Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. Are the given families of curves orthogonal trajectories of each other? that is, is every curve in one family orthogonal to every curve in the other family?.
Answers
The given families of curves are orthogonal trajectories of each other if every curve in one family is orthogonal to every curve in the other family. To determine if this is the case, we need to check if the tangent lines of the curves in one family are perpendicular to the tangent lines of the curves in the other family at each point of intersection.
Here's a step-by-step explanation to help you understand:
1. Start with the first family of curves. Take a curve from this family and find its tangent line at any given point of intersection with a curve from the second family.
2. Similarly, take a curve from the second family and find its tangent line at the same point of intersection with the curve from the first family.
3. If the tangent lines are perpendicular at every point of intersection, then the families of curves are orthogonal trajectories of each other.
4. Conversely, if the tangent lines are not perpendicular at any point of intersection, then the families of curves are not orthogonal trajectories of each other.
To summarize, for the given families of curves to be orthogonal trajectories of each other, the tangent lines of the curves in one family must be perpendicular to the tangent lines of the curves in the other family at every point of intersection.
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Related Questions
A scientist selected a random sample of seven varieties of peach ice cream to investigate the relationship between the density, in pounds per cubic inch, of the varieties of ice cream and the percent concentration of peaches in the ice cream. Assuming all conditions for inference are met, which of the following significance tests should be used to investigate whether there is convincing evidence at the 0.05 level of significance that a greater percent of peaches in the ice cream is associated with an increase in the density of the ice cream?NOTA chi-square test of independenceNOTA two-sample t-test for a difference between meansNOTA two-sample z-test for a difference between proportions
Answers
Answer: Two-sample t-test for a difference between means is used nvestigate whether there is convincing evidence at the 0.05 level of significance that a greater percent of peaches in the ice cream is associated with an increase in the density of the ice cream
Step-by-step explanation:
When a scientist selected a random sample of seven varieties of peach ice cream to investigate the relationship between the density, in pounds per cubic inch, of the varieties of ice cream and the percent concentration of peaches in the ice cream, the following significance test should be used to investigate whether there is convincing evidence at the 0.05 level of significance that a greater percent of peaches in the ice cream is associated with an increase in the density of the ice cream: two-sample t-test for a difference between means.
What is a t-test?
A t-test is a statistical test that compares two groups of data to determine whether there is a significant difference between the two. The t-test determines the degree of difference between the two groups relative to the variation in the data.
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Please help i really need to do this :D
Answers
Answer:
\(17\)
Step-by-step explanation:
Since h=17 we use that
\(h(t) = \sqrt{17t} \)
\(h(t) = \sqrt{289} = 17\)
The circumference of a circle is 98.596 millimeters. What is the radius of the circle? Use 3.14 for π.
197.2 mm
49.3 mm
31.4 mm
15.7 mm
Answers
Answer: D) 15.7
Step-by-step explanation:
Start with the formula C=2 πr
Then solve for r r=C2π = 98.62·π = 15.69(7)204
The radius of the circle is 15.7 mm.
What is Circumference?The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.
We have,
The circumference of Circle = 2πr
Also, The circumference of a circle is 98.596 millimeters.
So, circumference of Circle = 2πr
98.596 = 2πr
98.596 = 6.28r
r= 98. 596 / 6.28
r = 15.7 mm
Thus, the radius is 15.7 mm.
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it is estimated that 52% of drivers text while driving. how many people should a police officer expect to pull over until she finds a driver not texting while driving? 1 2 3 4 5
Answers
the police officer should expect to pull over approximately 4 drivers until she finds a driver who is not texting while driving.
What is Probability?
Probability refers to the measure of the likelihood or chance of an event occurring. It quantifies the uncertainty associated with an event or outcome and is expressed as a value between 0 and 1. A probability of 0 indicates an impossible event, while a probability of 1 represents a certain event.
To find the number of people a police officer should expect to pull over until she finds a driver not texting while driving, we can use the concept of probabilities.
The probability of a driver not texting while driving is given by (100% - 52%) = 48%.
Now, let's calculate the probability of encountering a driver who is texting while driving for different numbers of drivers pulled over:
For the first driver pulled over, the probability of encountering a driver who is texting while driving is 52% or 0.52.
For the second driver pulled over, the probability of both the first and second drivers texting while driving is 0.52 * 0.52 = 0.2704, and the probability of the second driver not texting while driving is (1 - 0.52) = 0.48.
For the third driver pulled over, the probability of all three drivers texting while driving is 0.52 * 0.52 * 0.52 = 0.140608, and the probability of the third driver not texting while driving is (1 - 0.52) = 0.48.
