The given statement states that the parametrization of both the tangent line there at designated position is 7x - 4y = 3.
What is parametrization?Finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, specified by an implicit equation, is the process of parametrization (or parameterization; see parameterization, parametrization). Implicitization is the term for the opposite process. The parametrization consists of one function of multiple real variables for each coordinate since the state of the system is typically controlled by a finite set of coordinates. The system's degree of freedom is equal to the number of parameters.
According to the given data:r(t) = cos(6t), sin(3t) , t = 4
= -6sin6t, 3cosjt , 1
The parameter of Tangent live is
L(t) = γ(t₀) + tr'(t₀)
therefore
γ(t₀) = γ(ππ₄)
= (0 , 1/√2 , π/4)γ (+0) = γ(π/4)
= ( 6, -3/√2 , 1)
putting in the formula we get:
L(t) = γ(t₀) + tr'(t₀)
L(t) = (0 , 1/√2 , π/4) + t( 6, -3/√2 , 1)
= \(\left(6 t-\frac{1}{\sqrt{2}}-\frac{3}{\sqrt{2}} t, \frac{\pi}{4}+t\right)$$\)
= 2.
Given
f(x, y ) = in(7x² - 4y²)
at the point(1, 1)
Δ f (m, y) = (fn , f4)
= \(\frac{14 x}{7 n^2-4 y^2}, \frac{-8 y}{7 x^2-4 y^2}\\\\\)
Δ f (1, 1)
= \(\left\langle\frac{14}{3}, \frac{-8}{3}\right\rangle\)
= (a ,b)
The equation of the tangent plane is
a(x - x₀) + 6dy - y₀ = 0
(14/3)(x - 1)- (8/3)(y -1 ) = 0
14x - 14 - 8y + 8 = 0
14x - 8y = 6
7x - 4y = 3
To know more about parametrization, visit;
https://brainly.com/question/14666291
#SPJ4
The mean is ? = 137.0 and the standard deviation is ? = 5.3.
Find the probability that X is between 134.4 and 140.1.
0.4069
0.6242
0.8138
1.0311
The probability that X is between 134.4 and 140.1 is approximately 0.4076, which is closest to the option 0.4069.
To calculate this probability, we need to standardize the values using the standard normal distribution. First, we find the z-scores for the lower and upper bounds:
z1 = (134.4 - 137.0) / 5.3 ≈ -0.4906
z2 = (140.1 - 137.0) / 5.3 ≈ 0.5849
Next, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability corresponding to z1 is P(Z < -0.4906) ≈ 0.3131, and the probability corresponding to z2 is P(Z < 0.5849) ≈ 0.7207.
To find the probability that X is between 134.4 and 140.1, we subtract the probability associated with the lower bound from the probability associated with the upper bound:
P(134.4 < X < 140.1) = P(Z < 0.5849) - P(Z < -0.4906) ≈ 0.7207 - 0.3131 = 0.4076.
As a result, the chance that X lies between 134.4 and 140.1 is roughly 0.4076, which is closest to the value of 0.4069 for the option.
To know more about probability, refer here:
https://brainly.com/question/12629667#
#SPJ11
(11x - 1)
(20x – 3)
151°
Answer:
x= 1.6 degrees
Step-by-step explanation:
to find the missing angle 180 degrees - 151 degrees
29° is the missing angle at the bottom ryt of the triangle.
all angles in triangle add upto 180°
so, 20x-3°+11x-1°+29°= 180°
31x=180°-25°
x= 1.6°
A polygon with three edges and three vertices is called a triangle.
x=1.6° is its value.
Explain about the triangle?Based on the lengths of its sides, triangles can be categorized into one of three groups: Scalene. Isosceles. Equilateral.
The trigon, a 3-sided polygon, is sometimes (though not often) referred to as a triangle. Every triangle has three sides and three angles, some of which might be the same.
The triangle's angles are created by joining its three sides end to end at a single point. The sum of the three angles of the triangle is 180degrees.
To identify the omitted angle between 180 and 151 degrees
The triangle's bottom right corner lacks a 29° angle.
triangle's angles sum up to 180°
so, 20x-3°+11x-1°+29°= 180°
31x=180°-25°
x =1.6 degree
To learn more about triangle refer to:
https://brainly.com/question/17335144
#SPJ2
I NEEEED answers WITH 5.3.3 in CONNEXUS FOR MATH PLSSS
A square has a perimeter of 12 units. One vertex is at the point left-parenthesis negative 1 comma 1 right-parenthesis, and another vertex is at the point left-parenthesis 2 comma 4 right-parenthesis. Which of the following points could be another vertex?
