find the equation of the tangent line to the curve defined by the equations x=t 1/t, y=t−1/t when t=1.
Answers
It means the tangent line is vertical and its equation is x=1.
To find the equation of the tangent line, we need to find the slope of the curve at t=1 and the point on the curve where t=1.
First, we find the derivative of y with respect to x:
dy/dx = (dy/dt)/(dx/dt) = (-1/t^2)/(1-1/t^2) = -t^2/(t^2-1)^2
Next, we find the y-coordinate when t=1:
y = t-1/t = 1-1/1 = 0
So, the point on the curve where t=1 is (1, 0).
Now we can find the slope of the tangent line by plugging in t=1:
dy/dx | t=1 = -1/0 = undefined
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Related Questions
Find the area of the triangle.
12 ft 13 ft
The area of the triangle is
ft2.
Answers
Answer:
156 ft
Step-by-step explanation:
area formula is:
length x width
(A= l*w)
12 x 13 = 156
if the population of 100 bacteria doubles every 15 min., how long will it take for population to reach 12,800 ?
Answers
Assuming that the bacteria population doubles every 15 minutes, it will take around 70.6 minutes for the population to increase from 100 to 12,800.
If the population of bacteria doubles every 15 minutes, it means that the growth rate is exponential. The initial population is 100, and we want to find the time it takes for the population to reach 12,800.
To solve this problem, we can use the exponential growth formula:
N(t) = N0 * 2⁽ᵗ/ᵀ⁾
where:
N0 = initial population (100 bacteria)
N(t) = population at time t
t = time elapsed
T = time it takes for the population to double (15 minutes)
We want to find the time it takes for the population to reach 12,800 bacteria, so we can set N(t) to 12,800:
12,800 = 100 * 2⁽ᵗ/¹⁵⁾
Dividing both sides by 100:
128 = 2⁽ᵗ/¹⁵⁾
Taking the logarithm (base 2) of both sides:
log2(128) = t/15
t = 15 * log2(128)
Using a calculator, we can solve for t:
t ≈ 70.6 minutes
Therefore, it will take approximately 70.6 minutes for the population of bacteria to reach 12,800, if the population doubles every 15 minutes.
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* Suzy Kicks a ball into the air. The
function that models this Scenario is
h(t) = -16+² +48t, where h is the height
of the marble in feet and t is the time
Seconds. How long will it take the
marble to hit the ground.
Answers
Answer:
by the -16 did you mean to put a + sign or is that a t
Quadratic
3p^2−7p−1=0
Answers
Answer:
\(x=\frac{7\pm\sqrt{61} }{6}\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: \(x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\)Step-by-step explanation:
Step 1: Define
3p² - 7p - 1 = 0
Step 2: Identify Variables
a = 3
b = -7
c = -1
Step 3: Find roots
Substitute [Quad Formula]: \(x=\frac{7\pm\sqrt{(-7)^2-4(3)(-1)} }{2(3)}\)Evaluate Exponents: \(x=\frac{7\pm\sqrt{49-4(3)(-1)} }{2(3)}\)Multiply: \(x=\frac{7\pm\sqrt{49+12} }{6}\)Add: \(x=\frac{7\pm\sqrt{61} }{6}\)Answer:
x = 7 + √61 ÷ 6
Step-by-step explanation:
3p² - 7p - 1 = 0 is a given equation
3p² - 7p - 1 = 0
Here,
a = 3
b = - 7
c = - 1
Now, Discriminant
D = b² - 4ac
= (- 7)² - 4 (3)(- 1)
= 49 + 12
D = 61 > 0
So, Quadratic Equation
ax² + bx + c = 0
x = - b ± √b² - 4ac ÷ 2a
x = - (- 7) ± √(- 7)² - 4 (3)(- 1) ÷ 2(3)
x = 7 ± √61 ÷ 6
x = 7 ± √61 ÷ 6
x = 7 + √61 ÷ 6 or x = 7 - √61 ÷ 6
∴ Not real Value
Thus, The real value of x is 7 + √61 ÷ 6
-TheUnknownScientist
Find the x and y intercepts of the line. 4x-2y=16 need in 5-to minutes PLEASE
Answers
i like apple pie
what’s ur favorite type of pie
Answers
Answer:
owo rawr pie jkjk
i never had pie but if i would try some i would go for cherry
Step-by-step explanation:
Answer:
I like nut pie
Step-by-step explanation:
it taste's good
PLEASE HELP! 90 POINTS!!!!! 4) Edward is playing a game where he draws cards with integers on them from a deck. If the integer is positive he moves forward that many steps; if the integer is negative he moves back that many steps. Edward drew the following cards: 3, -3, -4, 5, 10, -7. How many TOTAL steps did he move?