Continuing this pattern, we can calculate the probabilities for the fourth and fifth drivers.
Therefore, the police officer should expect to pull over approximately 4 drivers until she finds a driver who is not texting while driving.
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Complete Qustion:
It is estimated that 52% of drivers text while driving. How many people should a police officer expect to pull over until she finds a driver not texting while driving? Consider each driver independently.
is (x + 1) a factor of x² + x³ + x + 1
Explanation please
Answers
Using synthetic division, we can write:
-1 | 1 1 0 1
| -1 0 -0
| ___________
| 1 0 0 1
Since the remainder is not zero, we can conclude that (x + 1) is not a factor of x² + x³ + x + 1.
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The data value that occurs most often in the data set is the ____________.
A. mean
B. median
C. mode
D. range
Answers
EXPLANATION:
In order to understand which one of these mean the data value the occurs the most, you need to know the definition for these basic math terms.
Mean= Average of All Numbers Given
Median= Middle Number (From Least to Greatest)
Mode= Number That Occurs the Most
Range= The Subtraction of the Smallest Number to the Biggest Number
Re-write the quadratic function below in Standard Form
y= 9(x - 1)(x + 7)
Answers
The value of quadratic function is,
⇒ y = 9x² + 54x - 63
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The equation is,
⇒ y = 9 (x - 1) (x + 7)
Now, We can find the quadratic equation as;
⇒ y = 9 (x - 1) (x + 7)
⇒ y = 9 (x² + 7x - x - 7)
⇒ y = 9 (x² + 6x - 7)
⇒ y = 9x² + 54x - 63
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4w<32
Help about to fail my math class lol
Answers
Explanation~ IN TESSA WE TRUST
1 meter of ribbon costs $3
how much do you pay for 2 3/4
If correct I will brainest u
Answers
Answer:
You pay $8 \(\frac{1}{4}\) for 2 \(\frac{3}{4}\) meters of ribbon
Step-by-step explanation:
Let us solve the question
∵ 1 meter of ribbon costs $3
∵ We need to find the cost of 2 \(\frac{3}{4}\) meters
→ Separate the length of the ribbon to a whole number and a fraction
∵ The length of the ribbon = 2 m + \(\frac{3}{4}\) m
→ Multiply each part by the cost of 1 meter
∵ The cost of 1 meter = 3 dollars
∴ The cost of the ribbon = 3 × 2 + 3 × \(\frac{3}{4}\)
∴ The cost of the ribbon = 6 + \(\frac{9}{4}\) dollars
→ Change the improper fraction \(\frac{9}{4}\) to a mixed number
∵ 9 ÷ 4 = 2 \(\frac{1}{4}\)
∴ The cost of the ribbon = 6 + 2 + \(\frac{1}{4}\)
∴ The cost of the ribbon = 8 + \(\frac{1}{4}\)
∴ The cost of the ribbon = 8 \(\frac{1}{4}\) dollars
∴ You pay $8 \(\frac{1}{4}\) for 2 \(\frac{3}{4}\) meters of ribbon
What is the truth value of the following statement? square root of 25 >- 5 or 3 grater than or equal to 3.
Answers
Answer:
the Square root of 25 = 5
Step-by-step explanation:
It's greater than -5 and greater than 3 by two.
Hopefully this helps.
Simplify each expression.
ab
Q=0,b=0
-222
4
0
55
6
6
57
00
8
Q
10
1
8 2.10
Answers
Step-by-step explanation:
remember that x^-n means 1/(x^n).
x^a × x^b = x^(a+b)
x^a / x^b = x^(a-b)
(x^a)^b = x^(a×b)
(x×y)^n = x^n × y^n
so,
a^2 / a^-2 = a^(2 - -2) = a^4
and
b^-3 / b^2 = b^(-3 - 2) = b^-5 = 1/(b^5)
that means we have then :
(a^4 × b^-5)^2 = (a^4)^2 × (b^-5)^2 = a^8 × b^-10 =
= a^8 / b^10 = a⁸/b¹⁰
Anyone know this?? I’m confused..
Answers
Answer:
jgh
side side side axioms
not sure
Answer:
\(\triangle CAB\cong \triangle ONP\)
Step-by-step explanation:
Triangles \(\triangle CAB\) and \(\triangle ONP\) share two corresponding angles and the inclusive side between them. This is known as ASA (angle-side-angle) and does prove congruence. Therefore, \(\triangle CAB\cong \triangle ONP\).
