Answer:
a) t = 4
b) v = pi j + 5 k
c) rt = 1i + (pi t) j + (20 +5t )k
Step-by-step explanation:
You have the following vector equation for the position of a particle:
[tex]r(t)=cos(\pi t)\hat{i}+sin(\pi t)\hat{j}+5t\hat{k}[/tex] (1)
(a) The height of the helix is given by the value of the third component of the position vector r, that is, the z-component.
For a height of 20 you have:
[tex]5t=20\\\\t=\frac{20}{5}=4[/tex]
(b) The velocity of the particle is the derivative, in time, of the vector position:
[tex]v(t)=\frac{dr(t)}{dt}=-\pi sin(\pi t)\hat{i}+\pi cos(\pi t)\hat{j}+5\hat{k}[/tex] (2)
and for t=4 (height = 20):
[tex]v(t=4)=-\pi sin(\pi (4))\hat{i}+\pi cos(\pi (4))\hat{j}+5\hat{k}\\\\v(t=4)=-0\hat{i}+\pi\hat{j}+5\hat{k}[/tex]
(c) The vector parametric equation of the tangent line is given by:
[tex]r_t(t)=r_o+vt[/tex] (3)
ro: position of the particle for t=4
[tex]r_o=cos(\pi (4))\hat{i}+sin(\pi (4))\hat{j}+20\hat{k}\\\\r_o=\hat{i}+0\hat{j}+20\hat{k}[/tex]
Then you replace ro and v in the equation (3):
[tex]r_t=(1\hat{i}+20\hat{k})+(\pi \hat{j}+5\hat{k})t\\\\r_t=1\hat{i}+\pi t \hat{j}+(20+5t)\hat{k}[/tex]
Part(a): The value of [tex]t=4[/tex]
Part(b): Required vector [tex]L(t)=(1\widehat{i}+0\widehat{j}+10\widehat{k})+(t-4)(0\widehat{i}+\pi \widehat{j}+5\widehat{k})[/tex]
Given vector equation is,
[tex]r(t)=cos(\pi t)\widehat{i}+sin(\pi t)\widehat{j}+5t\widehat{j}[/tex]
Vector equation:
A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector, and with an arrow indicating the direction.
Part(a):
When the particle has a height of 20
[tex]5t=20\\t=4[/tex]
Part(b):
The point on the curve is [tex](cos(4\pi),sin(4\pi),20) =(1,0,20)[/tex]
Differentiating the given equation with respect to [tex]t[/tex].
[tex]r'(t)=- \pi sin(\pi t)\widehat{i}+\pi cos(\pi t)\widehat{j}+5\widehat{k}\\r'(t)=- \pi sin(4\pi t)\widehat{i}+\pi cos(4\pi t)\widehat{j}+5\widehat{k}\\r'(4)=0\widehat{i}+\pi \widehat{j}+5\widehat{k}\\L(t)=r(4)+(t-4)r'(4)\\L(t)=(1\widehat{i}+0\widehat{j}+10\widehat{k})+(t-4)(0\widehat{i}+\pi \widehat{j}+5\widehat{k})[/tex]
Learn more about the topic Vector equation:
https://brainly.com/question/24906745
The number 65 is decreased to 62. What is the percentage by which the number was decreased, to the nearest tenth of a percent?
Answer:4.6
Step-by-step explanation:
Percentage decrease=(65-62)/65 x 100
Percentage decrease=3/65 x 100
Percentage decrease=(3x100)/65
Percentage decrease=300/65
percentage decrease=4.6
Find the slope, if it exists, of the line containing the points (-1,-15) and (-17,-20)
The slope is _____________________
29. Find the circumference.
11
a. 3.14
b. 69.08
c. 121
Answer:
b.69.08
Step-by-step explanation:
formula:
c=2(pi)r
c=2(pi)11
Answer:b
Step-by-step explanation:
radius=r=11
π=3.14
Circumference=2 x π x r
Circumference=2 x 3.14 x 11
Circumference=69.08
5×60=5×___tens
=_____tens
=______
Answer:
300
Step-by-step explanation:
5x60=5x6 tens it equal to 30 tens. 30 tens equals 300
Answer:
see below
Step-by-step explanation:
there are 6 tens in 60!
5x60 = 5 x 6 tens
= 30 tens
= 300
what is the sum of this arithmetic series? 586+564+542+...+212
Answer:
Basically it's asking for the sum of 212 + 216 + 220 + ..... 586
Each number is 22 more than the previous one.
