Answer:
[tex]\begin{aligned} \frac{dy}{dx} &= \frac{\cos(t) + \sin(t)}{\cos(t) - \sin(t)} \end{aligned}[/tex] given that [tex]a \ne 0[/tex] and that [tex]\cos(t) - \sin(t) \ne 0[/tex].
Step-by-step explanation:
The relation between the [tex]y[/tex] and the [tex]x[/tex] in this question is given by parametric equations (with [tex]t[/tex] as the parameter.)
Make use of the fact that:
[tex]\begin{aligned} \frac{dy}{dx} = \quad \text{$\frac{dy/dt}{dx/dt}$ given that $\frac{dx}{dt} \ne 0$} \end{aligned}[/tex].
Find [tex]\begin{aligned} \frac{dx}{dt} \end{aligned}[/tex] and [tex]\begin{aligned} \frac{dy}{dt} \end{aligned}[/tex] as follows:
[tex]\begin{aligned} \frac{dx}{dt} &= \frac{d}{dt} [a\, (\cos(t) + \sin(t))] \\ &= a\, (-\sin(t) + \cos(t)) \\ &= a\, (\cos(t) - \sin(t))\end{aligned}[/tex].
[tex]\begin{aligned} \frac{dx}{dt} \ne 0 \end{aligned}[/tex] as long as [tex]a \ne 0[/tex] and [tex]\cos(t) - \sin(t) \ne 0[/tex].
[tex]\begin{aligned} \frac{dy}{dt} &= \frac{d}{dt} [a\, (\sin(t) - \cos(t))] \\ &= a\, (\cos(t) - (-\sin(t))) \\ &= a\, (\cos(t) + \sin(t))\end{aligned}[/tex].
Calculate [tex]\begin{aligned} \frac{dy}{dx} \end{aligned}[/tex] using the fact that [tex]\begin{aligned} \frac{dy}{dx} = \text{$\frac{dy/dt}{dx/dt}$ given that $\frac{dx}{dt} \ne 0$} \end{aligned}[/tex]. Assume that [tex]a \ne 0[/tex] and [tex]\cos(t) - \sin(t) \ne 0[/tex]:
[tex]\begin{aligned} \frac{dy}{dx} &= \frac{dy/dt}{dx/dt} \\ &= \frac{a\, (\cos(t) + \sin(t))}{a\, (\cos(t) - \sin(t))} \\ &= \frac{\cos(t) + \sin(t)}{\cos(t) - \sin(t)}\end{aligned}[/tex].
simplify (2/3 of 21/4)
Answer: 3 1/2
Step-by-step explanation:
"Of" is the same as multiplication so,
2/3 × 21/4=?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
2 × 2/13 × 4 = 42/12
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 42 and 12 using
GCF(4/2 , 1/2) = 6
4/2 ÷ 6 1/2 ÷ 6 = 7/2
The fraction
7/2
is the same as
7÷2
Convert to a mixed number using
long division for 7 ÷ 2 = 3R1, so
7/2 = 3 1/2
Therefore:
2/3 of 21/4 = 3 1/2
Hopefully, I Helped
Please give this in steps
Answer:
(x - y)²
Step-by-step explanation:
Given
(x + y)² - 4xy
= x² + 2xy + y² - 4xy
= x² - 2xy + y²
= (x - y)²
Answer:
[tex] {(x + y)}^{2} - 4xy = {x}^{2} + 2xy + {y}^{2} - 4xy \\ = {x}^{2} - 2xy + {y}^{2} \\ = {(x - y)}^{2} \\ thank \: you[/tex]
a person runs at a constant speed of 9.2 miles per hour for 6 minutes and 30 seconds. How far did they travel in yards.
Given:
Speed[tex]= \bold{9.2 \ \frac{miles}{hour}}[/tex]
[tex]\therefore \\\\[/tex]
1-hour= 60 minutes
1-minutes=60 second
So
1-hour= 3600 second
Converting the given time into seconds:
Time= 6 minutes and 30 second
[tex]=\bold{6\times 60 \ second + 30 \ second }\\\\=\bold{360\ second+30\ second}\\\\=\bold{390\ second}\\\\[/tex]
When 3600 seconds covers=9.2 miles
Then equation:
[tex]=\bold{\frac{9.2}{3600}}\\\\[/tex]
390 seconds covers:
[tex]=\bold{\frac{9.2}{3600}\times 390 \ miles} \\\\[/tex]
Let
[tex]\bold{1 \ miles= 1760\ yard}\\\\[/tex]
Convert the traveling value into yards:
[tex]=\bold{ \frac{9.2}{3600}\times 390\times 1760}\\\\=\bold{ \frac{9.2}{36}\times 39\times 176}\\\\=\bold{ \frac{9.2}{12}\times 13\times 176}\\\\=\bold{ \frac{9.2}{12}\times 2288}\\\\=\bold{ 9.2\times 190.66}\\\\=\bold{ 1754.072\ yards}\\\\[/tex]
Therefore, total traveling yards are"1754.072".
