How do you find the equation of the tangent line to the curve x2+y2=169 at the point (5,-12)?
Answers
Answer:
\(5x+12y+119=0\)
Step-by-step explanation:
\(\mathrm{The\ equation\ of\ the\ curve\ is:}\\x^2+y^2=169\\or,\ x^2+y^2=13^2\\\\\mathrm{Differentiating\ both\ sides\ with\ respect\ to\ x,}\\\frac{d(x^2+y^2)}{dx}=0\\\\\mathrm{or,} \frac{dx^2}{dx}+\frac{dy^2}{dx}=0\\\\\mathrm{or,}\ 2x+\frac{dy^2}{dy}\times \frac{dy}{dx}=0\\\\\mathrm{or,}\ 2x+2y\times \frac{dy}{dx}=0\\\\\mathrm{or,}\ \frac{dy}{dx}=-\frac{x}{y}\\\\\mathrm{This\ gives\ the\ slope\ of\ any\ line\ that\ is\ tangent\ to\ the\ curve\ at\ (x,y).}\)
\(\mathrm{Now,}\\\mathrm{Slope\ of\ tangent(m)=}-\frac{5}{-12}=-\frac{5}{12}\\\mathrm{The\ equation\ of\ a\ line\ passing\ through\ (5,-12)\ and\ having\ slope\ - \frac{5}{12}\ is:}\\y-(-12)=-\frac{5}{12}(x-5)\\\mathrm{or,}\ 12(y+12)=-5(x-5)\\\mathrm{or,}\ 12y+144=-5x+25\\\mathrm{or,\ 5x+12y+119=0\ is\ the\ required\ equation\ of\ the\ tangent.}\)
Thus, the equation of the tangent line to the curve x² + y² = 169 at the point (5,-12) is:y = (5/12)x - 169/12.
The equation of the tangent line can be found by computing the derivative of the curve and using it to find the slope of the tangent at the point (5,-12). The tangent line can then be written using the point-slope form of the equation of a line.What is a tangent line?The tangent line is a straight line that intersects a given curve at exactly one point, known as the point of tangency. This line describes the slope of the curve at that particular point. The slope of the tangent line to a curve at a specific point is equivalent to the value of the derivative of the curve at that point.The equation of the curve x² + y² = 169 is the equation of a circle with radius 13 and center at the origin. To find the equation of the tangent line at the point (5,-12), we must first find the derivative of the curve. Taking the derivative of the curve yields:2x + 2y dy/dx = 0dy/dx = -x/yWe can substitute x = 5 and y = -12 to get the slope of the tangent line at the point (5,-12):dy/dx = -5/-12 = 5/12Therefore, the slope of the tangent line is 5/12. Using the point-slope form of the equation of a line, we can write the equation of the tangent line:y - y1 = m(x - x1)where (x1,y1) is the point on the line, and m is the slope of the line. Plugging in the values we get:y + 12 = (5/12)(x - 5)Expanding, we get:y = (5/12)x - 169/12Thus, the equation of the tangent line to the curve x² + y² = 169 at the point (5,-12) is:y = (5/12)x - 169/12.
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Related Questions
what is the probability that the random variable will assume a value between 45 and 55 (to 4 decimals)?
Answers
Answer:
Step-by-step explanation:
When answering questions on Brainly, it is important to be factually accurate, professional, and friendly. One should be concise and not provide extraneous amounts of detail, while also ensuring to answer the entire question asked. It is important to use the terms and concepts relevant to the subject and question at hand in order to provide a clear and accurate answer. Furthermore, it is important to refrain from using any offensive or derogatory language or behavior, as Brainly values respect and positivity in its community. Finally, it is important to cite any sources used to support one's answer, and to avoid plagiarism by providing original and unique responses.
Now coming to your question, the given random variable lies between 45 and 55. Hence the required probability is given by:P(45 < X < 55)So, the probability that the random variable will assume a value between 45 and 55 is P(45 < X < 55) to 4 decimals.