A. left-parenthesis 1 comma 2 right-parenthesis
B. left-parenthesis 2 comma 1 right-parenthesis
C. left-parenthesis 1 comma negative 2 right-parenthesis
D. left-parenthesis 2 comma negative 1 right-parenthesis
Another possible vertex of the square is determined as (2, 1).
option B is the correct answer.
What is the vertex of the square?The vertex of a figure is the point of intersection of two sides of the shape.
The perimeter of the square is given as 12 units, the length of each side of the square is calculated as follows;
P = 12 units
a side length = 12 units / 4 = 3 units
To determine another possible vertex of the square, the length between the points must be equal to 3.
Let's consider point A;
A = (1, 2)
given vertex = (-1, 1)
distance between the points = √ (-1 -1)² + (1 - 2)² = √5
Let's consider point B;
B = (2, 1)
given vertex = (-1, 1)
distance between the points = √ (-1 -2)² + (1 - 1)² = √9 = 3
Thus, point B is another possible vertex of the square.
Learn more about vertex of a square here: https://brainly.com/question/23627218
#SPJ1
Hey, can someone help me with my math homework?
aqueell ears hanan pus
Exit Find the digit 5 in each of these numbers. 15.2 3.5 The 5 in 3.5 is 1 place to the right of the 5 in 15.2. Which sentence correctly compares the values? A. The value of the 5 in 3.5 is times the value of the 5 in 15.2. B. The value of the 5 in 3.5 is times the value of the 5 in 15.2. C. The value of the 5 in 3.5 is 10 times the value of the 5 in 15.2. D. The value of the 5 in 3.5 is 100 times the value of the 5 in 15.2.
Answer:
The value of the 5 in 3.5 is 1/10 times the value of the 5 in 15.2
Step-by-step explanation:
15.2
2 = tenth = 2/10 = 0.2
5 = unit = 5
1 = tens = 10
3.5
5 = tenth = 5/10 = 0.5
3 = units =3
5 tenth ÷ 5 units
= 5/10 ÷ 5
= 5/10 × 1/5
= 5/50
= 1/10
Check:
1/10 × 5
= 5/10
= 0.5
Given that the line y=ax+b passes through the points A(-1,7)and B(3,-1)), how do I find the values of a and b?
The coefficients a and b for the linear function are given by:
a = -2, b = 5.
What is a linear function?A linear function is modeled by:
y = ax + b
In which:
a is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Given two points, the slope is given by change in y divided by change in x, hence, for points AB:
a = (-1 - 7)/(3 - (-1)) = -8/4 = -2.
Hence:
y = -2x + b.
When x = -1, y = 7, hence the value of b is found as follows:
7 = -2(-1) + b
b = 5.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
PLEASE HELP ILL GIVE BRAINLIEST!! i don’t understand this at all!
Amelia bought a violin that had a regular price of $150 and was marked down 20%. How much did Amelia pay for the violin?
hurry pleasee
Answer:
$120
Step-by-step explanation:
ticket prices at an outdoor theatre performance are $2.50 for children and $5.00 for adults. one evening, $6350 is collected from a total of 1900 people attending. how many adults and how many children attend?:
As the ticket prices at an outdoor theatre performance are $2.50 for children and $5.00 for adults. one evening, $6350 is collected from a total of 1900 people attending. There are 640 adult and 1260 childrens.
Given in the questions:
Ticket price in outdoor Theater = $2.50
For Children = $5.00
Total tickets collected in evening = $6350(collected from 1900 people)
Let p be the adult and
1900 - p be the children's who attained the show.
Now,
2.5 × (1900- p) +5p = 6350
⇒ 4750 - 2.5p +5p =6350
⇒ 2.5p = 1600
⇒ p = 1600/2.5
⇒ p = 640
Since,
p = 640
Therefore,
1900 - p = children
⇒ Children = 1900 - 640
⇒ Children = 1260
Therefore, there are total 640 adults and 1260 children's in the theater.
Learn more about Price:
https://brainly.com/question/19091385
#SPJ4
19 out of 34 as a percentage
Answer:
6.46%
Step-by-step explanation:
19*34= 646
646/100= 6.46
Hope this helps! :)
Answer:
55
Step-by-step explanation:
To be exact it is 55.8823529412%
Locate the point (-3.5, -1) on the coordinate plane:
3
2
1
-3
-2
-1
2.