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Speed of the person has been given as 9.2 miles per hour.
Therefore, speed of the person in miles per minute = [tex]\frac{9.2}{60}[/tex]
Duration for which the person is running = 6 minutes and 30 seconds
= 6 minutes and [tex]\frac{30}{60}[/tex] minutes
= 6.5 minutes
Since, Distance = Speed × Time
By substituting the values in the expression we can get the distance traveled.
Distance = [tex]\frac{9.2}{60}\times 6.5[/tex]
= 0.9967 miles
Since, 1 mile = 1760 yards
Therefore, 0.99667 miles = 1760 × 0.99667
= 1754.13 yards
Total distance traveled by the person is 1754.13 yards.
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Find the AREA of the shape
Step-by-step explanation:
LxB
8x7
equals :56
Area equals to 56cm
Danny got a raise and now makes $58,965.95 a year. Round this number to the
nearest:
a) dollar
b) thousand dollars
c) ten thousand dollars
Answer:
c) ten thousand dollars
Step-by-step explanation:
SOMER HELP ON GIS ONEEEE
Answer:
2 one
Step-by-step explanation:
well if u go the other way for it to go right it is mf
Part A
The formula for the volume V of a cylinder is V = πr2h, where r is the radius of the base and h is the height of the cylinder. Solve the formula for h.
Choose the correct formula.
A. h=Vπr2
B. h=Vπr2
C. h=Vr2π
D. h=Vπr2
Part B
Find the height of a cylinder with a volume of 36π cm3 and a base with a radius of 3 cm.
h =
cm
Answer:
Part A. [tex]h=\frac{V}{\pi r^2}[/tex]
Part B. h= 4cm
Step-by-step explanation:
Two cylinders are similar the volume of one is 27cm^3 the volume of the other cylinder is 1331cm^3 what is the scale factor between them
Answer:
scale factor = 3 : 11
Step-by-step explanation:
Given 2 similar figures with scale factor a : b , then
ratio of volumes = a³ : b³
Here
ratio of volumes = 27 : 1331 . so
scale factor = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{1331}[/tex] = 3 : 11
Answer:
3:11
Step-by-step explanation:
I need some help with the homework problem. I have a list of formulas, but can't seem to get it done.
[tex]\int\frac{9}{\sqrt{1+e^{2x}}} \, dx[/tex]
I started by taking the constant out and setting u = [tex]\sqrt{1+e^{2x\\}}[/tex]
After this I can't seem to progress.
After setting [tex]u=\sqrt{1+e^{2x}}[/tex], partially solving for x in terms of u gives
[tex]u = sqrt{1+e^{2x}} \implies u^2 = 1 + e^{2x} \implies e^{2x} = u^2 - 1[/tex]
Then taking differentials, you get
[tex]2 e^{2x} \,\mathrm dx = 2u \, \mathrm du \implies \mathrm dx = \dfrac{u}{u^2-1}\,\mathrm du[/tex]
Replacing everything in the original integral then gives
[tex]\displaystyle \int \frac9{\sqrt{1+e^{2x}}}\,\mathrm dx = \int \frac9u \times \frac u{u^2-1}\,\mathrm du = 9 \int \frac{\mathrm du}{u^2-1}[/tex]
Split up the integrand into partial fractions:
[tex]\dfrac1{u^2-1} = \dfrac a{u-1} + \dfrac b{u+1} \\\\ 1 = a(u+1) + b(u-1) = (a+b)u + a-b \\\\ \implies \begin{cases}a+b=0\\a-b=1\end{cases} \implies a=\dfrac12,b=-\dfrac12[/tex]
so that
[tex]\displaystyle 9 \int \frac{\mathrm du}{u^2-1} = \frac92 \int \left(\frac1{u-1} - \frac1{u+1}\right) \,\mathrm du \\\\ = \frac92 \left(\ln|u-1| - \ln|u+1|\right) + C \\\\ = \frac92 \ln\left|\frac{u-1}{u+1}\right| + C \\\\ = \frac92 \ln\left(\frac{\sqrt{1+e^{2x}}-1}{\sqrt{1+e^{2x}}+1}\right) + C[/tex]
1. If a = -1 , the value of3a + 1 is
Answer:
[tex]f(a) = 3a + 1 \\ Now,\: a = - 1 \\ f( - 1) = 3( - 1) + 1 \\ f( - 1) = - 3 + 1 \\ \boxed{ f( - 1) = - 2}[/tex]
Therefore, -2 is the right answer.Find - 36
.