The four proofs of congruence include SSS (side-side-side), SAS(side-angle-side), ASA (angle-side-angle) and AAS (angle-angle-side). No other pair of triangles demonstrate any of these.
Determine all values of h and f for which the system x + 3y = h and -4x + ky = -9 has no solution.
Answers
For any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.
To determine the values of h and okay for which the device of equations has no answer, we want to locate the situations underneath which the equations are inconsistent or parallel.
The given system of equations is:
Equation 1: x + 3y = h
Equation 2: -4x + ky = -9
For the gadget to haven't any answer, the lines represented with the aid of these equations should be parallel and in no way intersect. In different phrases, the slopes of the traces need to be equal, but the y-intercepts should be specific.
Let's first discover the slopes of the traces. The slope-intercept form of Equation 1 is y = (-1/3)x + (h/3), wherein the slope is -1/3. The slope-intercept shape of Equation 2 is y = (4/k)x - (9/k), wherein the slope is 4/k.
For the strains to be parallel, the slopes should be equal. Therefore, we have the condition: -1/3 = 4/k.
To locate the values of h and okay for which the gadget has no answer, we need to locate the values of h that satisfy the situation -1/3 = 4/k.
Solving this equation for ok, we've got:
-1/3 = 4/k
-1 = 12/k
k = -12
Substituting k = -12 returned into the equation -1/3 = 4/k, we've:
-1/3 = 4/(-12)
-1/3 = -1/3
Since the equation holds real for any value of h, there aren't any restrictions at the price of h.
Therefore, for any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.
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The system of equations has no solution when k is equal to 12. The value of h can be any real number.
To determine the values of h and f for which the system has no solution, we need to analyze the coefficients of the variables and the constants in the equations.
The given system of equations is:
x + 3y = h
-4x + ky = -9
We can rewrite the second equation as:
-4x + ky = -9
Dividing both sides of the equation by -4, we get:
x - (k/4)y = 9/4
Comparing the coefficients of x and y in the two equations, we can see that the slopes of the lines represented by the equations are different when k is not equal to 12.
Therefore, for the system to have no solution, k must be equal to 12.
As for the value of h, it can be any real number since it does not affect the slopes of the lines.
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Which of the following is not a property of quadrilaterals?
A.
There are four sides.
B.
There are four diagonals.
C.
There are four vertices.
D.
The measures of the interior angles add up to 360 degrees
Please select the best answer from the choices provided
Answers
Answer:
The correct answer for this question is letter "(B) There are four diagonals." It is not a property of quadrilaterals.
Answer:
b
it has 2 diagonals crossing each other
Suppose you are titrating a sulfuric acid solution of unknown concentration with a sodium hydroxide solution according to the equation
H2SO4+2NaOH⟶2H2O+Na2SO4HX2SOX4+2NaOH⟶2HX2O+NaX2SOX4
If you require 25.95 mL of 0.657 M NaOHNaOH solution to titrate 215.7 mL of H2SO4HX2SOX4 solution, what is the concentration of the H2SO4HX2SOX4 solution?
Answers
The concentration of the H2SO4 solution is 0.0395 M.
To find the concentration of the H2SO4 solution, we can use the balanced equation and the concept of stoichiometry. From the equation, we can see that 1 mole of H2SO4 reacts with 2 moles of NaOH.
First, find the moles of NaOH used in the titration:
moles of NaOH = volume of NaOH (L) × concentration of NaOH (M)
moles of NaOH = 0.02595 L × 0.657 M = 0.01704 moles
Now, using the stoichiometry of the balanced equation, we can find the moles of H2SO4:
moles of H2SO4 = moles of NaOH ÷ 2 = 0.01704 moles ÷ 2 = 0.00852 moles
Next, find the concentration of the H2SO4 solution:
concentration of H2SO4 (M) = moles of H2SO4 ÷ volume of H2SO4 (L)
concentration of H2SO4 (M) = 0.00852 moles ÷ 0.2157 L = 0.0395 M
So, the concentration of the H2SO4 solution is 0.0395 M.
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how much 44 f to c ?
Answers
44 °F was found out to be equivalent to approximately 6.67 °C using conversion formula of Fahrenheit to Celsius.
To convert a temperature from Fahrenheit to Celsius, you can use the following formula:
°C = (°F - 32) x 5/9
where °C is the temperature in Celsius, and °F is the temperature in Fahrenheit.
Using this formula, we can convert 44 °F to Celsius as follows:
°C = (44 - 32) x 5/9
= 12 x 5/9
= 6.67 °C (rounded to two decimal places)
Therefore, 44 °F is equivalent to approximately 6.67 °C.
