Find parametrization for the tangent line at time t0=13.
Use the equation of the tangent line such that the point of tangency occurs when t=t0 .
(Write your solution using the form (*,*,*). Use t for the parameter that takes all real values. Simplify all trigonometric expressions by evaluating them. Express numbers in exact form. Use symbolic notation and fractions as needed.)
Where will this line intersect the - plane?
(Write your solution using the form (*,*,*). Express numbers in exact form. Use symbolic notation and fractions where needed.)
Answers
The parametrization for the tangent line at time [tex]t_{0}[/tex] is (41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)
The point of intersection is (40, -4, 0)
What is the parametrization for the tangent line at time [tex]t_{0}[/tex] and point of intersection?The given curve is defined parametrically by the equations
x = 3t + 2
y = 4 cos t
z = 4 sin t
To find the parametrization for the tangent line at time t0 = 13, we need to find the point of tangency and the direction vector of the tangent line.
The point of tangency is the position of the curve at time t0, which is
(3 * 13 + 2, 4 cos 13, 4 sin 13) = (41, -4/3, 4/3)
The direction vector of the tangent line is the derivative of the curve at time t0, which is
(3, -4 sin 13, 4 cos 13) = (3, -4/3, 4/3)
Therefore, the parametrization for the tangent line is
(41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)
b. To find the point where this line intersects the -plane, we set z = 0 and solve for t. This gives us
4/3 + 4t/3 = 0
t = -1/2
Therefore, the point of intersection is
(41 - 3/2, -2, 0) = (40, -4, 0).
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Related Questions
The diagram shows a field, ABCD, on horizontal ground. (a) There is a vertical post at C. From B, the angle of elevation of the top of the post is 19º. Find the height of the post.
Answers
36.8 units
tan (19) = h/BC
tan (19) x BC = h
tan (19) x 107 = h
h = 36.84 units
The teenager from the question above rejoins the group and another teenager is picked at random.
What is the probability that the teenager picked at random is male and their favourite hobby is playing video games? You can simplify this fraction if you wish
Answers
Using it's concept, the probability that the teenager picked at random is male and their favorite hobby is playing video games is:
[tex]\frac{1}{16}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, it is found that out of 32 teenagers, 2 are males who prefer playing videogames, hence the probability is:
[tex]p = \frac{2}{32} = \frac{1}{16}[/tex]
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what the difference between graph and inequalities ?
what the difference between graphing lines and graphing inequalities?
Answers
You don't shade a region when graphing just a line, but you do when graphing an inequality.
It should be noted that a graph is a diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.
How to illustrate the information?It should be noted that an inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.
This is used most often to compare the two numbers on the number line by their size.
On the other hand, the graphing inequalities shows what part of the number line contains values that will be able to satisfy the given inequality.
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WHAT IS 5+6+6+^6 DIVDED BY 7
Answers
The value of the given expression is 11.57
Division of numberDivision are written as a ratio of two values. Given the expression below
5+6+6+2^6 ÷ 7
Simplify to have:
(11+6+64)÷ 7
Simplify the expression in parenthesis
81÷ 7
11.57
Hence the value of the given expression is 11.57
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10 points please answer correctly (due soon)
Let’ pretend that in an American city there were 2000 new cases on Monday which is a 12% decrease from two weeks ago.
1. Write a linear/exponential equation that
models this situation (consistent with the data
provided). Time is the explanatory variable, and
New Cases is the response variable.
B) Explain what the slope/multiplier (consistent
with your choice above) means in this context
of the problem. Be sure to use units.
Answers
The exponential equation of the model is A(t) = 2583 * 0.88^t and the multiplier means that the number of new cases in a week is 88% of the previous week
The function that models the dataThe given parameters are:
New, A(t) = 2000
Rate, r = 12%
The function is represented as:
A(t) = A * (1 - r)^t
So, we have:
2000 = A * (1 - 12%)^t
This gives
2000 = A * (0.88)^t
2 weeks ago implies that;
t = 2
So, we have:
2000 = A * 0.88^2
Evaluate
2000 = A * 0.7744
Divide by 0.7744
A = 2583
Substitute A = 2583 in A(t) = A * 0.88^t
A(t) = 2583 * 0.88^t
Hence, the exponential equation of the model is A(t) = 2583 * 0.88^t
The interpretation of the multiplierIn this case, the multiplier is 88% or 0.88
This means that the number of new cases in a week is 88% of the previous week
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Suppose that the annual rainfall in Ferndale, California, is known to be normally distributed, with a mean of 35.5 inches and a standard deviation of 2.5 inches. About 2.4% of the years, the annual rainfall will exceed how many inches? (Round your answer to one decimal place.)