A) -32
B) -4
C) 4
D) 32
Answers
1st card : 3 steps forward
2nd card: 3 steps back
3rd card: 4 steps back
4th card: 5 steps forward
5th card: 10 steps forward
6th card: 7 steps back
Total steps : 3 + 3 + 4 +5 +10 + 7 = 32
Answer: D) 32
What is the slope of the line that passes through (−2, −4) and (3, 7) ?
A.9/ 7 B. 11/ 5 C. 3 D. I don't know.
Answers
Answer:
11/5
Step-by-step explanation:
-4 - 7 = -11
-2 - 3 = -5
11/5
Answer:
B. 11/5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)Step-by-step explanation:
Step 1: Define
Point (-2, -4)
Point (3, 7)
Step 2: Find slope m
Substitute: \(m=\frac{7+4}{3+2}\)Add: \(m=\frac{11}{5}\)Convert the following base-ten numerals to a numeral in the indicated bases. a. 837 in base six b. 8387 in base fifteen c. 64 in base two
Answers
To convert base-ten numerals to a different base, we divide the given number by the base repeatedly and record the remainders. Reading the remainders in reverse order, the numeral in base two is 1000000.
a. To convert 837 to base six, we repeatedly divide 837 by 6 and record the remainders.
Dividing 837 by 6 gives a quotient of 139 and a remainder of 3.
Dividing 139 by 6 gives a quotient of 23 and a remainder of 5.
Dividing 23 by 6 gives a quotient of 3 and a remainder of 5.
Finally, dividing 3 by 6 gives a quotient of 0 and a remainder of 3.
Reading the remainders in reverse order, we have the numeral 3553 in base six.
b. To convert 8387 to base fifteen, we follow the same procedure.
Dividing 8387 by 15 gives a quotient of 559 and a remainder of 2.
Dividing 559 by 15 gives a quotient of 37 and a remainder of 4.
Dividing 37 by 15 gives a quotient of 2 and a remainder of 7.
Finally, dividing 2 by 15 gives a quotient of 0 and a remainder of 2.
The numeral in base fifteen is 2742.
c. To convert 64 to base two, we divide 64 by 2 repeatedly.
Dividing 64 by 2 gives a quotient of 32 and a remainder of 0.
Dividing 32 by 2 gives a quotient of 16 and a remainder of 0.
Dividing 16 by 2 gives a quotient of 8 and a remainder of 0.
Dividing 8 by 2 gives a quotient of 4 and a remainder of 0.
Dividing 4 by 2 gives a quotient of 2 and a remainder of 0.
Finally, dividing 2 by 2 gives a quotient of 1 and a remainder of 0.
Reading the remainders in reverse order, the numeral in base two is 1000000.
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1/4 + 1/6 = 1/6 + 1/4
Answers
Answer:
This is true
Step-by-step explanation:
The fractions are just switched around.
Help? This 9th grade math
Answers
Answer:
17*
Step-by-step explanation:
180*-163*=17*
a design engineer is mapping out a new neighborhood with parallel streets. if one street passes through (6, 4) and (5, 2), what is the equation for a parallel street that passes through (−2, 6)?
Answers
Answer:
Therefore, the equation for a parallel street that passes through (−2, 6) is y = -2x - 2.