On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.
On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.
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What is the largest number of three consecutive integers whose sum is 42? O A. 13 B. 17 O C. 15 D. 12
Answers
Answer: 13
Step-by-step explanation:
3X + 3 - 3 = 42 - 3
3X = 39
3X/3 = 39/3
X = 13
Which means that the first number is 13, the second number is 13 + 1 and the third number is 13 + 2. Therefore, three consecutive integers that add up to 42 are 13, 14, and 15.
13 + 14 + 15 = 42
We know our answer is correct because 13 + 14 + 15 equals 42 as displayed above.
3. There are 5,280 feet in a mile. Round answers to the nearest unit.
a. How many miles does a car traveling at 42 mi/h go in one hour?
b. How many feet does a car traveling at 42 mi/h go in one hour?
c. How many feet does a car traveling at 42 mi/h go in one minute?
d. How many feet does a car traveling at 42 mi/h go in one second?
e. How many miles does a car traveling at x mi/h go in one hour?
f. How many feet does a car traveling at x mi/h go in one hour?
g. How many feet does a car traveling at x mi/h go in one
minute?
h. How many feet does a car traveling at x mi/h go in one
second?
Answers
Answer:
a. How many miles does a car traveling at 42 mi/h go in one hour?
42 miles in one hour
b. How many feet does a car traveling at 42 mi/h go in one hour?
221,760 feet
c. How many feet does a car traveling at 42 mi/h go in one minute?
3696 ft
d. How many feet does a car traveling at 42 mi/h go in one second?
62 ft
e. How many miles does a car traveling at x mi/h go in one hour?
goes x miles in one hour
f. How many feet does a car traveling at x mi/h go in one hour?
5280 x feet
g. How many feet does a car traveling at x mi/h go in one
minute?
88 x ft
h. How many feet does a car traveling at x mi/h go in one
second?
0.024x ft
________________________________
All answers are in BOLD
which value for s will make this equation true
s(11-s)=24
Answers
Answer:
It is 3 or 8
Step-by-step explanation:
Reduce to simplest form.
12/11 - (-2/3)
Answers
Answer:
58/33
Step-by-step explanation:
hope i could help yk
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!!
Answers
Answer:
D
Step-by-step explanation:
A is not true because from the graph, they make less money at $13 compared to $10 even though 13 > 10. B isn't true either because when the app price is more than $7 the profit decreases, not increases. D is true because the y-coordinate of the vertex (which is the maximum in this case) is about 40 million, and if we know the maximum already we know that C is false because 40 ≠ 7.
a You have a bet where you win $50 with a probability of 40% and lose $50 with a probability of 60%. What is the standard deviation of the outcome (to the nearest dollar)? O 55 O 51 O 49 053
Answers
The standard deviation of the outcome for the given bet is approximately $51.
To obtain this result, we can use the following formula for the standard deviation of a random variable with two possible outcomes (winning or losing in this case):SD = √(p(1-p)w² + p(1-p)l²),where SD is the standard deviation, p is the probability of winning (0.4 in this case), w is the amount won ($50 in this case), and l is the amount lost ($50 in this case).
Plugging in the values, we get:SD = √(0.4(1-0.4)(50²) + 0.6(1-0.6)(-50²))≈ $51
Therefore, the standard deviation of the outcome of the given bet is approximately $51.Explanation:In statistics, the standard deviation is a measure of how spread out the values in a data set are.
A higher standard deviation indicates that the values are more spread out, while a lower standard deviation indicates that the values are more clustered together.
In the context of this problem, we are asked to find the standard deviation of the outcome of a bet. The outcome can either be a win of $50 with a probability of 40% or a loss of $50 with a probability of 60%.
To find the standard deviation of this random variable, we can use the formula:SD = √(p(1-p)w² + p(1-p)l²),where SD is the standard deviation, p is the probability of winning, w is the amount won, and l is the amount lost.
Plugging in the values, we get:SD = √(0.4(1-0.4)(50²) + 0.6(1-0.6)(-50²))≈ $51Therefore, the standard deviation of the outcome of the given bet is approximately $51.
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What is an equation of the line that passes through the points (-7, -6) and (-1, 0)?
Answers
Answer:
Y = x + 1
Step-by-step explanation:
m = y2-y1 / x2-x1
Hope this helps. Pls give brainliest.
an old modem can take anywhere from 0 to 30 seconds to establish a connection, with all times between 0 and 30 being equally likely. a. what is the probability that if you use this modem you will have to wait more than 15 seconds to connect? b. given that you have already waited 10 seconds, what is the probability of having to wait at least 10 more seconds?