Answers
The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.
What is the average annual rainfall?Generally, the equation for the probability is mathematically given as
[tex]P( X < x) = p( Z < x - \mu / \sigma)[/tex]
Therefore
[tex]P( X > x) = 0.021[/tex]
[tex]P( X < x ) = 1 - 0.021\\\\\p( X < x) = 0.979[/tex]
[tex]P( Z < x - \mu / \sigma) = 0.979[/tex]
The z score for the probability of 0.979 is 2.034, according to the table of z values.
[tex]x - \mu / \sigma \\\\x= 2.034[/tex]
In the given equation, replace the values of mu and sigma with their respective values, and then solve for x.
[tex]x - 35.5 / 2.5 \\x= 2.034[/tex]
In conclusion, The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.
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4/10x - 2x + 8/5 = 4/5
Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4}{10}\times x\right)-(2 \times x)+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]
Reduce the fraction 4/10, to its minimum expression, extracting and canceling 2.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{2}{5}x-2x+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]Combine [tex]\bf{\frac{2}{5}x }[/tex] and -2x to get [tex]\bf{-\frac{8}{5}x}[/tex].
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x+\frac{8}{5}=\frac{4}{5} \ \end{gathered}$}[/tex]Subtract 8/5 from both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4}{5}-\frac{8}{5} \ \ \end{gathered}$}[/tex]Since 4/5 and 5/8 have the same denominator, join their numerators to subtract them.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4-8}{5} \end{gathered}$}[/tex]Subtract 8 from 4 to get -4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=-\frac{4}{5} \end{gathered}$}[/tex]Multiply both sides by [tex]\bf{-\frac{5}{8}}[/tex], the reciprocal of [tex]\bf{-\frac{5}{8}}[/tex].
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-\frac{4}{5}\left(-\frac{5}{8}\right) \end{gathered}$}[/tex]Multiply -4/5 by -5/8 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-4(-5)}{5\times8} \ \to \ \ Multiply \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{40} \end{gathered}$}[/tex]Reduce the fraction 20/40 to its lowest expression by extracting and canceling 20.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf x=\frac{1}{2} \end{gathered}$}}[/tex]Good luck in your studies
Given that y varies directly with x in the table, find the
value of y if the value of x is 5.
Answers
We know that this ratio is directly because the two magnitudes go up.
In this case we will get the proportionality constant by dividing any term of the second magnitude by the first.
For example:[tex]9 \: \div \: 3 \: = \: \boxed{3}[/tex]
Now that we know that k = 3, we can know how much "y" will be if x = 5.
We just multiply:
[tex]3 \: \times \: 5 \: = \: \boxed{ \bold{ 15}}[/tex]
Answer: y = 15A carpenter built a square table with side length x. Next, he will build a rectangular table by tripling one side and halving the other. The area of the rectangular table is represented by the expression (3 x)(one-half x).
A square with sides x. A rectangle with side one-half x and side 3 x.
What is the simplified expression for the area of the rectangular table?
Three-halves x squared
Three-halves x
Five-halves x squared
Five-halves x
Answers
The simplified expression for the area of the rectangular table is Three-halves x squared, 3x²/2
What is the area of the rectangular table?Since the carpenter built a square table with side length x. Next, he will build a rectangular table by tripling one side and halving the other.
To find the area of the rectangular table, we know that Area, A = LW where
L = length and W = widthNow, since the length of the square is x, and the rectangular table has one side of the square tripled and halving the other side .