Step-by-step explanation:
The slope of the line passing through (6, 4) and (5, 2) is (2-4)/(5-6) = -2/1 = -2.
The equation of a line passing through (-2, 6) with a slope of -2 is y - 6 = -2(x + 2).
Solving for y, we get y = -2x - 2.
Therefore, the equation for a parallel street that passes through (−2, 6) is y = -2x - 2.
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A car is traveling at a speed of 30 miles per hour. What is the car's speed in kilometers per hour? How many kilometers will the car travel in 3 hours? In your
computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers.
Answers
Answer:
144.84
Step-by-step explanation:
A sample of 800 items produced on new machine showed that 48 of them are defective. The factory will get rid the machine if the data indicates that the proportion of defective items is significantly more than 5%- At a significance level of 5% is there enough evidence to get rid of the machine? The following steps should be indicated in your answer: (10 points) Null and Alternative Hypothesis (both in symbols and statement form) Level of Significance; sample size; test statistics Decision Rule Computation: Paste here the solution you made using Excel; or write your manual computation_ Decision AND Conclusion:
Answers
At a significance level of 5%, with a sample size of 800 items produced on a new machine and 48 of them being defective, the null hypothesis is that the proportion of defective items is not significantly more than 5%, while the alternative hypothesis is that it is significantly more than 5%. The level of significance is 0.05. Using a z-test for proportion with a one-tailed test, the calculated test statistic is 3.45. Since the calculated test statistic is greater than the critical value of 1.645, we reject the null hypothesis. Therefore, there is enough evidence to get rid of the machine.
Null Hypothesis: p = 0.05
Alternative Hypothesis: p > 0.05
Level of Significance: α = 0.05
Sample Size: n = 800
Number of Defective Items: x = 48
Sample Proportion:P= x/n = 48/800 = 0.06
Since the sample size is large, we can use the normal distribution to approximate the binomial distribution.
Test Statistic: z = (P - p) / sqrt(p * (1 - p) / n)
Under the null hypothesis, the test statistic follows a standard normal distribution.
Decision Rule: Reject the null hypothesis if z > zα, where zα is the z-score that corresponds to a cumulative probability of 1 - α.
From the standard normal distribution table, we have:
zα = 1.645
Computation:
z = (0.06 - 0.05) / sqrt(0.05 * 0.95 / 800) = 1.33
Since z (1.33) is less than zα (1.645), we fail to reject the null hypothesis.
Conclusion: At a significance level of 5%, there is not enough evidence to conclude that the proportion of defective items produced by the new machine is significantly more than 5%. Therefore, the factory should not get rid of the machine based on this sample data.
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what is x? 6(x+4)+3x-2
Answers
in problems 13–20, solve the given initial value problem. 13. y′′ 2y′-8y = 0; y102 = 3, y′102 = -12
Answers
The solution to the initial value problem is:
y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)
To solve a second-order linear homogeneous differential equation the equation is y′′ 2y′-8y = 0.
Given initial conditions: y(102) = 3 and y′(102) = -12.
To solve this differential equation, we can use the characteristic equation: r^2 + 2r - 8 = 0
Factoring this equation, we get: (r + 4)(r - 2) = 0
So the roots of the characteristic equation are r = -4 and r = 2.
The general solution to the differential equation is:
y(t) = c1 * e^-4t + c2 * e^2t
To find the values of c1 and c2, we can use the initial conditions.
We know that y(102) = 3, so we can substitute t = 2 into the general solution:
3 = c1 * e^-8 + c2 * e^4
We also know that y′(102) = -12, so we can take the derivative of the general solution and substitute t = 2:
y′(t) = -4c1 * e^-4t + 2c2 * e^2t
y′(102) = -4c1 * e^-8 + 2c2 * e^4 = -12
Solving for c1, we get:
c1 = (-3/4) * e^4 + (3/4) * e^-8
Solving for c2, we get:
c2 = (3/8) * e^8 - (3/8) * e^-4
Therefore, the solution to the initial value problem is:
y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)
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Leo walks at an average speed of b feet
per second for n seconds with a distance
of 172 feet. Write an equation to represent
the given problem.
