Solution :
Given parametric equation for :
[tex]$x=1+2 \sqrt t$[/tex]
[tex]$y=t^3-t$[/tex]
[tex]z=t^3+t[/tex]
The point is (3, 0, 2)
The vector equation is equal to :
[tex]$r(t) = \left<1+2 \sqrt t, t^3 -t, t^3+t \right>$[/tex]
Solving for r'(t) by differentiating each of the components of r(t) w.r.t. to t,
[tex]$r'(t)= \left< \frac{1}{\sqrt t}, \ 3t^2-1, \ 3t^2+1 \right>$[/tex]
The parameter value corresponding to (3, 0, 2) is t = 1. Putting in t=1 into r'(t) to solve for r'(t), we get
[tex]$r'(1) = \left< \frac{1}{\sqrt 1}, \ 3(1)^2-1, \ 3(1)^2+1 \right>$[/tex]
We know that parametric equation for line through the point [tex]$(x_0, y_0, z_0)$[/tex] and parallel to the direction vector <a, b, c > are
[tex]$x=x_0+at$[/tex]
[tex]$y=y_0+bt$[/tex]
[tex]z=z_0+ct[/tex]
Now substituting the [tex]$(x_0, y_0, z_0)$[/tex] = (3, 0, 2) and <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get:
[tex]$x=3+(1)t$[/tex]
x = 3 + t
y = (0) + (2)t
y = 2t
z = (2) + (4)t
z = 2 + 4t
A cosmetics salesman earns a basic wage of $2000 per month plus 10% commission on all sales he makes. Calculate his total wage for the month when he sold $89,000 worth of cosmetics.
Which of the following fraction pairs are equivalent?
Answer:
8/12 and 12/18
Step-by-step explanation:
8/12 and 12/18
both equal 2/3
The expression w^4 - 36 is equivalent to
Answer:
(w² + 6)(w² - 6)
Step-by-step explanation:
difference of squares
w⁴ - 36 = (w² + 6)(w² - 6)
Round 51,939 to the nearest thousands
Answer:
50,000
Step-by-step explanation:
in my opinion I would think this would be the answer because you are rounding to the nearest 10,000
Which is the polynomial function of lowest degree with leading coefficient of 4 and roots 7 and 3?
O f(x)= x2 – 3x-+3-17
O f(x)= 4x² -1245x+3/7
O f(x)=x2 – 3x? – X+21
O x) = 4x° - 12x - 28x+84
Answer:
Step-by-step explanation:
If the roots are 7 and 3, then x = 7 and x = 3 are solutions. In factor form, x = 7 is (x - 7); in factor form, x = 3 is (x - 3). We FOIL these together to get
[tex]x^2-3x-7x+21[/tex] which simplifies to
[tex]x^2-10x+21[/tex] and we distribute in the 4:
[tex]4(x^2-10x+21)[/tex] to get
[tex]4x^2-40x+84[/tex] which is another way to write the last choice you're given.
Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.)
f(x) = 8|x − 6|
f(−2) =
f(0) =
f (1/2)=
f(2) =
f(x + 1) =
f(x2 + 7) =
Step-by-step explanation:
my answer is in the image above
Find the 22nd term of the arithmetic sequence whose common difference is d =3 and whose first term is a_1=-20
Q2 find the degree of the polynomial
x4(4x+1)
Step-by-step explanation:
x⁴(4x+1)
4x⁵+x⁴
degree is 5
Find the difference quotient of f; that is, find f(x+h)-f(x) , h ≠ 0 for the following function
f (x)=6x+8
f(x+h)-f (x)/h =
Which is the graph of the function y = 3x?
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The graph that includes the point (1, 3) will be the one that is a graph of ...
y = 3^x
What is the slope of the line passing through (-3, 5) and (5, -3)?
Answer:
The line has a slope of -1.
Step-by-step explanation:
To solve for the slope of the line, use the rise over run formula. The rise over run formula is a measure of how much something changes vertically compared to how much it changes in the horizontal direction. The rise over run formula calculates the difference between the two points in the vertical direction (rise) and then divide it by the difference in the horizontal direction (run). The formula looks like [tex]\frac{rise}{run}[/tex], but in terms of finding a slope, it looks like [tex]\frac{y_{2 }-y_{1} }{x_{2} -x_{1} }[/tex].
For finding the slope of this line with the points (-3,5) and (5,-3), start by writing down the information given from the question.
[tex]y_{2}=-3[/tex]
[tex]y_{1}= 5[/tex]
[tex]x_{2}=5[/tex]
[tex]x_{1} =-3[/tex]
Next, plug in the information given from the question into the formula, and the formula will look like [tex]\frac{-3-(5)}{5-(-3)}[/tex]. Then, simplify the equation, which will look like [tex]\frac{-8}{8}=-1[/tex]. The final answer will be -1.