3
-1
-2
-3
Answer:
go to the left 3.5 units then go down one and that's your point
The 42 students on the conservation trip picked up trash at the beach. The girls picked up 15 pounds each and the boys picked up 12 pounds each for a total of 576 pounds. Use b and g for each of the equations.
Answer: number of boys = 18
Number of girls = 24
Step-by-step explanation:
Based on the information given, we can form this into an equation which will be:
b + g = 42 ....... i
12b + 15g = 576 ...... ii
Multiply equation i by 12
Multiply equation ii by 1
12b + 12g = 504 ....... iii
12b + 15g = 576 ........ iv
Subtract iii from iv
3g = 72
g = 72/3
g = 24
Since b + g = 42
b + 24 = 42
b = 42 - 24.
b = 18
Therefore, number of boys = 18
Number of girls = 24
Does someone mind helping me with this? Thank you!
a. What is the nth fraction in the following sequence? 2
1
, 4
1
, 8
1
, 16
1
, 32
1
,… b. What is the sum of the first n of those fractions? To what number is the sum getting closer and closer? Two forces, A=80 N and B=44 N, act in opposite directions on a box, as shown in the diagram. What is the mass of the box (in kg ) if its acceleration is 4 m/s 2
?
A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.
a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`
Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`
b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)
`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)
`Simplifying:`S_n = 2*(2^n - 1)
`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.
Thus, the sum is getting closer and closer to infinity.
Know more about sequence here,
https://brainly.com/question/30262438
#SPJ11
The value of a home increases by 7%each year. Explain why the value of the home doubles approximately once each decade
The value of a home increases by 7%each year, by compounding the value of the home doubles approximately once each decade.
What is compounding?Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.
It is given by the formula,
A=P(1+r)^t
where A is the value after t period of time,
P is the value of the asset at the beginning, and,
r is the rate of interest.
The value of the home doubles once each decade.
Given to us
The value of a home increases by 7% each year.
As it is given that the value of a home increases by 7% each year, therefore, the value of the home is compounding every year.
We know the formula of compounding,
A=P(1+r)^t
Why does the value doubles?
Now, let's assume a house whose value is 'P' today, therefore, substitute the value of the house in the formula of compounding,
A=P(1+r)^t
Substitute the rate at which the value is increasing,
A=P(1+0.07)^t
We know that in a decade there are 10 years,
A=P(1+0.07)^10=P(1.07)^10
=1.967P
Approximately
=2P
As we can see that the value of the home is almost 2 times the 'P' therefore, twice the value of the home at the beginning.
Hence, the value of the home doubles once each decade.
To Learn more about Compounding:
https//brainly.com/question/25857212
#SPJ1
find the volume of the solud that results when the region enclosed by y = square root x, y = 0, and x = 9 is revolved about the line x = 9
The volume of the solid that results when the region enclosed by y = √x, y = 0, and x = 9 is revolved about the line x = 9 is 54π/5 cubic units.
To solve this problem
We can use the method of cylindrical shells to find the volume of the solid that results when the region enclosed by y = √x, y = 0, and x = 9 is revolved about the line x = 9.
First, we need to find the height of each cylindrical shell. Since we are revolving the region about the line x = 9, the radius of each shell will be 9 - x.
The height of each shell will be the difference between the upper and lower bounds of the region, which is y = √x and y = 0:
height = √x - 0
= √x
So the volume of each cylindrical shell will be:
dV = 2π(9 - x)√x dx
To find the total volume of the solid, we integrate this expression from x = 0 to x = 9:
V = ∫(from 0 to 9) 2π(9 - x)√x dx
We can simplify this integral by making the substitution u = √x, which gives us:
V = 2π∫(from 0 to 3) (9 - u^2)u^2 du
Expanding the integrand and integrating term by term, we get:
V = 2π(27/5 - 9/3)
= 2π(27/5 - 27/9)
= 2π(162/45 - 135/45)
= 54π/5
Therefore, the volume of the solid that results when the region enclosed by y = √x, y = 0, and x = 9 is revolved about the line x = 9 is 54π/5 cubic units.
Learn more about cylindrical shells here: brainly.com/question/30501297
#SPJ1
Which container would most likely have a capacity that is measured in liters? A.Drinking Glass
B.Watering Can
C.Baby Bottle
D.Soup Spoon
136 oz is how many pounds
A.6.8 pounds
B.8.5 pounds
C.1088 pounds
D.2,176 pounds
Answer:
B 8.5 Pounds
Step-by-step explanation:
I hope this helps!