Answers
Answer:
the anwser is 67
Step-by-step explanation:
thanks fotr points
What is the correct answer
Answers
Answer:
cột số 2
Step-by-step explanation:
Consider the tables created using an initial investment of $1,000 and quarterly compounding of interest.
table a represents the function that models the total amount of one investment, a(x), based on the annual interest rate, x, as a percent.
table b represents the function that models the interest rate, r(d), as a percent, based on the total amount at the end of the investment, d.
use the values in the table to verify the relationship between the functions representing the investments. which conclusion can be made?
the functions are inverses because the domain of table a is the same as the range of table b.
the functions are inverses because the range of table a is different from the domain of table b.
the functions are not inverses because for each ordered pair (x, y) for one function, there is no corresponding ordered pair (x, y) for the other function.
the functions are not inverses because for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function.
Answers
Option fourth "The functions are not inverses because, for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function." is correct.
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.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have two tables shown in the picture.
Table (A) have values of x and a(x)
Table (B) have values of d and r(d)
As we know if the function has an inverse of it and (x, y) satisfies the function then (y, x) must satisfy the inverse of a function.
Thus, the option fourth "The functions are not inverses because, for each ordered pair (x, y) for one function, there is no corresponding ordered pair (y, x) for the other function." is correct.
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Whoever can help me answer this will be mark Brainliest!
Answers
The equation of the given parabola is expressed as: y = (-5/4)(x - 4)² + 3
What is the equation of the parabola?We can see that the given parabola curve comes with x-coordinates and axis of symmetry.
The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y = ax² + bx + c , the axis of symmetry is a vertical line x = −b/2a .
The coordinates of the axis of symmetry are: (4, 3)
Thus:
4 = −b/2a
The equation of a parabola written in vertex form is:
y = a(x - h)² + k
where:
(h, k) is the coordinate of the vertex.
We have that (h, k) = (4, 3)
Thus:
y = a(x - 4)² + 3
At the coordinate (6, -2), we have:
-2 = a(6 - 4)² + 3
-2 = 4a + 3
4a = -5
a = -5/4
Thus:
y = (-5/4)(x - 4)² + 3
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find the hypotenuse: c =
Answers
I need help with this problem
Answers
The linear equation that passes through these two points is:
y = (3/2)*x - 3
How to find the equation of the line?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
slope = (y2 - y1)/(x2 - x1)
Here we have the points (-3, -15/2) and (1, -3/2), then the slope will be:
a = ( -3/2 +15/2)/(1 + 3) = 6/4 = 3/2
y = (3/2)*x + b
To find the value of b we can use one of the points, like (1, -3/2), replacing the values there we will get:
-3/2 = (3/2)*1 + b
-3/2 - 3/2 = b
-6/2 = b
-3 = b
The linear equation is:
y = (3/2)*x - 3
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Insert a monomial into each trinomial such that the result of a perfect square.
...+12x+1
Answers
The sentence above shows that the monomial of the equation is \(36x^2\).
Give an example of a monomial.A monomial is indeed a polynomial with something like a single term. A monomial algebraic expression normally has one term, although it can also include many variables and be of a higher degree. For example, 9x³yz is a term where the coefficients are 9, the variables are x, y, and z, and indeed the degree of something like the monomial seems to be 3.
Is 42 a monomial number?Only those coefficient & powers on the inside of a monomial must be non-negative real values. A few examples of monomials are 42, five x, three y towards the degree of four, and two p doubled q.
Briefing:...+12x+1
so,
\(=(6x+1)^2\\\\=(6x+1)(6x+1)\\\\=36x^2+6x+6x+1\\\\=36^2+12x+1\)
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dose -8+a=-6 over 2 equal 2
Answers
Answer:
2
Step-by-step explanation:
Answer:
2
because BLA BLA I just need points
A restaurant needs to hand out 11,340 fliers for their grand opening. They hire 27 workers to hand out the fliers. If each worker hands out the same number of fliers, how many fliers will each worker hand out?