So,
let
length of the rectangular table = L = x/2 and width of rectangular = W = 3xSo, the area of the rectangular table A = LW
= x/2 × 3x
= 3x²/2
So, the simplified expression for the area of the rectangular table is Three-halves x squared, 3x²/2
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I need help with this question.
Answers
the point-slope form is:
y + 5 = -(9/11)*(x - 3)
How to get the linear equation?A line that passes through a point (x₁, y₁) and has a slope m, can be written in point-slope form as:
y - y₁ = m*(x - x₁)
Here we know that the line passes through (3, -5) and (-8, 4).
Then the slope is:
[tex]m = \frac{-5 - 4}{3 - (-8)} = \frac{-9}{11}[/tex]
And we can use (3, -5) as the point (x₁, y₁), then the point-slope form is:
y + 5 = -(9/11)*(x - 3)
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Simplify the following
Answers
= 4×8 +2×3 -1+9
___________
20
= 8+6-9
_______
20
= 14 - 9
_______
20
= 5
____
20
Given the graph of g(x), describes the transformation of the parent function f(x)=2^x.
Answers
If the parent function is transformed by:
Shifting 1 unit to the right, the image function is given by g(x) = (x - 1)²Shifting 1 unit to the left, the image function is given by g(x) = (x + 1)².Shifting 1 unit downward, the image function is given by g(x) = x² - 1.Transformation of the parent function.The graph of the parent function is a parabolic curve which opens in the y-axis direction and with its vertex at the origin on a cartesian coordinate.
By critically observing the graph of this parent function [f(x) = x²], we can infer and logically deduce that the transformed curve is a downward opening parabola which has a vertex at (-5, -2).
Thus, if the parent function is transformed by:
Shifting 1 unit to the right, the image function is given by g(x) = (x - 1)²Shifting 1 unit to the left, the image function is given by g(x) = (x + 1)².Shifting 1 unit downward, the image function is given by g(x) = x² - 1.Read more on transformation here: https://brainly.com/question/17586310
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Using traditional methods, it takes 103 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 60 students and observed that they had a mean of 102 hours. Assume the variance is known to be 9. A level of significance of 0.01 will be used to determine if the technique performs differently than the traditional method. Find the value of the test statistic. Round your answer to 2 decimal places. Enter the value of the test statistic.
Answers
The test statistic based on the probability illustrated is -2.57.
How to calculate the probability?The basic training is given as 103 hours. The variance is also given as 9.
The test statistic will be:
= (102 - 104/3/✓60)
= -1/(3/7.7)
= -2.57.
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39. Solve for x. SHOW ALL WORK FOR FULL CREDIT m n 6x-4 112°
Answers
Answer:
x = 12
Step-by-step explanation:
6x - 4 and 112 are same- side interior angles and sum to 180° , that is
6x - 4 + 112 = 180
6x + 108 = 180 ( subtract 108 from both sides )
6x = 72 ( divide both sides by 6 )
x = 12
Answer:
x = 12
Step-by-step explanation:
Consecutive Interior Angles Theorem
When a straight line intersects two parallel straight lines, the consecutive interior angles formed are are supplementary (sum to 180°).
Therefore:
⇒ 6x - 4 + 112 = 180
⇒ 6x + 108 = 180
⇒ 6x + 108 - 108 = 180 - 108
⇒ 6x = 72
⇒ 6x ÷ 6 = 72 ÷ 6
⇒ x = 12
Let f(x)=4x-1 and g(x)=2x^2+3
(f+g)(x)
Answers
Step-by-step explanation:
(f+g)(x)=4x-1+2x²+3===> 2x²+4x+2
.....................
Answers
Answer: 5020
Step-by-step explanation:
10^3= 1000
1000*5.02=5020
Explain how to draw a line segments that measures 2 7/16 inches.
Answers
Answer: draw the line using a ruler on which you have identified points 2 7/16 inches apart.
Step-by-step explanation: On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches long.