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A type IV hip has an alpha angle of _______________ degrees and a beta angle of _______________ degrees. * 5 points Less than 60; greater than 40 Immeasurable; less than 60 Less than 43; greater than 77 Less than 43; immeasurable
Answers
A type IV hip has an alpha angle of less than 43 degrees and a beta angle that is immeasurable. The alpha angle is a measurement used to assess the shape of the femoral head-neck junction. In a type IV hip, the alpha angle is typically less than 43 degrees, indicating a relatively shallow and abnormal angle.
The beta angle, on the other hand, is used to evaluate the orientation of the acetabulum. In a type IV hip, the beta angle is often immeasurable, suggesting a severely abnormal orientation of the acetabulum. It is important to note that these angle measurements are used in the classification of developmental hip dysplasia and are indicative of specific abnormalities in hip anatomy.
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David descarga un video de 72 megabytes en 8 minutos ¿cuantos megabytes descargara en 13 minutos ?
Answers
Answer:
117 megabytes
Step-by-step explanation:
Por regla de tres:
72 mb son a 8 mins
D mb son a 13 minutos
D = 13*72/8
D = 117 mb
A line is perpendicular to y = -1/5x + 1 and intersects the point negative (-5,1) what is the equation of this perpendicular line?
Answers
Answer: y = 5x + 26
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.
We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 1 = 5(x - (-5))
Simplifying further:
y - 1 = 5(x + 5)
Expanding the brackets:
y - 1 = 5x + 25
Rearranging the equation to the slope-intercept form (y = mx + b):
y = 5x + 26
Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.
If the following figure was reflected across the x-axis, what would be the coordinates of D'?
Answers
Answer: 5, -4
Step-by-step explanation:
imagine a mirror on the x axis and just make it look symmetrical and that will help you. Its also the complete opposite of the point
Please help me graph
Y=1.5x
Will mark brainliest!!
Answers
1. The product of 6, and a number increased by 2, is -24. What is the number?
Answers
Answer:
Step-by-step explanation: 6* (N + 6) = -24
6*n + 6*6=-24
6n+36=-24
-36 -24
6n=-60
n=-10
Please help me with my math
Answers
+ 12 +12
3z = 75
z = 25
x + 63 = 180
- 63 - 63
x = 117°
Given m||n, Find the value of x. Need help.
Answers
9514 1404 393
Answer:
x = 12
Step-by-step explanation:
The two marked angles are a linear pair, so are supplementary.
(8x -20)° +(8x +8)° = 180°
16x -12 = 180 . . . . . . . . . . . divide by °, collect terms
16x = 192 . . . . . . . . . . . add 12
x = 12 . . . . . . . . . . . divide by 16
Help please I need to find x and y
Answers
Answer:
\(x=6\\y=12\)
Step-by-step explanation:
To find the value of x you can use sin rule
\(sin(60)=\frac{oppoaite}{hypotenuse}\\\frac{\sqrt{3} }{2} =\frac{x}{4\sqrt{3} } \\\)
Use cross multiplication
\(4*\sqrt{3} *\sqrt{3} =2x\\4*3=2x\\12=2x\\\frac{12}{2} =\frac{2x}{2} \\6 =x\)
To find the value of y you have to use sin rule again
\(sin(30)=\frac{opposite}{hypotenuse}\\\frac{1}{2} =\frac{x}{y} \\\frac{1}{2} =\frac{6}{y} \\\)
Use cross multiplication
\(y=6*2\\y=12\)
Hope this helps you.
Let me know if you have any other questions :-)
x = 5.9 units (just round it to 6)
y= 11.8 units (round it to 12)
Steps:
1) Use Soh Cah Toa to identify the unknown sides.
The side across the angle is the opposite. Therefore, the x side is opposite.
4√5 = 6.9 ( this side is the hypotenuse).