Therefore the sum will be 212 + (212+22) + (212+22*2) + (212+22*3)
the amount of numbers from 212 through 586 is 18.
Therefore we will need 212 plus 212 * 17 = 3,816 *******************
We will also need all those 22's.
We must add 22 *1 plus 22*2 plus 22*3 ..... plus 22*17
Which equals 22 + 44 + 66 + 88 ... 374
Which totals 3,366 *****************
So, we total 3,816 + 3,366 which equals 7,182
Step-by-step explanation:
[tex]\displaystyle\bf\\Sum=586+564+542+...+212\\\\Sum=212+234+256+...+586\\\\\textbf{We calculate the number of terms (n):}\\\\n=\frac{586-212}{22}+1=\frac{374}{22}+1=17+1=18\\\\\boxed{\bf~n=18~terms}\\\\Sum=\frac{n(586+212)}{2}\\\\Sum=\frac{18\times 798}{2}\\\\Sum=9\times798\\\\\boxed{\bf~Sum=7182}[/tex]
What is the volume of a right circular cylinder with a radius of 5 cm and a height of 12 cm?
Unit Te
4.05 Unit
EN OP
60 cm
120 cm
3007 cm
12007 cm
Answer:742 cm^3
Step-by-step explanation:
Height=h=12cm
Radius=r=5cm
π=3.14
volume of cylinder=π x r^2 x h
Volume of cylinder=π x r x r x h
Volume of cylinder=3.14 x 5 x 5 x 12
Volume of cylinder=742 cm^3
What is the sixth term in the sequence 3, 6, 11, 18
Answer:
38
Step-by-step explanation:
3 to 6 is an add by 3 then 6 to 11 is an add by 5 then 11 to 18 is an add by 7 each add is increased by 2 so the next add will be 9 giving you 27 then you will add 11 because it's increased by two giving you 38
The average mark of c
andidates in an aptitude test was 128.5 with a standard deviation of
8.2. Three scores extracted from the test are; 148, 102, 152. What is the average of the
extracted scores that are extreme values (outliers)?
Answer:
The average of the extracted scores that are extreme values (outliers) = 102
Step-by-step explanation:
With the logical assumption that the population size is large enough, for a normal distribution,
68% of the data lies within 1 standard deviation of the mean.
95% of the data lies between 2 standard deviations of the mean.
99.7% of the data lies within 3 standard deviations of the mean.
So, the outliers for a normal distribution are usually beyond 3 standard deviations of the mean.
The mean = 128.5
Standard deviation = 8.2
The range of scores within 3 standard deviations of the mean is obtainable thus
(Mean ± 3standard deviations)
3 × standard deviations = 3 × 8.2 = 24.6
(128.5 ± 24.6) = (103.9, 153.1)
The 3 extracted scores are 148, 102 and 152. The only extreme value of these 3 extracted scores is 102. The two other scores are within the range of 3 standard deviations of the mean.
Hence, the average of the extracted scores that are extreme values (outliers) = 102
Hope this Helps!!!
To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3,500, and the commission for each new account opened is $5,000. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account.
(a) Determine the equation for computing Gustin's profit per seminar, given values of the relevant parameters. Profit = (New Accounts Opened × ) –
(b) What type of random variable is the number of new accounts opened? (Hint: Review Appendix 11.1 for descriptions of various types of probability distributions.)
(c) Choose the appropriate spreadsheet simulation model to analyze the profitability of Gustin's seminars. (I) (II) (III) (IV) Would you recommend that Gustin continue running the seminars?
(d) How many attendees (in a multiple of five, i.e., 25, 30, 35, . . .) does Gustin need before a seminar's average expected profit is greater than zero?
Answer:
a) profit = (new account opened x 5000) -3500
b) Opening account is binomial distribution with n =25 and p = 0.01
c) Probability of loss is 0.77781 --I don't recommend the company that it running the seminar
d) n ≅ 71
Step-by-step explanation:
See attached image
The height of a triangle is 18 inches. Find the length of the base if the area of the triangle is 63 square inches
Answer:
7 inches
Step-by-step explanation:
The area of a triangle is found by
A = 1/2 bh
We know the height is 18 and the area is 63
63 = 1/2 (b)(18)
63 = 9b
Divide each side by 9
63/9 = 9b/9
7 = b
The base is 7 inches
Answer:
7 inches
Step-by-step explanation:
Area = ½ base × height
63 = ½ × base × 18
63 = 9 × base
base = 7 inches
Solve 20x = 10 for x. A. x = 1/2 B. x = 1.5 C. x = 2 D. x = 10
Answer:
A. 1/2
Step-by-step explanation:
20x=10
Divide 20 on both sides of the equation to get x by itself
20x=10
___. __
20. 20
x =1/2
Answer:
A) x= 1/2
Step-by-step explanation:
20x= 10 we then divide 10 by 20 to get x= 10/20 or if we simplify x= 1/2. Thus answer choice A) is correct!
