It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.
Let θ be the angle between the force vector F and the displacement vector r. The work W done by F in the direction of r is
W = F • r cos(θ)
The cosine of the angle between the vectors can be obtained from the dot product identity,
a • b = ||a|| ||b|| cos(θ) ==> cos(θ) = (a • b) / (||a|| ||b||)
so that
W = (F • r)² / (||F|| ||r||)
For instance, if F = 3i + j + k and r = 7i - 7j - k (which is my closest guess to the given vectors' components), then the work done by F along r is
W = ((3i + j + k) • (7i - 7j - k))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))
==> W ≈ 5.12 J
(assuming F and r are measured in Newtons (N) and meters (m), respectively).
What is tan 0 when csc 0= 2/3
Answer:
[tex]\tan{\theta} = \frac{\sqrt{11}}{11}[/tex]
Step-by-step explanation:
Cosecant:
The cosecant is one divided by the sine. Thus:
[tex]\csc{\theta} = \frac{1}{\sin{\theta}}[/tex]
Tangent is sine divided by cosine, so we first find the sine, then the cosine, to find the tangent.
Sine and cosine:
[tex]\sin{\theta} = \frac{1}{\csc{\theta}} = \frac{1}{2\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{6}[/tex]
[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]
[tex]\cos^{2}{\theta} = 1 - \sin^{2}{\theta}[/tex]
[tex]\cos^{2}{\theta} = 1 - (\frac{\sqrt{3}}{6})^2[/tex]
[tex]\cos^{2}{\theta} = 1 - \frac{3}{36}[/tex]
[tex]\cos^{2}{\theta} = \frac{33}{36}[/tex]
First quadrant, so the cosine is positive. Then
[tex]\cos^{2}{\theta} = \sqrt{\frac{33}{36}} = \frac{\sqrt{33}}{6}[/tex]
Tangent:
Sine divided by cosine. So
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{\frac{\sqrt{3}}{6}}{\frac{\sqrt{33}}{6}} = \frac{\sqrt{3}}{\sqrt{33}} = \frac{\sqrt{3}}{\sqrt{3}\sqrt{11}} = \frac{1}{\sqrt{11}} \times \frac{\sqrt{11}}{\sqrt{11}} = \frac{\sqrt{11}}{11}[/tex]
The answer is:
[tex]\tan{\theta} = \frac{\sqrt{11}}{11}[/tex]
John estimated the height of his office building to be 13m . The actual height of his office building was 14.7m .
Find the absolute error and the percent error of John's estimate. If necessary, round your answers to the nearest tenth.
Answer:
Percent error = 11.6%
Step-by-step explanation:
Given the following data;
Actual height, A = 14.7 m
Estimated height, E = 13 m
a. To find the absolute error;
Absolute error = A - E
Absolute error = 14.7 - 13
Absolute error = 1.7
b. To find the percent error;
Percent error can be defined as a measure of the extent to which an experimental (estimated) value differs from the actual or theoretical value.
Mathematically, it is given by this expression;
[tex] Percent \; error = \frac {experimental \;value - theoretical \; value}{ theoretical \;value} *100[/tex]
Substituting into the equation, we have;
[tex] Percent \; error = \frac {13 - 14.7}{14.7} *100[/tex]
[tex] Percent \; error = \frac {1.7}{14.7} *100[/tex]
[tex] Percent \; error = 0.1157 *100[/tex]
Percent error = 11.57 ≈ 11.6%
Evaluate -2yx - 4y what's the answer
Answer:
-2y (x+2)
Step-by-step explanation:
remove greatest common factors.
both terms have a (y) and a (-2)
Answer:
-2y ( x - 2 )
Step-by-step explanation:
- 2yx - 4y
factor out -2y from the equation
-2y ( x - 2 )
3x + 1 over 4y2
What is the value of the expression above when x = 3 and y = 4? You must show all work and calculations to receive full credit.