Answer: 8.5
Step-by-step explanation:
16 ounces is a pound
so we divide 136 by 16 and get 8.5
The expression denotes the z-score with an area of _______ to its right.
The given expression represents the z-score with an area to its right, indicating the probability of observing a value greater than the z-score.
The z-score, also known as the standard score, measures the distance between a given data point and the mean of a distribution in terms of standard deviations. It is calculated by subtracting the mean from the data point and dividing the result by the standard deviation. The resulting z-score represents the number of standard deviations a data point is away from the mean.
When we refer to the expression denoting the z-score with an area to its right, we are essentially talking about the cumulative probability associated with the z-score. This probability represents the area under the normal distribution curve to the right of the given z-score. In other words, it indicates the likelihood of observing a value greater than the z-score.
By utilizing statistical tables or software, we can determine the exact value of the area or probability associated with a given z-score. This information is useful in various applications, such as hypothesis testing, confidence intervals, and determining percentiles in a distribution. It allows us to make inferences and draw conclusions based on the relative position of a data point within a distribution.
Learn more about probability here: https://brainly.com/question/31828911
#SPJ11
solve this system using substitution x+5y=-32 y=3x
\( \huge \colorbox{pink}{Question } \)
solve this system using substitution x+5y=-32 y=3x
Substitute 3x for y in x + 5y = - 32\(x + 5y = - 32 \\ x + 5(3x) = - 32 \\ x + 15x = - 32 \\ 16x = - 32 \\ \frac{16x}{16} = \frac{ - 32}{16} \\ x = - 2\)
Substitute - 2 for for x in y = 3x\(y = 3x \\ y = 3( - 2) \\ y = - 6\)
\( \huge \colorbox{pink}{Answer} \)
x = - 2y = - 6Hope it helps ^_^
What are the vertex, focus, and directrix of the parabola whose equation is y-5= 1/12 (x – 3)2?
Answer:
Step-by-step explanation:
Use the vertex form, y=a(x−h)2+k y = a ( x - h ) 2 + k , to determine the values of a a , h h , and k k . a=−112 a = - 1 12. h=3 h = 3. k=−2 k = - 2.
How much grain can this container hold?
Answer:
953.78 in³
Step-by-step explanation:
Area of circle = πr²
The area of the base
= 3.14×(9÷2)²
= 63.585 in²
The capacity of the container
= 63.585×15
= 953.775 in³
which of the following statements is true of a continuous probability distribution? a.) all outcomes can be listed. b.) the outcomes can take any value within a given range. c.) the distribution can be described with a table. d.) the outcomes have a finite number of possibilities.
a continuous probability distribution the outcomes can take any value within a given range.
What is continuous probability distribution ?A probability distribution where the random variable X can have any value is known as a continuous probability distribution (is continuous). The likelihood of X taking on any one particular value is zero because there are an unlimited number of possible values for it. As a result, we frequently use ranges of values (p(X>0) =.50).In the case of the binomial distribution, as is common knowledge, it is described as the likelihood that a discrete random variable or mass will produce a specific value. The accompanying function is known as a probability mass function, and this distribution is also known as a probability mass distribution.
To learn more about binomial distribution, refer,
https://brainly.com/question/9325204
#SPJ4
Choose A Point Below That Lies On The Function Y+5=-2(X+3)(-3, -5) (3,5) (-2,-3)(-5,3)
Answer:
(-3, -5)
Explanation:
Given the function:
\(y+5=-2(x+3)\)First, make y the subject of the equation.
\(y=-2(x+3)-5\)To choose a point that lies on the line, we test the x-values and see if we get the corresponding y-value.
\(\begin{gathered} \text{ At }x=-3, \\ y=-2\left(-3+3\right)-5 \\ =-2\left(0\right)-5 \\ =0-5 \\ =-5 \end{gathered}\)Since the y-value corresponds to the point (-3, -5), the point that lies on the function is (-3, -5).
Melissa rented a Segway, a stand up scooter, in downtown Austin, Tx. The store charges a $3.25 initial charge plus $2.50 per mile. Which equation can be used to find y, the total cost of the rental, if x represents the number of miles Melissa rode on the Segway?
pls it has to be like "y=mx+b"
Answer:
y = x(2.50)+3.25
Step-by-step explanation:
y (total cost )= x (miles rode) * 2.50 (cost per mile) + 3.25 (initial cost)
I’m struggling.help please.