A company needs to hire a new director of advertising. It has decided to try to hire person A or B, who are assistant advertising directors for its major competitor. To decide between A or B, the company finds that A is in charge of 2/3 of the total accounts while Peron B is in charge of only 1/3 of the accounts. Also, A’s campaigns have satisfactory results 3 out of 4 times, while B’s campaigns has satisfactory results only 2 out of 5 times. Suppose one of the competitors ad campaigns is selected randomly
a) Draw the tree diagram of the info above
b) Find the probability that A is in charge of the selected campaign and that is produces satisfactory results
c) Find the probability that the selected campaign is satisfactory
Answer:
b) 0.5
c) 0.633
Step-by-step explanation:
a) Please find the attached image - tree diagram
b) b) The probability that A is in charge of the selected campaign and that it produces satisfactory results = 2/3 * 3/4 = 1/2 = 0.5
c) P (selected campaign is satisfactory)
= P(A's campaign and satisfactory) + P(B's campaign and satisfactory)
= 2/3*3/4 + 1/3*2/5
= 0.6333
The table shows the displacement-time data for a ship relative to a shore.
t(hours) 2.95 3.15 3.75 3.95 3.99 4.00
s(0 (miles) 14.95 17.61 27.23 31.01 31.80 32.00
Estimate the instantaneous velocity of the ship at t = 4 hours.
A.
20.00 mi./h.
B.
20.15 mi./h.
C.
20.25 mi./h.
OD.
20.50 mi./h.
Answer:
Step-by-step explanation:
Which of the following is not an example of a parent function?
y=x
y=2x^3
y=1/2
y=2^x
9514 1404 393
Answer:
(b) y=2x^3
Step-by-step explanation:
The function y=2x^3 is an example of the parent function y=x^3 being vertically scaled by a factor of 2. As such, it is not the parent function.
_____
Additional comment
A parent function is one that has not been translated or scaled in any way. One could argue that the parent function of the form y=constant is y=1, so that the function y=1/2 has been scaled by a factor of 1/2. In this problem, we recognize the parent function y=x^3 has clearly been scaled to get y=2x^3, so the latter is not an example of a parent function.
If this is a "check all that apply" question, then y=1/2 is another reasonable answer.
Answer:(b) y=2x^3
Step-by-step explanation:
Olivia can bake 95 cookies in 5 hours. At this rate, how many cookies can she bake
in 11 hours?
Answer:
Olivia will make 209 cookies on 11 hours
Step-by-step explanation:
if she makes 95 per 5 hours
we can make
5 + 5 = 10
this is the same as doing
95 + 95 = 190
now, for the 1 hour
95 : 5 = 19
now to verify it
19 x 5 = 95
now you make
95 + 95 + 15 = 209
Oops, srry my bad, i fixed the thing i did wrong
I need help with this math problem please
Answer:
option D
Step-by-step explanation:
[tex]9x^2 + 6x - 17 = 0 , \ where \ a = 9 \ , \ b = 6 \ , c = - 17[/tex]
[tex]x = \frac{ - b \ \pm \sqrt{b^2 - 4ac}}{2a} \\\\x = \frac{-6 \pm \sqrt{36 - (4 \times 9 \times -17)}}{2 \times 9}\\\\x = \frac{-6 \pm \sqrt{ 36 + 612}}{18}\\\\x = \frac{-6 \pm \sqrt{ 648}}{18}\\\\x = \frac{-6 \pm \sqrt{ 2^3 \times 3^4}}{18}\\\\x = \frac{-6 \pm \sqrt{2 \times 2^2 \times 3^ 4 }}{18}\\\\x = \frac{-6 \pm ( 2 \times 9 )\sqrt{ 2}}{18}\\\\x = \frac{-6 \pm 18\sqrt{2}}{18}\\\\x = \frac{-1 \pm 3 \sqrt{ 2}}{3}[/tex]
Darla decides to buy books and magazines with her money. Books cost $16 each and magazines cost $8 each. Write a function that shows the function of the total money that she spends.
Answer:
m=16x+8y
Step-by-step explanation:
let the amount of money she spend be 'm'
m=16x+8y
Answer:
a=16x+8y
Step-by-step explanation:
Let the amt of money she spends be a.
hope it helps!!!
Pls I’ve been stuck on this
Area of a circle is pi x radius^2
Area = pi x 22 ^2
Area = pi x 484
Area = 1,519.8 mm^2
Answer:
1520.5mm²
Step-by-step explanation:
Area of a circle=πr²
π(22mm)²
π484mm²
1520.5308443374599mm²
to one decimal place
1520.5mm²
Jason leaves Detroit at 4:00 PM and drives at a constant speed west along I-94. He passes Ann Arbor, 40 mi from Detroit, at 4:40 PM. (a) Express the distance d traveled in terms of the time t (in hours) elapsed. d(t)
PLEASE HELP ME WILL GIVE BRAINLIEST
Answer:
Reason 5
Step-by-step explanation:
Reason 1 and 2 are Given
Reason 3 is Reflexive
Reason 4 is Side-Side-Side congruency
Answer:
Reason 5
Step-by-step explanation:
It helps to know what CPCTC means and how it's used.
CPCTC means "corresponding parts of congruent triangles are congruent."
To use it, you must first either prove two triangles to be congruent or be given that two triangles are congruent.
Once you have the congruent triangles, then you state that two corresponding parts of those triangles are congruent, and you use CPCTC as the reason.