Answer: Pretty sure its the value of the expression is 11
Step-by-step explanation:
Step 1. Add and evaluate 4x and 1/3y^2
Step 2. After evaluating, add 4(2) and 1/3 (3)^2
Step 3. 8 + 1/3(9)
Step 4. 8 + 3 = 11
Step 5. Value of Expression = 11
Answer:
13
Step-by-step explanation:
What is the equation of the following line? Be sure to scroll down first to see
(-1/2, 3) (0,0)
A. y = 1/2 X
B. y = -1/2 X
C. y = 3 X
D. y= 2X
E. y= 6
F. y= -6

a p e x :(
Answer: (f)
Step-by-step explanation:
Given
Line that passes through [tex](-\frac{1}{2},3)[/tex] and [tex](0,0)[/tex]
Using two point form, equation of a line is given by
[tex]\Rightarrow \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Insert the values
[tex]\Rightarrow \dfrac{y-0}{x-0}=\dfrac{3-0}{-\frac{1}{2}-0}\\\\\Rightarrow \dfrac{y}{x}=-6\\\\\Rightarrow y=-6x[/tex]
Thus, option (f) is correct
Can I get the awnsers for these two? Any help is appreciated.
Answer:
y = 4x - 5
Step-by-step explanation:
for slope intercept form
y = mx + c
where m is the slop so
M = 4
point = (1, -1)
a point on the line must satisfy the equation so replacing y and x by -1 and 1 respectively to get to c.
-1 = 4 × 1 + c
-1 - 4 = c
-5 = c
placing these values in y = mx + c
y = 4x - 5
Answer:
y = 4x - 5.
Step-by-step explanation:
First write it in point-slope form:
y - y1 = m(x - x1)
y - (-1) = 4(x - 1)
y + 1 = 4x - 4
y = 4x - 4 - 1
y = 4x - 5. <------- Slope-intercept.
Question 5
Refer to the data that you recorded in part D. In each row, compare the slope of ABto the slope of the perpendicular line. What is the
relationship between the two slopes? What conclusion can you draw about the relationship between the slopes of any two perpendicular lines?
Ok
Answer:
Step-by-step explanation:
Answer:
The product of the slopes of and the line perpendicular to through C is -1 in all cases. So, I can conclude that any two perpendicular lines have slopes that are negative reciprocals of each other.
Step-by-step explanation:
its correct
see image for question
Answer:
no because it is apporxametely 1/4th of the pizza
Step-by-step explanation:
this is not a trick question, anyone adding more than 2 sentances on their explanation is tricking themselves and is thinking too hard
Answer:
No I actually received 1/4 of the pizza
Step-by-step explanation:
Piece B shows 1/4 of the pizza meaning I'm receiving less than half of the pizza
If I receiveed 2/4 of the pizza, it would've maked senes for me to receive 1/2 of the pizza because 2/4 = 1/2
Anita had $400 in her savings account when she went to college. Her parents will add $200 to her account each month.
Miguel had $25 in his savings account. His parents will double the amount in his account each month.
If Anita and Miguel do not take any money from their accounts, whose account will grow faster? Explain why.
Answer:
Miguel's account
Step-by-step explanation:
Miguel's account savings are doubled every month. Hence, they will eventually surpass the savings of Anita, even though Anita's account has more money atm.
Answer:
Miguel's account
Step-by-step explanation:
Even though Anita had more money at first compared to Miguel, Miguel savings will double each month while Anita will get only $200 each month. As a result, Miguel's account will grow faster compared to Anita's.
Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation for the sphere of radius 5 centered at the origin incylindricalcoordinates.(b) Write an equation for a cylinder of radius 1 centered at the origin and running parallel to thez-axis inspherical coordinates.
To find:
(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates
(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates
Solution:
(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:
[tex](x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}[/tex]
Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,
[tex]a=b=c=0,p=5[/tex]
That is, the equation of the sphere in cartesian coordinates is,
[tex](x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}[/tex]
[tex]\Rightarrow x^{2}+y^{2}+z^{2}=25[/tex]
Now, the cylindrical coordinate system is represented by [tex](r, \theta,z)[/tex]
The relation between cartesian and cylindrical coordinates is given by,
[tex]x=rcos\theta,y=rsin\theta,z=z[/tex]
[tex]r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z[/tex]
Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,
[tex]r^{2}+z^{2}=25[/tex]
This is the required equation of the given sphere in cylindrical coordinates.
(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.