Ο +6
-6
9Ο
Ο 18
Answer:
+or-6
Step-by-step explanation:
This is a trick question. The answer would be the first choice since you're multiplying -6 by +or-6, meaning that it could still end up as a negative or a positive.
Answer:
Step-by-step explanation:
8th grade math
5. What is the probability of rolling a 3 on a 6-sided number cube and then NOT rolling 2 or 4 on a 6-sided number cube?
Answer:
5 in 12 chance or 42% probability of happening
I|I is an integer between 11 and 17
Yes, there is. It's 14. Hope this helps.
Hours worked in a week - 32; Total Pay - $160.00; What is the hourly rate?
Answer:
$5
Step-by-step explanation:
Number of hours worked = 32
Total pay = $160
So, hourly rate
= Total pay/number of hours worked
= $160/32
= $5
4. In a class of 35 students, 20 offer Physics,
18 offer Chemistry and 2 offer neither
Physics nor Chemistry
1) Illustrate the information on a Venn
diagram
il) How many students offer all the two
subjects?
1) How many students offer Physics!
1) How many students offer only one
subject
5 students offers all the two subjects.
Student that offers Physic only = 15 students
Student that offers chemistry only = 13 students
Students that offers only one subject = 28 students
How to solve a Venn diagram?Total student in the class = 35
20 offer physics.
18 offer chemistry
2 offer neither physics nor chemistry.
Therefore,
x = student that offer both subject
35 = 20 + 18 - x + 2
35 - 2 - 20 - 18 = -x
-5 = -x
x = 5
Therefore, 5 students offers all the two subjects.
Student that offers Physic only = 20 - 5 = 15
Student that offers chemistry only = 18 - 5 = 13
Students that offers only one subject = 13 + 15 = 28
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(5pg)3=125pg. Is wrong or correct
Answer:
125 p^3 g^3
Step-by-step explanation:
(5pg)^3
We know that (ab)^c = a^c * b^c
5^3 p^3 g^3
125 p^3 g^3
Complete the following equation using <, >, or =
7 _ 24/4
A. =
B. >
C. <
Answer:
7 > 24/4
Step-by-step explanation:
7 _ 24/4
Simplify 24/4
24/4 = 6
7 is greater than 6
7 > 24/4
7 is greater than the fraction 24/4 so we use the ">" symbol between them. Hence, the complete equation is 7 > 24/4.
Comparison of two numbers involves determining the relationship between them. Here are a few possible outcomes when comparing two numbers:
1: If the first number is greater than the second number, we can say that the first number is "greater than" or "larger than" the second number.
2: If the first number is less than the second number, we can say that the first number is "smaller than" or "less than" the second number.
3: If the first number is equal to the second number, we can say that the numbers are "equal" to each other.
The given numbers are:
7 and 24/4
To compare these numbers,
Convert the fraction 24/4 into the simplest form
Therefore,
[tex]\frac{24}{4} = 6[/tex]
Now since 7 is greater than 6 so we use ">" between them.
Hence,
The complete equation will be 7 > 24/4.
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A room has to be painted and worker A does 1/3 of the work then leaves. Next worker B does 1/4 of the remaining work and then leaves and finally worker C does 1/5 of the remaining work and then leaves.
What fraction of the room still needs to be painted?
a)3/5
b)2/5
c)13/60
d)7/15
Here, we are given that a room is painted by A, B and C so here three of them have done the work. So, we'll add all these fractions and assume the total work as 1 after that we will substract all the added ones from 1
Let us assume the room completely painted be 1
Now,
A has done 1/3, B has done 1/4 and C has done 1/5 work of the remaining
So, let us add them
A + B + C ⅓ + ¼ + ⅕Getting the L.C.M. The L.C.M of 3,4,5 is 60
20/60 + 15/60 + 12/6047/60Hence, 47/60 room has been painted
Remaining to paint
Total is assumed as 1
Work done = 47/60
Fraction of room needs to painted = 1 - 47/60
(60 - 47)/6013/6013/60 of the room needs to be painted, OPTION C IS CORRECT
Based on this equation 3/4 (8y +12) = 3y - 15, what is 2y - 3?