PLEASE HELP AND GIVE A FULL EXPLANATION I WILL GIVE BRAINLEST PLEASE SOMEONE
Answers
Answer:
shown in explanation
Step-by-step explanation:
a) ∆EPB similar to ∆ERG
b) angle BEP = angle GER (common angle shared)
angle EPB = angle ERG (corresponding angles, PB//RG, parallelogram)
therefore through Angle-Angle similarity test, ∆EPB is similar to ∆ERG
or explanation can also be shortened to
∆EPB is similar to ∆ERG (AA, similarity)
c) since proven they are similar ∆, then we can proceed to use property of ratio of corresponding sides being equal
[tex] \frac{pb}{rg} = \frac{ep}{er} [/tex]
RG = 200+300=500m
[tex] \frac{200}{500} = \frac{ep}{ep + 350} [/tex]
cross multiply (from what I've learnt)
2ep+700=5ep
ep= 700/3 = 233 ⅓m (answer for length EP)
Do the same for length BE(using ratio of corresponding sides)
[tex] \frac{be}{ge} = \frac{pb}{rg} [/tex]
[tex] \frac{be}{be + 400} = \frac{200}{500} [/tex]
cross multiply again to get:
5BE = 2BE + 800
BE = 800/3 = 266 ⅔ m (answer for length BE)
The value of Kayla's investment can be modeled by the equation y=2650(1.05)x where x is the number of years invested and y is the value in dollars. What will be the value of the investment after 25 years? Round your answer to the nearest dollar.
Answers
Answer:
8,974 dollars
Step-by-step explanation:
y=2650.(1.05)^x
x=25
2650(1.05)^25 = 8974 dollars
Solve equation -1/9 / (-1/3)
Answers
Answer: 1/3
Step-by-step explanation:
-1/9 / -1/3 = ?
Keep: -1/9
Change: *
Flip: -3/1
Solve: -1/9 * -3/1 = 3/9
Simplify: 1/3
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{-\dfrac{1}{9}\div - \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{-\dfrac{1}{9}\div - \dfrac{1}{3}}[/tex]
[tex]\huge\textsf{Convert:}[/tex]
[tex]\mathsf{= -\dfrac{1}{9} \times -\dfrac{3}{1}}[/tex]
[tex]\huge\textsf{Multiply:}[/tex]
[tex]\mathsf{= \dfrac{-1\times3}{9\times -1}}[/tex]
[tex]\mathsf{= \dfrac{-3}{-9}}[/tex]
[tex]\mathsf{= \dfrac{-3 \div -3}{-9\div-3}}[/tex]
[tex]\mathsf{= \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\dfrac{1}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
I need some help with this question for a self-taught course
Answers
The support pole must be approximately 7.8 meters long.
What is the length of the support pole?
Based on all the information given in the statement, we prepare a geometric diagram that describes the system formed by the high-security fence and the support pole. The representation is attached below. Lastly, the length of the pole is found by using the law of sines:
l/sin 84° = 6 m /sin 50°
l = 6 m × (sin 84°/sin 50°)
l ≈ 7.790 m
The support pole must be approximately 7.8 meters long.
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The segment below is dilated by a scale factor of 22 to form I ′J ′ What is the measure of I ′J ′ ?
Answers
Answer:
18
Step-by-step explanation:
When dilating a segment by a scale factor, we multiply the original length by the scale factor to find the length.
2*9 = 18
What’s the volume of this cone?
Answers
volume = (1/3) * π * r² * h
= 1/3* 22/7 * (3.5*3.5) * 5 ( 22/7 is the value of π)
=64.1
Answer:
If you need a pi in your answer: 20.417 [tex]\pi[/tex] (rounded to the nearest thousanth)
If you don't: 64.141 (rounded to the nearest thousanth)
Step-by-step explanation:
The formula of the volume of a cone: [tex]V = \pi r^2\frac{h}{3}[/tex]
--> V = Volume, r = Radius, h = Height
In other words, the volume of the cone is the area of the circle x height x 1/3 x pi.
Since the radius of the cone is 3.5, you square that number.
--> (3.5)^2 = 12.25
The height is 5, so h/3 will be 5/3.
The volume = [tex]\pi[/tex] x 12.25 x 5/3
--> 20.416666... [tex]\pi[/tex]
--> 64.14085....
Special Right Triangles
Find x.