That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,
[tex](x-a)^{2}+(y-b)^{2}=p^{2}[/tex]
Here, it is given that the center is at origin & radius is 1. That is, here, we have, [tex]a=b=0,p=1[/tex]. Then the equation of the cylinder in cartesian coordinates is,
[tex]x^{2}+y^{2}=1[/tex]
Now, the spherical coordinate system is represented by [tex](\rho,\theta,\phi)[/tex]
The relation between cartesian and spherical coordinates is given by,
[tex]x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi[/tex]
Thus, the equation of the cylinder can be rewritten in spherical coordinates as,
[tex](\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1[/tex]
[tex]\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1[/tex]
[tex]\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1[/tex]
[tex]\Rightarrow \rho^{2} sin^{2}\phi=1[/tex] (As [tex]sin^{2}\theta+cos^{2}\theta=1[/tex])
Note that [tex]\rho[/tex] represents the distance of a point from the origin, which is always positive. [tex]\phi[/tex] represents the angle made by the line segment joining the point with z-axis. The range of [tex]\phi[/tex] is given as [tex]0\leq \phi\leq \pi[/tex]. We know that in this range the sine function is positive. Thus, we can say that [tex]sin\phi[/tex] is always positive.
Thus, we can square root both sides and only consider the positive root as,
[tex]\Rightarrow \rho sin\phi=1[/tex]
This is the required equation of the cylinder in spherical coordinates.
Final answer:
(a) The equation of the given sphere in cylindrical coordinates is [tex]r^{2}+z^{2}=25[/tex]
(b) The equation of the given cylinder in spherical coordinates is [tex]\rho sin\phi=1[/tex]
Jacob knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help him see if college students are different from the adult population. From a sample of 101 students, Jacob tabulated that his sample of students got an average of 7.3 hours of sleep each night, with a standard deviation of 2.6.
Required:
What is the t- statistic that Jacob calculates?
Answer:
The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]
Step-by-step explanation:
Jacob knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help him see if college students are different from the adult population.
At the null hypothesis, we test if the mean is of 8 hours, that is:
[tex]H_0: \mu = 8[/tex]
At the alternative hypothesis, we test if the mean is different of 8 hours, that is:
[tex]H_1: \mu \neq 8[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
8 is tested at the null hypothesis:
This means that [tex]\mu = 8[/tex]
From a sample of 101 students, Jacob tabulated that his sample of students got an average of 7.3 hours of sleep each night, with a standard deviation of 2.6.
This means that [tex]n = 101, X = 7.3, s = 2.6[/tex]
What is the t-statistic that Jacob calculates?
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{7.3 - 8}{\frac{2.6}{\sqrt{101}}}[/tex]
[tex]t = -2.71[/tex]
The t-statistic that Jacob calculates is [tex]t = -2.71[/tex]
Seven-eighths of a number is -35. What is the number?
Let the number be x
7/8 of the number is 7/8x and it equals -35:
7/8x = -35
Find x by dividing both sides by 7/8
When you divide by a fraction, flip the fraction over and then multiply:
x = -35 x 8/7 = (-35 x 8) / 7 = -280/7 = -40
The number is -40
I cannot get the range on this one right, can someone help? I had (-infinity, -5) and it said it was wrong.
Answer and Step-by-step explanation:
Try putting a bracket ( ] ), so it looks like this:
(-infinity, -5]
this is because the -5 is included and that's where it stops.
#teamtrees #PAW (Plant And Water)
Step-by-step explanation:
The range of a parabola that opens up starts at its vertex (1,−5)(1,-5) and extends to infinity.
Interval Notation:
[−5,∞)[-5,∞)
Set-Builder Notation:
{y|y≥−5}{y|y≥-5}
Determine the domain and range.
Domain: (−∞,∞),{x|x∈R}(-∞,∞),{x|x∈ℝ}
Range: [−5,∞),{y|y≥−5}
I already did the equation for you, but can somebody tell me the answer?
Answer:
if you put that equation into a graphing calculator the answer is 4188.37
Which sequence of transformations maps quadrilateral ABCD onto quadrilateral EFGH
Answer:
C. reflection across the x-axis, translation 6 units left
15 friends want to order pizza for dinner. If each friend can eat 1/3 of a pizza, how many pizzas should they order?
Answer:
5
Step-by-step explanation:
[tex]\frac{15}{3} =5\\3 friends=1 pizza\\15 friends=5 pizzas\\[/tex]
The equation y = 50(1.05)x models the growth of a mule deer population introduced into Guadalupe National Park in December 2015. "X" represents the number of years after December 2015 while "y" represents the population at time "x". In what year will the mule deer population first reach 1500?