Answer:
21,23,25,27,29... and etc
Step-by-step explanation:
13,15,17,19, your going by 2, so.. 21,23,25,27,29. and counties. I don't know how long it goes but there you go hopefully this helps <3.
Answer:
2n + 11
Step-by-step explanation:
2(1) + 11 = 13
2(2) + 11 = 15
2(3) + 11 = 17
the 2 is the constant difference between the first 2 terms.
the numbers in brackets are the term number.
you have to multiply the difference with the term number.
then you will have to take that answer and subtract it from the first term number.
hope it helps xxx
y = x-2
y = 3x+4. Solutions of system of equation
Answer:
x=-3 and y=-5
Step-by-step explanation:
hope this helps!
Answer:
Y = x-2; y= 3x + 4
Step-by-step explanation:
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
39 feet
Step-by-step explanation:
plug in 1.5 into t
Question One:
Zahir bought a house 15 years ago, and it is now valued $548 900.00.
Determine the initial value of the home when Zahir purchased it, if it's value
has grown at a rate of 4.8% compounded annually. (2 marks)
Question Two:
Kiran purchases a sofa for $1791.99 (taxes already included). The
department store offers her a promotion of 0% interest with no payments
for one year. If Kiran does not pay the amount in full within one year,
interest will be charged from the date of purchase at an annual rate of
27.93%, compounded monthly.
a) If Kiran does not make any payments, what will the department store bill
her one year after the date of purchase? Show your work. (2 marks)
b) Describe a different compounding period such that the overall cost of the
sofa is lower than if the annual interest rate were compounded monthly. Use
an example to help your explanation. (2 mark)
A. Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.
B. In this case, the overall cost of the sofa would be approximately $2,284.08
How to solve the problemsTo find the initial value of the home when Zahir purchased it, we can use the compound interest formula:
Future Value = Initial Value * (1 + (interest rate))^years
Let Initial Value be P. We are given the Future Value as $548,900, the interest rate as 4.8%, and the number of years as 15.
548,900 = P * (1 + 0.048)^15
Now, we'll solve for P:
P = 548,900 / (1 + 0.048)^15
P ≈ 305,113.48
a. Future Value = Initial Value * (1 + (interest rate / number of periods))^(years * number of periods)
Initial Value = $1,791.99
Interest Rate = 27.93% (0.2793)
Number of periods = 12 (monthly)
Years = 1
Future Value = 1,791.99 * (1 + (0.2793 / 12))^(1 * 12)
Future Value ≈ 2284.33
Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.
b. interest were compounded annually:
Future Value = Initial Value * (1 + interest rate)^years
Future Value = 1,791.99 * (1 + 0.2793)^1
Future Value ≈ 2284.08
In this case, the overall cost of the sofa would be approximately $2,284.08, which is slightly lower than if the interest were compounded monthly ($2,284.33).
Read more on compounding here:https://brainly.com/question/24274034
#SPJ1
Two spheres have volumes of 87 cm³ and 647 cm³. If the surface area of the smaller sphere is 167 cm², what is the
surface area of the larger sphere?
64 cm²
96 cm²
128 cm²
256 cm²
The surface area of the larger sphere is equal to 636.365 square centimeters.
How to determine the surface area of the sphere by the use of direct variation formulas
In this question we must estimate the surface area of the smaller sphere. By geometry we know that the volume of a sphere is directly proportional to the cube of its radius and the surface area is directly proportional to the square of radius, then the volume to surface area ratio is equal to:
V/A = k · r (1)
Where:
r - Radiusk - Proportionality constantThen, we can derive the following relationship between the two spheres by eliminating the proportionality constant:
V/(A · r) = V'/(A' · R) (2)
Where:
r - Radius of the smaller sphere.R - Radius of the larger sphere.First, we need to determine the radii of the spheres:
Larger radius
R = ∛(3 · V' / 4π)
R = ∛(3 · 647 / 4π)
R ≈ 5.365 cm
Smaller sphere
r = ∛(3 · V / 4π)
r = ∛(3 · 87 / 4π)
r ≈ 2.749 cm
Lastly, we find the surface area of the larger sphere:
A · r · V' = A' · R · V
A' = (A · r · V') / (R · V)
A' = (167 · 2.749 · 647) / (5.365 · 87)
A' = 636.365 cm²
The surface area of the larger sphere is equal to 636.365 square centimeters.
To learn more on spheres: https://brainly.com/question/11374994
#SPJ1