Answers
Answer:
420fliers per worker
Step-by-step explanation:
Given parameters:
Number of fliers to hand out = 11340
Number of workers = 27
Unknown:
Number of fliers handed out by each worker = ?
Solution:
Number of fliers handed out by each worker = \(\frac{number of fliers}{number of workers}\)
Input the parameters and solve;
= \(\frac{11340}{27}\)
= 420fliers per worker
Answer:
420 fliers
Step-by-step explanation:
11,240 divided by 27 would equal 420 fliers.
A person's Body Mass Index (BMI) is a measure of the mount of fat in their body. The relationship between antioxidant food consumption per day in cups and the BMI of an individual is modeled by the following line of best fit: y = -0.1x + 22. Interpret the slope and intercept of the trend line within the context of the data.
Answers
Answer:
Check explanation
Step-by-step explanation:
Given:
y = -0.1x + 22
Where,
y = BMI of an individual
x = antioxidant food consumption per day in cups
Equation of a slope
y = mx + c
Where,
m = slope
c = y - intercept
Therefore,
From the equation
y = -0.1x + 22
slope, m = -0.1
y - intercept, c = 22
Answer:
The y-intercept tells us that a person who doesn’t have any antioxidant foods can expect to have a BMI of 26. For every cup of antioxidant food that is consumed one can expect to lower their BMI by 1.2.
Step-by-step explanation:
i used this for test and it was right.
What is the equation of a circle whose center is at the origin and whose radius is 16?
x 2 + y 2 = 4
x 2 + y 2 = 16
x 2 + y 2 = 256
Answers
Best luck with your studying
Answer:
x^2 + y^2 = 256
good luck and have an awesome Day/Night
Susan and bonnie are shopping for school clothes. Susan has $50 and a coupon for a $10 discount at a clothing store where each shirt cost $12. Susan thinks that she can buy three shirts, but bonnie says Susan can by five shirts. The equations used to model the problem are listed below .Solve each equation algebraically ,justify your steps, and determine who is correct.
Answers
Answer:
Bonnie is correct
Step-by-step explanation: from the above question:
Susan and bonnie are shopping for school clothes.
Susan has $50 and a coupon for a $10 discount at a clothing store where each shirt cost $12.
Susan thinks that she can buy three shirts, but bonnie says Susan can by five shirts.
Hence:
Discount = $10, Discounted price always carries the minus(-) sign
The cost of 1 shirt = $12
Let the number of shirts she can buy = x
Hence our Equation =
$12 × x - $10 = $50
12x = $50 + 10
12x = $60
x = $60/12
x = 5 shirts
Therefore, Bonnie is correct because she can only buy 5 shirts
a package is weighed at 8 kg to the nearest kg.find the largest possible weight for the package.
Answers
The largest possible weight would be 8.5 kg. When a package is weighed at 8 kg to the nearest kilogram, it means that the recorded weight could be off by a maximum of 0.5 kg in either direction. In this case, the package could actually weight anywhere between 7.5 kg and 8.5 kg.
To determine the largest possible weight for the package, we need to consider the upper limit of this range. Thus, the largest possible weight would be 8.5 kg. This value represents the scenario where the package's actual weight is at the highest end of the possible range.
It's important to note that the recorded weight of 8 kg is an approximation due to the nearest kilogram rounding. The actual weight of the package may differ from the recorded weight by a small margin. However, based on the given information, 8.5 kg is the largest weight that the package could possibly have, considering the rounding to the nearest kilogram.
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how many positive odd factors of 48 are greater than 2 and less than 10
Answers
Answer:
Just 1 positive, odd factor
Step-by-step explanation:
48 has many factors. But not many odd factors. Only 3 is odd and bigger than 2 and less than 10.
So, just one odd, positive factor.