Answer:
-y+5
Step-by-step explanation:
3/4 (8y +12) = 3y - 15
3(2y+3)=3y-15
2y+3=y-5
-(2y-3)=y-5
2y-3=y-5/-1
2y-3=-y+5
Answer: -19
Step-by-step explanation:
Given equation
(3/4) (8y + 12) = 3y - 15
Divide (3/4) on both sides
(REMEMBER division of fraction can be converted to multiplication by using the reciprocal of the fraction)
(3/4) (8y + 12) ÷ (3/4) = (3y - 15) ÷ (3/4)
(3/4) (8y + 12) × (4/3) = (3y - 15) × (4/3)
8y + 12 = 4y - 20
Subtract 4y on both sides
8y + 12 - 4y = 4y - 20 - 4y
4y + 12 = -20
Subtract 12 on both sides
4y + 12 - 12 = -20 - 12
4y = -32
Divide 4 on both sides
4y / 4 = -32 / 4
y = -8
Evaluate the expression basing on the [y] value
2y - 3 ⇔ Given expression
=2(-8) - 3 ⇔ Substitute values into the expression
=-16 - 3 ⇔ Simplify by multiplication
=[tex]\boxed{-19}[/tex] ⇔ Simplify by subtraction
Hope this helps!! :)
Please let me know if you have any questions
Write the equation of the line that
passes through (5,-7) and (0, -1)
4,3,2,1,0,-1, -2, -3, -4,
Equation of a line can be given by :
y = mx + b
Let's find the slope of the line (m) :
[tex] \mathcal{ \hookrightarrow \: \dfrac{y_2 - y_1}{x_2 - x_1} }[/tex]
[tex] \mathcal{ \hookrightarrow \: \dfrac{ - 1 - ( - 7)}{0 - 5} }[/tex]
[tex] \hookrightarrow \: \dfrac{6}{ - 5} [/tex]
[tex] \hookrightarrow \: m = \dfrac{ - 6}{5} [/tex]
now let's solve for b :
[tex] \hookrightarrow \: y = mx + b[/tex]
Let's plug the values of x and y from the coordinates of a point .
[tex] \hookrightarrow \: - 7 = (\dfrac{ - 6}{5} \times 5) + b[/tex]
[tex] \hookrightarrow \: - 7 = - 6 + b[/tex]
[tex] \hookrightarrow \: b = - 1[/tex]
now, let's put the value of m (slope) and b (y-intercept) in the equation.
[tex] \hookrightarrow \: y = mx + b[/tex]
[tex] \boxed{ \boxed{\: y = \dfrac{ - 6}{5}x - 1 }}[/tex]
That's All, I hope it helped ya
PLZ HELP ASAP I NEED PLZZZ!!!!!!
Fill in the blank with the correct response. The slope of the graph of y = -2/3x is __.
Answer:
Solution given:
Equation of line is:
y=-⅔x
comparing above equation with
y=mx+c
we get
m=-⅔
So
slope is -⅔Answer:
slope is -2/3
Step-by-step explanation:
I. It's linear equation
y = mx + b
when y is output, x is input, m is slope and b is addition.
The statment above is y = -2/3x + 0
So -2/3 is slope or m.value
Hope that help :D
A total of 574 tickets were sold for the school play. They were either adult tickets or student tickets. There were 74 more student tickets sold than adult tickets. How many adult tickets were sold?
411 is not correct
The answer is: 250 adult tickets were sold.
To be safe, prove that your answer is correct.
If there are 74 more student tickets than adult tickets, the amount of adult tickets must obviously be less.
Explanation:
74 more than 250, or 250+74 is 324.
250+324=574.
Now, you know the answer is correct. It satisfies all of the given conditions.
Also, note that the difference between the number of student tickets and adult tickets is 74.
So, there are 250 adult tickets and 324 student tickets.
Solve. − 18 + ( − 4 ) =
Answer:
-22
Step-by-step explanation:
-18 + (-4) = -18 - 4 = -22
X¹² - 1 แยกตัวประกอบของพหูนาม
Answer:
[tex]\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)[/tex]
Step-by-step explanation:
Factor of [tex]x^{12}-1[/tex] is
[tex]\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)[/tex]
in a class of 80 students in Debre Berhan university,45 good in mathematics,15 are good in both Mathematics and English,13 are good in both Mathematics and Psychology, 16 are good in both in English and psychology,20 are good in Psychology and 9 are good in both of the three courses A,how many students are good in mathematics only? B,how many students are not good in any of three courses?
The relationship between the number of students that are good at a given subject is an illustration of sets.