Answers
Answer:
8
Step-by-step explanation:
The cos of 30 is [tex]\sqrt{x}[/tex] / 2. Since the adjacent angle is 4 times that. We would multiply 2 x 4 and get 8
ramon is a parking lot attendant. he estimates that 30% of the cars in the lot are sedans, 10% are minivans, and 20% are suvs. he designs a simulation. let 0,1, and 2 represent sedans. let 3 represent minivans. let 4 and 5 represent suvs. let 6,7,8 and 9 represent other cars. the table show the simulation results. what is the probability that at least one of the next four cars the enter the lot is a sedan?
Answers
The probability that the nest set of cars that would enter the lot is a sedan is given as 80 percent
How to solve for the probabilityThe total number of trials can be seen to be 20 in number. The numbers that represents the sedan are 0, 1, 2
Now we would have to count the number of trials in these 20 that have 0, 1, 2
In the table we have 16 of these 0, 1 or 2 numbers
Hence we would have
16 /20
= 0.8
= 80 percent
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2. Which of the following graphs show a function with domain 1 ≤ x ≤ 6? Select two that
apply.
Answers
Answer:
Graphs A and B
Step-by-step explanation:
Graphs A & B are using x-values 1-6 and stop there, which is what the domain is trying to find. Though, for the other graphs, these graphs are rather starting at 1 via the domain, while not going up to 6 on the domain.
Can someone please explain the steps to get too the second answer also please answer too thank you
Answers
Explanation :
So y = x × 9. Then if x = 9, mutiply it by 9 and equals 81.
Hope it helps !
WILL GIVE BRAINLIEST
given: RTSU is a rectangle with vertices R (0,0), S (0, a), T(a,a) and U, (a,0) where a ≠ 0
Prove: RTSU is a square
look at image
Answers
The correct order of reasons that complete the proof about the rectangle and square is that D. definition of congruence, distance formula if two consecutive sides of a rectangle are congruent, then it's a square.
What is congruence?It should be noted that congruence simply means an agreement or a correspondence between shapes.
In geoemtry, it should be noted that figures are said to be congruent if it is possible to superpose one of them on another.
It should be noted that the opposite sides of a rectangle are parallel while in a square, all the sides that are given are equal.
Therefore, the correct order of reasons that complete the proof about the rectangle and square is the definition of congruence, and that if two consecutive sides of a rectangle are congruent, then it's a square.
In conclusion, the correct option is D.
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Please answer ASAP need steps.
Answers
Answer:
The ANSWER is 1/2 x (3/5) : (9/15) (-6/4) : (4/1) = -3/16 = -0.1875
Step-by-step explanation:
Multiple: 1/2 * 3/5 = 1 · 3/2 · 5 = 3/10
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(3, 10) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one half multiplied by three fifths is three tenths.
Divide: the result of step No. 1 : 9/15 = 3/10 : 9/15 = 3/10 · 15/9 = 3 · 15/10 · 9 = 45/90 = 45 · 1/45 · 2 = 1/2
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 9/
15 is 15/9) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 45 gives 1/2.
In other words - three tenths divided by nine fifteenths is one half.
the result of step No. 2 * (-6/4) = 1/2* (-6/4) = 1 · (-6)/2 · 4 = -6/8 = -3 · 2/4 · 2= -3/4
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-6, 8) = 2. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one half multiplied by minus six quarters is minus three quarters.
Divide: the result of step No. 3 : 4 = -3/
4 : 4 = -3/4 · 1/4 = -3 · 1/4 · 4 = -3/16
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 4/
1 is 1/4) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - minus three quarters divided by four is minus three sixteenths.
look at the pictures
Answers
Factorize and get the value of x and then substitute into any of the equation to get the solution in coordinate form (x, y)
Inequality functionsFor us to determine if a set of inequality function has a solution, we will equate the functions and determine the point of intersection if there are any,
Given the inequalities
y ≤ x^2 - 3
y > -x^2 + 2
Equate
x^2 - x = -x^2 + 2
Collect like terms
2x^2 - x - 2 = 0
In order to determine the value of x, we will factorize and get the value of x and then substitute into any of the equation to get the solution in coordinate form (x, y)
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