So we have the opposite side and the hypotenuse side. Therefore, we will use sine
2) Sin theta = opp/hyp
Sin 60 = opp/6.9
Multiply both sides by 6.9
6.9(sin60) = opp
5.9 = opp
3) now that you have side x, we will use x to figure out side y.
Identify the sides first. Side x is opposite and side y is the hypotenuse. Use sine to solve for side y
Sin theta = opp/hyp
Sin 30 = 5.9/hyp
0.5 = 5.9/hyp
Divide 0.5 and bring it over to the other side.
= 5.9/ hyp ÷ 0.5/1
= 5.9/hyp x 1/0.5
= 5.9/0.5
= 11.8 units (side Y)
A pair of shoes was originally priced at $100. The store owner gives a discount, and the shoes are now priced at $60.
Enter the percent discount for the pair of shoes.
Answers
Answer:
The discount is $40
Step-by-step explanation:
To find the discount you'll need to subtract the new price from the old one.
100 - 60 = 40
Answer:
60%
Step-by-step explanation:
60/100 x/100
60 * 100 = 6000
6000/100 = 60
= 60%
e table shows the weights of several great white sharks. use the data to answer the statistical question, "whatis the weightof a great white shark?
Answers
The table provided shows the weights of several great white sharks, but we cannot determine what the exact weight of a great white shark is simply by looking at the data. However, we can use the data to make some observations and inferences.
Firstly, we can see that the weights of the sharks in the table range from 500 pounds to 2500 pounds. This tells us that great white sharks can vary greatly in weight and there is no one definitive answer to the question of what the weight of a great white shark is.
Secondly, we can look at measures of central tendency such as the mean or median weight of the sharks in the table. If we calculate the mean weight of the sharks in the table, we get approximately 1367 pounds. This means that if we were to randomly select a great white shark from the group represented in the table, it is likely that its weight would be around 1367 pounds. However, it's important to note that this only applies to the sharks represented in the table and not necessarily to all great white sharks in general.
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evaluate the expression m=10 2m+10
Answers
because (2)(10) + 10
20+10=30
the 10 came from the m!!
is the product of two rational numbers always a rational number?
Answers
Answer:
Yes, it's always rational.
Step-by-step explanation:
Line e has a slope of -7/3. Line f is parallel to line e. What is the slope of line f?
Answers
Answer:
-7/3
Step-by-step explanation:
Parallel lines have same slopes.
what is the mean mark in5,8,4,3,7,6,2,9 and 1
Answers
Answer:
Mean= 5+8+4+3+7+6+2+9+1÷9
=5
Step-by-step explanation: The mean is 5
9,000x0.34
Plss help me
Answers
Answer:
3060
Step-by-step explanation:
Answer:
3,060
Step-by-step explanation:
9000 x 0.34 = 9000 x 34/100
9000 x 34/100 = 306000/100
306000/100 and 100/100 = 3060
Whats the answer y’all
Answers
The expressions that will give you a difference of 5 are: -3 - (-8) and 1 - (-4).
What is the Difference of Two Expressions?The difference of two expressions is determined by subtracting one from the other.
Find the difference of each of the expressions given to determine which will give us 5.
-3 - (-8)
= -3 + 8
= 5
-2 - 3 = -5 [this is not the same as 5]
1 - (-4)
= 1 + 4
= 5
7 - (-2)
= 7 + 2
= 9
-3 - (-8) and 1 - (-4) will give us a difference of 5.
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The probability Peanuts will score above 89% on his probability theory homeworks is 0.50. Peanuts will complete twelve homeworks this semester.
(a). What is the probability of Peanuts scores above 89% on exactly six out of the twelve homeworks? (Round your answer to 4 decimal spots
(b). What is the probability of Peanuts will score above 89% on at least 3 out of the twelve homeworks?
Answers
the probability of Peanuts scoring above 89% on at least 3 out of the twelve homeworks is approximately 0.9814
(a) To calculate the probability of Peanuts scoring above 89% on exactly six out of the twelve homeworks, we can use the binomial probability formula.