26 students are good at Mathematics only.28 students are not good at all.We use the following representations:
[tex]M \to[/tex] Mathematics
[tex]E \to[/tex] English
[tex]P \to[/tex] Psychology
From the question, we have the following parameters
[tex]M = 45[/tex] -- Mathematics
[tex]M\ n\ E =15[/tex] -- Mathematics and English
[tex]M\ n\ P =13[/tex] -- Mathematics and Psychology
[tex]E\ n\ P =16[/tex] -- English and Psychology
[tex]P=20[/tex] -- Psychology
[tex]All = 9[/tex] -- All 3 subjects
[tex]Total = 80[/tex] -- All students
The number of students that are good at mathematics only is as follows:
First, we calculate those that are good at mathematics and English only
[tex](M\ n\ E)' = M\ n\ E - All[/tex]
[tex](M\ n\ E)' = 15 - 9 = 6[/tex]
Then those that are good at mathematics and psychology only
[tex](M\ n\ P)' = M\ n\ P - All[/tex]
[tex](M\ n\ P)' = 13 - 9 = 4[/tex]
So, the students that are good at mathematics only are:
[tex]M' = M - (M\ n\ E)' -(M\ n\ P)' - All[/tex]
[tex]M' = 45 - 6 -4 -9[/tex]
[tex]M' = 26[/tex]
Hence, 26 students are good at Mathematics only.
To calculate the number of students that are not good in any of the subjects, we make use of the complement rule
[tex]A + A' = Total[/tex]
Where:
[tex]A \to[/tex] Students that are not good in any
[tex]A' \to[/tex] Students that are good in at least one
So, we have:
[tex]A' =M' + (M\ n\ E)' + (M\ n\ P)' + (E\ n\ P)' + All[/tex]
Where:
[tex](E\ n\ P) = (E\ n\ P)' - All[/tex]
[tex](E\ n\ P) = 16-9 = 7[/tex]
The equation becomes:
[tex]A' =26 + 6 + 4+7+9[/tex]
[tex]A' =52[/tex]
Recall that:
[tex]A + A' = Total[/tex]
[tex]A = Total - A'[/tex]
[tex]A = 80 - 52[/tex]
[tex]A = 28[/tex]
Hence, 28 students are not good at all.
Read more about sets at:
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Homework pikcuts
Pleas
Answer:
[tex] \frac{12 - 23 \sqrt{2} }{46} [/tex]
Step-by-step explanation:
you find the LCM
If X= 9 and Y = 3, what is XY
Answer:
The most basic question I have ever seen lol
XY = 9*3 = 27
PLZ HELP ME I NEED HELP PLZZZ!!!!!
Select all that apply.
Given the points (-6, 8) and (-3, 4), which of the following are true about the line passing through these points?
The line represents a direct variation function.
The line has a slope of -3/4 .
The point (9, -12) is also on the line.
The line has a slope of 3/4 .
Answer:
the point (9,-12) is also on the line
Step-by-step explanation:
by using the 2 points the equation is y=-4/3x
use x of 9
y = -12
it will also represent a direct variation function
so two of the 4 will be correct
Answer:
The point (9,-12) is also on the line
Step-by-step explanation:
Please give brainliest
Simplify 3 (5x-2y) +2 (4X-37)
Answer:
3x - 6y - 74
Step-by-step explanation:
Given
3(5x - 2y) + 2(4x - 37) ← distribute parenthesis
= 15x - 6y + 8x - 74 ← collect like terms
= 23x - 6y - 74
Answer:
Distribute
3
(
5
−
2
)
+
2
(
4
−
3
7
)
{\color{#c92786}{3(5x-2y)}}+2(4x-37)
3(5x−2y)+2(4x−37)
1
5
−
6
+
2
(
4
−
3
7
)
{\color{#c92786}{15x-6y}}+2(4x-37)
15x−6y+2(4x−37)
2
Distribute
1
5
−
6
+
2
(
4
−
3
7
)
15x-6y+{\color{#c92786}{2(4x-37)}}
15x−6y+2(4x−37)
1
5
−
6
+
8
−
7
4
15x-6y+{\color{#c92786}{8x-74}}
15x−6y+8x−74
3
Combine like terms
1
5
−
6
+
8
−
7
4
15x−6y+8x−74
2
3
−
6
−
7
423x}}-6y-74
23x−6y−74
Solution
2
3
−
6
−
7
4
Step-by-step explanation:
If f(x, y, z) = z sin (xy), find the rate of change of f at the point P(0, 0, 2) in the direction from P to Q(3, 0, 0)
Answer:
0
Step-by-step explanation:
We are looking for the directional derivative of f at P in the direction of PQ.
First we compute
[tex]\nabla f=\langle yz\cos(xy),zx\cos(xy),\sin(xy)\rangle\\\nabla f(0,0,2) =\langle 0,0,0\rangle[/tex]
But if we dot any vector to the zero vector we always get 0. So the rate of change is zero.