Answers
The probability to wait more than 15 seconds to connect is 50% and the probability to wait at least 10 more seconds after waiting 10 seconds is 33.33%.
How to calculate the probability?x = old modem establish connection = [0, 30]
Probability density function or PDF is
f(x) = \(\frac{1}{b-a}\); 0 ≤ x ≤ 30
Probability to wait more than 15 seconds to connect is
f(X>5) = \(\int\limits^{30}_{15} {f(x)} \, dx\)
= \(\int\limits^{30}_{15} {\frac{1}{b-a}} \, dx\)
= \(\frac{1}{30-0} \, [x]^{30}_{15}\)
= \(\frac{30-15}{30}\)
= 0.5 or 50%
Probability if already waited 10 seconds and having to wait at least 10 more seconds is equal to wait at least 20 seconds from start. So,
f(X>5) = \(\int\limits^{30}_{20} {f(x)} \, dx\)
= \(\int\limits^{30}_{20} {\frac{1}{b-a}} \, dx\)
= \(\frac{1}{30-0} \, [x]^{30}_{20}\)
= \(\frac{30-20}{30}\)
= 0.3333 or 33.33%
Thus, the 50% probability to wait more than 15 seconds to connect and 33.33% probability to wait at least 20 seconds to connect.
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What is the equation of the line that passes through the point (-5, 4) and has a
slope of – 3 over 5
Answers
Answer:
y=-3/5(x+5)+4
Step-by-step explanation:
y=m(x-h)+k
y=-3/5(x+5)+4
Is square root of 36 plus 3 a rational or irrational number?
Your answer:
Rational because the square root of 36 is a whole number, and all whole numbers are rational
Rational because the square root of 36 equals 6, 6+3=9, and 9 is a terminating decimal
Irrational because there is a square root symbol in the expression
Irrational because adding a whole number with a square root is impossible
Answers
Answer:
The answer is D
Step-by-step explanation:
D
When a graph is symmetric about the origin, it is an function.
When a graph is symmetric about the y-axis, it is an function.
A function is considered if f(-x) =
f(x), and it is considered
=
if f(-x) = -f(x).
Answers
Answer:
odd; even; even; odd
Step-by-step explanation:
The answers are odd, even, even, and odd respectively the graph is symmetric about the y axis it is an even function.
What is a function?It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We know when the graph is symmetric about the origin it is an off function.
When the graph is symmetric about the y axis it is an even function.
When f(-x) = f(x) it is an even function
When f(-x) = -f(x) it is an odd function.
Thus, the answers are odd, even, even, and odd respectively the graph is symmetric about the y axis it is an even function.
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A box of chocolates contains 18 chocolate squares. 10 of the squares are milk chocolate five or dark chocolate and three or white chocolate. If Christina randomly chooses a chocolate out of the box what is the probability of her choosing a white chocolate square
Answers
Answer: 55% she chooses a white chocolate
Step-by-step explanation: Just do the total number of squares which is 18, and divide that into the number of squares of the chocolate your trying to find the % or probability of.
10/18=.55 or 55%
multiplying polynomials is done by applying the ___ property when necessary.
Answers
Answer: Distributive property
Step-by-step explanation:
10. A manufacturer makes conical funnels for
professional painters. The funnels are
formed from plastic with a 9-inch
diameter base and a height of 9 inches.
After the cones cool, a machine cuts off
1 inch of the tip to leave a 1-inch
diameter hole in the end. What is the
volume of the funnel? Show your work.
Answers
Answer:
The volume of the cone after the tip is cut off equals 150 cubic inches
Step-by-step explanation:
The dimensions of the cone formed from the funnel are given as height equals 9 inches and, radius equals 4 inches (radius = 8/2).
The volume of a cone is determined as follows;
Volume = πr²h/3
Volume = π x 4² x (9/3)
Volume = π x 16 x 3
Volume = 48π
When a portion of the cone is cut off from the tip, the height from the cut off part is 1 inch and the radius is 0.5 inch (radius = 1/2).
The volume of the cut off portion can now be calculated as;
Volume = πr²h/3
Volume = π x 0.5² x (3/3)
Volume = π x 0.25 x 1
Volume = 0.25π
Hence the volume of the cone after the tip has been cut off is now derived as follows;
Volume = 48π - 0.25π
Volume = 47.75π
Volume = 47.75 x 3.14
Volume = 149.935
Volume ≈ 150 cubic inches (Rounded to the nearest whole number)
I hope this helps :)