F.2084
G.2044
H.2043
J.2085
9514 1404 393
Answer:
J. 2085
Step-by-step explanation:
Fill in the desired value for y and solve for x.
1500 = 50(1.05^x)
30 = 1.05^x . . . . . . . divide by 50
log(30) = x·log(1.05) . . . . . take logarithms
x = log(30)/log(1.05) ≈ 69.71
Since x represents years after December 2015, x = 69.7 will be some time in mid 2085.
Question 18 of 28 Which of the following equations can be used to find the length of EF in the triangle below? A. (EA)2 = 242-122 B. (ER2 = 242 +122 O C. EF = 24 - 12 D. EF = 24 + 12
Answer: A
Step-by-step explanation:
76 is what percent of 79
Answer:
79
100
0.79%
76
100
0.76%
How many years (to two decimal places) will it take $15000 to grow to $17500 if it is invested at 8% compounded semi- annually?
Answer:
1.97 years
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 8/100
r = 0.08 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(17,500.00/15,000.00) / ( 2 × [ln(1 + 0.08/2)] )
t = ln(17,500.00/15,000.00) / ( 2 × [ln(1 + 0.04)] )
t = 1.965 years
:D
PLSSS HELP I WILL GIVE BRAINLIEST
PLEASE NO LINKS I CAN'T SEE THEM
Which equation represents the solution of the equation 7x + 12 = 6?
A. x = 18 / 7
B. x = 6/7
C. x = - 6/7
D. x = - 18/7
Answer:
c
Step-by-step explanation:
because I have a great day and I will be in the representation
Step-by-step explanation:
7x + 12 = 6
7x=-6
x=-6/7
Don't enter into link, it contains viruses
You are having a birthday party and are inviting 6 friends. You have 9 cupcakes, and you are going to share the cupcakes fairly among you and your 6 friends.
Which equation describes how many cupcakes each of you will receive?
Answer:
split the other three in half
Step-by-step explanation:
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP MEEEEEEEEEEEEEEEEEEEEEEEEE
Task #1 Creating A Table Task
Create a table of x and y values that represents a proportional relationship.
a) Explain how you know the relationship is proportional.
b) What equation models the values in the table?
2) Create a table of x and y values that represents a linear, non-proportional relationship.
a) Explain how you know the relationship is non-proportional.
b) What equation models the values in the table?
Answer:
b
Step-by-step explanation:
PLEASE CHECK MY WORK
The function given in the table is quadratic:
true***
false
Answer:
false
Step-by-step explanation:
The function given in the table is a linear function:
f(x) = 3x+2
Find the area and circumference of each circle
Answer:
Step-by-step explanation:
Area = [tex]Area = \pi r^2 = \pi(3)^2 = 9\pi = 28.27\\Circumference = 2\pi r = 2\pi 3 = 6\pi = 18.85[/tex]
Answer:
[tex]area = 28.27 {m}^{2} \\ c = 18.84m[/tex]
Explanation is attached to the picture
Hope this helps you.
Please please help me please I really need help please just tap on picture and you will see the question
Answer:
No , it is not a right angle triangle
Step-by-step explanation:
according to the pythagoras theorem in right angled triangle sum of square of two sides is equal to the square of it's hypotenuse.
using pythagoras theorem
a^2 + b^2 = c^2
9^2 + 16^2 = 25^2
81 + 256 = 625
337 = 625
since sum of square of two smallest sides of a triangle is not equal to the square of it's hypotenuse it can be concluded that the given figure does not form right angle triangle.
Convert the rational expression to radical form.
x^{4/3}y^{1/3}z^{2/5}
Plz help
Answer:
[tex]a \frac{x}{n} = \sqrt[n]{a}^x .
\sqrt[3]{x}^4 \sqrt[3]{y} \sqrt[5]{z}^2 [/tex]
Malachy rolls a fair dice 720 times.
How many times would Malachy expect to roll a five?
Answer:
120 times
Step-by-step explanation:
On a dice, there are 6 sides.
Since one of these sides is a 5, the chance of rolling a five is 1/6.
Find how many times Malachy can expect to roll a five by multiplying 720 by 1/6:
720(1/6)
= 120
So, Malachy can expect to roll a five 120 times
Solve for c. 2 abc + d=3