/2(x-3)² + 5 reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.
What is graph?In mathematics, a graph is a visual representation of a set of objects (called vertices or nodes) and the connections (called edges) between them.
The equation y = -1/2(x-3)² + 5 is a quadratic function in vertex form. The vertex of this parabola is at the point (3, 5), and the coefficient of the x² term is negative (-1/2), which tells us that the parabola opens downwards. This means that the graph of this equation reduces.
To see why this is the case, consider the behavior of the y-values as x moves away from the vertex. Since the leading coefficient is negative, the y-values will decrease as x moves to the left or right from the vertex. Additionally, the squared term inside the parentheses means that the graph will be symmetric around the x-coordinate of the vertex, which is 3 in this case.
Thus, as x moves away from the vertex to the left or right, the y-values decrease in a symmetric manner, resulting in a graph that reduces. This can be seen in the shape of the parabola as it curves downwards from the vertex.
Therefore, the equation y = -1/2(x-3)² + 5 reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.
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