The formula for the probability of exactly k successes in n independent Bernoulli trials with probability p of success is:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of exactly k successes,
C(n, k) is the number of combinations of n items taken k at a time,
p is the probability of success on a single trial, and
n is the total number of trials.
In this case:
p = 0.50 (probability of scoring above 89%)
n = 12 (total number of homeworks)
k = 6 (number of homeworks Peanuts scores above 89%)
Using the formula, we can calculate the probability:
P(X = 6) = C(12, 6) * (0.50)^6 * (1-0.50)^(12-6)
Using a calculator or software, we can find:
C(12, 6) = 924
Plugging in the values:
P(X = 6) = 924 * (0.50)^6 * (0.50)^6
P(X = 6) = 924 * (0.50)^12
P(X = 6) ≈ 0.0059
Therefore, the probability of Peanuts scoring above 89% on exactly six out of the twelve homeworks is approximately 0.0059.
(b) To calculate the probability of Peanuts scoring above 89% on at least 3 out of the twelve homeworks, we need to find the sum of probabilities for scoring above 89% on 3, 4, 5, ..., 12 homeworks.
P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) + ... + P(X = 12)
Using the binomial probability formula, we can calculate each individual probability and sum them up.
P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) + ... + P(X = 12)
= [C(12, 3) * (0.50)^3 * (1-0.50)^(12-3)] + [C(12, 4) * (0.50)^4 * (1-0.50)^(12-4)] + ... + [C(12, 12) * (0.50)^12 * (1-0.50)^(12-12)]
Using a calculator or software, we can calculate the probabilities and sum them up.
P(X ≥ 3) ≈ 0.9814
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Evaluate. Answer has to be in scientific notation
(8 x 10^6) + (7.3 x 10^4)
Answers
Answer:
8.0730000*10^6
Answer:
8,073,000
=8.1 × 10⁶
Step-by-step explanation:
The answer is above
PLEASE HELP ME
PLEASE HELP ME
Find the lateral surface area of
the following square pyramid:
4 cm
6 cm
LA = [?] cm2
Answers
Length of base (a)=6cm
Slant height (l)=4 cm
Now,
LSA=2al
= 2*6*4
=48cm^2
Answer:
Surrounding area of pyramid = area of a side face multiplied by 4
Step-by-step explanation:
The area of a side face is the area of the triangle:
\(\frac{1}{2} *6*4\) = 12
So the perimeter of the pyramid is:
12×4=48
Explanation: because the side faces have the same area.
Simplify the algebraic expression by combining like (or similar) terms.6x + 5x2 + 2 - 6x2
Answers
Answer: \(-x^{2} +6x+2\)
Please help!! I will give brainliest.
Answers
Answer:
7.) 0.7
8.) 1
9.) 4.24
Step-by-step explanation:
Answer:
4.24
Step-by-step explanation:
Write the equation that expresses the table below.
Answers
Answer:
10x=y
Step-by-step explanation:
Divide your outputs by your inputs. In other words, divide 20 by 2, 50 by 5, and 70 by 7. These all equal 10. Therefore, 10 times x will equal y.
can one of you unhelpful users answer the question without putting links as a d a m n answer?
1. A line goes through the points (1, 6) and (–2, 8). Write the equation of the line in Point-Slope form. Show your work algebraically for full credit.
2. A line goes through the points (1, 6) and (–2, 8). Write the equation of the line in Slope-intercept form. Show your work algebraically for full credit. Hint: this is the same line as in #1.
Answers
Answer:
1) \(y-6=-\frac{2}{3} (x-1)\) and 2) \(y=-\frac{2}{3} x+\frac{20}{3}\)
Step-by-step explanation:
Ikr the bots are annoying.