If the base-ten blocks shown are to be divided into 5 equal groups, what should be done first?
Answer:
2 divided
Step-by-step explanation:
Fie triunghiul ABC isoscel cu AB=AC=3 cm daca mediatoarea laturi AC intersectat cu latura BC in M si perimetrul thriunghiului AMC=12 cm.Calculati MC
Answer:
MC = 4.5cm
Step-by-step explanation:
Question:
Let the isosceles triangle ABC with AB = AC = 3 cm. if the mediator of the sides AC intersects with the side BC in M and the perimeter of the triangle AMC = 12 cm. Calculate MC.
Solution:
Find attached the diagram used in solving the question.
Given:
∆ABC is an isosceles triangle (two sides and angles are equal)
AB = BC = 3cm
Perimeter of ∆AMC = 12cm
From the diagram, M cuts AC at the the middle.
AD = CD = AC/2 = 3/2
Perimeter of Right angled ∆AMD = AM + AD + MD
= 3/2 + AM +MD
Perimeter of Right angled ∆CMD =CM + CD + MD
= 3/2 + CM +MD
Right angled ∆AMD = Right angled ∆CMD
CM = AM
Therefore ∆AMC is an isosceles triangle
CM = AM (two sides of an isosceles triangle are equal)
Let CM = AM = x
Perimeter of ∆AMC = AM + CM + AC
12 = x + x + 3
12 = 2x + 3
2x = 12-3
2x = 9
x = 9/2 = 4.5
CM = AM = 4.5cm
MC = CM = 4.5cm
please help me with this question
Answer: yes
Step-by-step explanation:
Answer:
Step-by-step explanation:
A = 3
B = 5.5
C = 11
Simplify the expression below.
14a8y3 - 7 Ay5 + 28a12y2
7aty
A.
OB.
2a²y3 - ay5 + 4a3y2
2a4y? - JA + 428 y
2a4y3 – 5 + 428 y?
D. 2012,4 - 2876 +4215,3
C.
Answer:
14a8y3 - 7 Ay5 + 28a12y2- 7ay2 • (4a11 + 2a7y - y3)
Step-by-step explanation:
Equation at the end of step 1 :
(((14•(a8))•(y3))-(7a•(y5)))+((22•7a12)•y2)
Step 2 :
Equation at the end of step 2 :
(((14•(a8))•(y3))-7ay5)+(22•7a12y2)
Step 3 :
Equation at the end of step 3 :
(((2•7a8) • y3) - 7ay5) + (22•7a12y2)
Pull out like factors
Answer: 7ay2 • (4a11 + 2a7y - y3)
Hope this helps.
Sam conducted a survey to determine your favorite flavor of ice cream is his hometown. 15 of the 50 people he surveyed liked strawberry best. How many of the 3,500 residents in the town would you expect to like strawberry best
Answer: 1050 people.
Step-by-step explanation: It's a rule of three question.
15/50 as x/3500
Then you have that 50x = 52500
x = 1050
There you have it.
Please help ASAP! I will mark BRAINLIEST! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY
Answer:
D. 96
F. 32
Step-by-step explanation:
The inequality 3x ≥ 96, means that x and 3 must be multiplied to get a product that is greater than 96. So to figure this out, you must plug in the numbers given for x, like so:
3x ≥ 96
A. 3(31) ≥ 96
93 ≥ 96 This is incorrect since 93 is not greater than 96
A tip that makes this easier is that, you can see that 31 multiplied by 3 is 93, which is only a couple numbers off 96, so all numbers after 31 will result in a product greater than 96. For example:
D. 3(96) ≥ 96
288 ≥ 96 This inequality is correct
F. 3(32) ≥ 96
96 ≥ 96
The inequality sign states that the number must be either greater or equal to 96, which it is.
Help ! I don’t know if I have it correct. Can somebody check it out. I got 81/65536 which I know has to be incorrect.
Work Shown:
In the numerator, we have 2^2*x^2, which is really just 4x^2. Replace x with 3 and we get 4*x^2 = 4*3^2 = 36.