In step 4, the triangles are proven congruent by SSS.
Then CPCTC can be used as reason 5 for stating that the corresponding angles A and C are congruent.
Triangle Q R S is cut by line segment V W. Point V is the midpoint of side Q S and point W is the midpoint of side R S. The length of Q R is 3 a + 6, the length of V W is 2 a minus 2, and the length of V S is 2 a.
If V is the midpoint of Line segment Q S and W is the midpoint of Line segment R S, then what is VS?
4 units
8 units
10 units
20 units
Answer:
20 units
Step-by-step explanation:
We can see that triangle QRS and triangle VWS are similar triangles.
Similar triangles are triangles in which the ratio of their corresponding sides are in the same proportion.
V is the midpoint of QS.
VS = 2a, QS = 2 * VS = 2(2a) = 4a
Since both triangles are similar triangles, hence:
\begin{gathered}\frac{VS}{QS}=\frac{VW}{QR}\\\\\frac{2a}{4a} =\frac{2a-2}{3a+6} \\\\\frac{2a-2}{3a+6} =\frac{1}{2} \\\\2(2a-2)=3a+6\\\\4a-4=3a+6\\\\a=10\ units\\\\VS=2a=2(10)=20\ units\end{gathered}
QS
VS
=
QR
VW
4a
2a
=
3a+6
2a−2
3a+6
2a−2
=
2
1
2(2a−2)=3a+6
4a−4=3a+6
a=10 units
VS=2a=2(10)=20 units
ur wlcm♥️♥️
Answer:
20 UNITS
Step-by-step explanation:
EDG 2020
What is the standard form polynomial that represents this product?
(-2m3+3m2-m) (4m2+m-5)
Environmental researchers have collected rain acidity data for several decades. They want to see if there is any evidence that attempts to reduce industrial pollution have produced a trend toward less acidic rainfall. They should display their data in a(n)... a. Bar graph b. Time plot c. Histogram d. Box plot
Answer:
Time plot
Step-by-step explanation:
The data from which a plot or graph is to be generated will have only one variable, which is the rain acidity, that is acidity level of Rainfall over a certain period. However, the data gbwre is time dependent, hence, it is a time series plot. Hence, this is a two dimensional univariate plot, with the acidity label of Rainfall on one axis and time on the other. Therefore, the graph which is best to display such information is the time series plot.
What is the distance between the points?
Answer:
[tex] \sqrt{113} [/tex]
Step-by-step explanation:
To find the distance between the two points, apply the distance formula given as:
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Where,
[tex] (-4, -5) = (x_1, y_1) [/tex]
[tex] (4, 2) = (x_2, y_2) [/tex]
Plug in the values
[tex] d = \sqrt{(4 -(-4))^2 + (2 -(-5))^2} [/tex]
[tex] d = \sqrt{(8)^2 + (7)^2} [/tex]
[tex] d = \sqrt{64 + 49} [/tex]
[tex] d = \sqrt{113} [/tex]
The formula in finding the distance between two points is given below:
[tex] \boxed{\bold{\:\:d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \:\:}}[/tex]Now, you know the distance formula. So, let us try solving the given problem using the distance formula.
Problem: Determine the distance between (-4, -5) and (4, 2).
From inspection on the given problem:
[tex]\sf (x_1, y_1) = (-4, -5)[/tex][tex]\sf (x_2, y_2) = (4, 2)[/tex]Substitute the given values into the distance formula and solve for d:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex][tex]\sf d = \sqrt{[4 - (-4)]^2 + [2 - (-5)]^2}[/tex][tex]\sf d = \sqrt{(8)^2 + (7)^2}[/tex][tex]\sf d = \sqrt{64 + 49}[/tex][tex]\bold{d = \sqrt{113} \approx 10.6 \: units}[/tex]Therefore, the distance between two points is [tex]\sqrt{113}[/tex] or 10.6 units.
[tex]\\[/tex]
Now, wasn't that easy? Try this sample problem:
Find the distance between P(1, 3) and Q(7, 11).From the sample problem above, you may solve it on your own to enhance your skill on calculating the distance.
For more information about the Distance Formula, just visit this link: https://brainly.com/question/18156437
Need help ASAP!! Giving brainliest!
High school students across the nation compete in a national financial capability challenge exam. students who score in the top 5 percent get recognized publically for their achievement by the Dept of Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
Answer:
2
Step-by-step explanation:
Follow the 68-95-99.7 rule
The answer is 2 standard deviations
What translation maps ABC to A'B'C'?
help me please it’s timed !!!
While
AB is A. 5Welcome :)how do your find solution to z^5 = *7776i
Answer:
you have to solve for z, z = 6\root(5)(i), this to the power of 5 equals 77761
Step-by-step explanation:
If the diameter of the Ferris wheel is 70 feet across, find the total distance traveled in one revolution.
Answer: Assuming pi is rounded off to 3.14, it is 219.8 feet; if not it is 70π feet
Circumference=one revoloution
Circumference=Diameter times pi
C=Dπ
C=3.14*70
=219.8
219.8 feet