Point-slope form is written as: \(y-y_1=m(x-x_1)\)
Slope intercept form is written as: \(y=mx+b\)
We also need to find the slope before putting it in this form, which can be done by \(m=\frac{y_2-y_1}{x_2-x_1}\)
1) Points given are (1,6) and (-2,8)
Slope: \(m=\frac{8-6}{-2-1} =-\frac{2}{3}\)
You can choose either of the two points to put into the formula. I just chose (1,6)
Answer: \(y-6=-\frac{2}{3} (x-1)\)
2) Same points as before and we have the same slope as before. All we need is to find the y intercept which is our b in the equation. You can easily do this by plugging in a point and solving for b. I will choose point (1,6) again.
\(6=-\frac{2}{3} (1)+b\)
\(6=-\frac{2}{3} +b\)
\(6+\frac{2}{3}=-\frac{2}{3} +\frac{2}{3} +b\)
\(b=6+\frac{2}{3}=\frac{20}{3}\)
Answer: \(y=-\frac{2}{3} x+\frac{20}{3}\)
help me out please explain too please :((
Answers
Answer:
bro I can’t do it TvT
HELP ME OLEASE
The number of integers between 1 and 2022 inclusive that are multiples of 11 but not multiples of 3 is
Answers
The number of integers between 1 and 2022 inclusive that are multiples of 11 but not multiples of 3, using arithmetic sequences, is of:
122.
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the rule presented as follows:
\(a_n = a_1 + (n - 1)d\)
In which \(a_1\) is the first term of the arithmetic sequence.
The sequence composed by the integer multiples of 11 between 1 and 2022 are given as follows:
(11, 22, ..., 2013)
The first term and the common ratio of the sequence are given as follows:
\(a_1 = 11, d = 11\)
The number of terms is obtained as follows:
2013 = 11 + 11(n - 1)
11n = 2013
n = 2013/11
n = 183.
The sequence composed by terms that are multiples of 11 and of 3 is given by:
(33, 66, ..., 2013).
The first term and the common ratio of the sequence are given as follows:
\(a_1 = 33, d = 33\)
The number of terms is obtained as follows:
2013 = 33 + 33(n - 1)
33n = 2013
n = 2013/33
n = 61.
Hence the number of integers that are multiples of 11 but not 3 is given by:
183 - 61 = 122.
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Two sides of a triangle measure 13 meters and 19 meters. If the perimeter of the triangle is 41 meters, what is the length of the third side?
9 m
73 m
32 m
33 m
Answers
The lengths of the sides satisfy the triangle inequality theorem, and the length of the third side is indeed 9 meters.
Explanation:
Let the length of the third side be x. According to the problem, we have two sides of the triangle measuring 13 meters and 19 meters, respectively, and the perimeter of the triangle is 41 meters. The perimeter of a triangle is the sum of its three sides, so we can write an equation:
13 + 19 + x = 41
Simplifying this equation gives us:
x = 41 - 13 - 19 = 9
Therefore, the length of the third side of the triangle is 9 meters. We can verify that this is indeed a valid length for the third side of the triangle, since it satisfies the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we have:
13 + 9 = 22 > 19
19 + 9 = 28 > 13
So, the lengths of the sides satisfy the triangle inequality theorem, and the length of the third side is indeed 9 meters.
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Jim builds a robot that travels no more than 10 feet per minute. Graph the inequality showing the relationship between the distance traveled and the time elapsed.
Is it possible for the robot to travel 27 feet in 3 minutes?
Answers
Answer:
no robot can travel 27 feet in 3 minutes
Step-by-step explanation:
which function has the largest rate of change?
O Y = 2
X
1
6
3
12
5
18
y
15
y=
0
1
2.5
WN
3
1.5
y
3
Answers
Answer:
The second one.
Step-by-step explanation:
For first function y = 2x the rate of change = 2.
Second function: rate of change = (12-6)/(3-1) = 6/2 = 3
Third: it's -0.2.
Fourth: it's (2.5 -3)/ 1= -0.5.