For the denominator, xy^2, we get
x*y^2 = 3*2^2 = 12
So far we have,
[tex]\frac{2^2x^2}{xy^2} = \frac{4x^2}{xy^2} = \frac{36}{12} = 3\\\\\text{ or simply} \\\\\frac{2^2x^2}{xy^2} = 3[/tex]
when x = 3 and y = 2.
Square both sides to end up with...
[tex]\frac{2^2x^2}{xy^2} = 3\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 3^2\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 9[/tex]
What is the classification for this polynomial?
7
Click on the correct answer.
monomial
binomial
trinomial
Answer:
7 is monomial
Step-by-step explanation:
An expression with only one term is called a monomial
✌️;)
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
A. X=6 only
Step-by-step explanation:
Can someone answer I barely have any points now :(
A. True, a rhombus is a parallelogram with equal sides. A rhombus has four congruent sides.
B. True, but there are two other ways to find the area of a rhombus: there is the "diagonals" method and the "trigonometry" method.
C. False, the area of a rhombus is not less than the area of a parallelogram because it will depend on the diagonals.
D. False, a parallelogram is not always a rhombus because the dimensions and other attributes of a parallelogram may vary while the rhombus will remain equal for all aspects.
E. True, if you use the base times height formula but if you used any of the other formulas this would be false.
What if f(x)=(1/7)(7x), what is f(3)
Answer:
3
Step-by-step explanation:
f(x) = (1/7)(7x) can be simplified to ...
f(x) = x
Then for x=3, ...
f(3) = 3
A recent survey showed 3 out of 65 Happy Meals contained a “special” prize. How many “special” prizes should a person expect to win if 130 Happy Meals were purchased?
Answer:
6
Step-by-step explanation:
The ratio would be 3:65, so to get it to ?:130 you would multiply by 2 (65•2=130). So all you have to do is do 3•2=6 to get the correct ratio which is 6:130. So that answer would be 6.
Need help on this assignment it is due VERY SOON
All have something to do with area of composite figures. Please help. I'd be very greatful.
Answer
the first photo answer is 174 (2nd photo is A) Answer to 3rd photo is 72. The last photo is 8100 ft²
Step-by-step explanation:
1st Photo
12 x 12 is 144
5 times 12 divided by 6 - (5 x 6) 30
144 plus 30 is 174
2nd Photo
3 x 5 15
15 is A
3rd Photo
6 x 12 is 72
72 for 3rd Photo
4th Photo
90 x 90 is
8,100
What point appears to be the solution to the system of
equations shown in the graph?
Answer:
x = -2
y= -5
is the solution of the system of equations
What is the slope of the line
Answer:
4/5
Step-by-step explanation:
There are so many points on the graph whose coordinates are impossible to estimate. Look for two "nice" points--points with integer coordinates. The line passes through (-2, 0) and (3, 4).
Slope = rise / run. It's the ratio of vertical change to horizontal change as you move from one point on the line to another.
Moving from (-2, 0) to (3, 4), the vertical change is 4 - 0 = 4.
The horizontal change is 3 - (-2) = 5.
The slope is 4/5
The base of a parallelogram measures 14 cm, and the height is unknown. The area of the parallelogram is more than 42 square cm. Which graph represents all possible values for the height of the parallelogram?
A number line going from negative 1 to positive 7. An open circle is at 3. Everything to the right of the circle is shaded.
A number line going from negative 1 to positive 7. An open circle is at 3. Everything to the left of the circle is shaded.
A number line going from 24 to 32. An open circle is at 28. Everything to the right of the circle is shaded.
A number line going from 24 to 32. An open circle is at 28. Everything to the left of the circle is shaded.
Answer:
A number line going from negative 1 to positive 7. An open circle is at 3. Everything to the right of the circle is shaded.
Step-by-step explanation:
The area of a parallelogram is given by the formula ...
A = bh
So, we have the condition that ...
A > 42
bh > 42 . . . . . substitute the expression for area
14h > 42 . . . . fill in the given base
h > 3 . . . . . . . divide by 14
Numbers greater than 3 are to the right of 3 on the number line.
_____
The relation is > rather than ≥, so the "or equal to" case is not included. That is why the circle is open, rather than solid.
Answer:
a).
Step-by-step explanation:
What’s the correct answer for this?
Solve (x + 6)2 = 64.
Answer:
x=26
Step-by-step explanation:
(x+6)2=64
x+6=32
x=26
Answer:
Here is the solution. Mark as brainlist please.
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY
Answer:
E 39
Step-by-step explanation:
x+6 = 45
Subtract 6 from each side
x+6-6 = 45-6
x = 39
