the answer would be -1,224 because the parentheses is your multiplication and the it is a negative
Test for exactness. If exact, solve it directly. Otherwise, use integrating factors to solve it. Solve the IVP (if given). 2xy + (x^2) y' = 0
sin(x) cos(y) + cos(x) sin(y) y' = 0
(x^2) + (y^2) - 2xyy' = 0
e^(2x).(2 cos(y) - sin(y) y') = 0, where y(0) = 0
• 2xy + x ² y' = 0
This DE is exact, since
∂(2xy)/∂y = 2x
∂(x ²)/∂x = 2x
are the same. Then there is a solution of the form f(x, y) = C such that
∂f/∂x = 2xy ==> f(x, y) = x ² y + g(y)
∂f/∂y = x ² = x ² + dg/dy ==> dg/dy = 0 ==> g(y) = C
==> f(x, y) = x ² y = C
• sin(x) cos(y) + cos(x) sin(y) y' = 0
is also exact because
∂(sin(x) cos(y))/∂y = -sin(x) sin(y)
∂(cos(x) sin(y))/∂x = -sin(x) sin(y)
Then
∂f/∂x = sin(x) cos(y) ==> f(x, y) = -cos(x) cos(y) + g(y)
∂f/∂y = cos(x) sin(y) = cos(x) sin(y) + dg/dy ==> dg/dy = 0 ==> g(y) = C
==> f(x, y) = -cos(x) cos(y) = C
• x ² + y ² - 2xyy' = 0
is not exact:
∂(x ² + y ²)/∂x = 2x
∂(-2xy)/∂y = -2x
So we look for an integrating factor µ(x, y) such that
µ (x ² + y ²) - 2µxyy' = 0
becomes exact, which would require that these be equal:
∂(µ (x ² + y ²))/∂y = (x ² + y ²) ∂µ/∂y + 2µy
∂(-2µxy)/∂x = -2xy ∂µ/∂x - 2µy
Observe that if µ(x, y) = µ(x), then ∂µ/∂y = 0 and ∂µ/∂x = dµ/dx, so we would have
2µy = -2xy dµ/dx - 2µy
==> -2xy dµ/dx = 4µy
==> dµ/µ = -2/x dx
Integrating both sides gives
∫ dµ/µ = ∫ -2/x dx ==> ln|µ| = -2 ln|x| ==> µ = 1/x ²
So in the modified DE, we have
(1 + y ²/x ²) - 2y/x y' = 0
which is now exact and ready to solve, since
∂(1 + y ²/x ²)/∂y = 2y/x ²
∂(-2y/x)/∂x = 2y/x ²
We get
∂f/∂x = 1 + y ²/x ² ==> f(x, y) = x - y ²/x + g(y)
∂f/∂y = -2y/x = -2y/x + dg/dy ==> dg/dy = 0 ==> g(y) = C
==> f(x, y) = x - y ²/x = C
• exp(2x) (2 cos(y) - sin(y) y' ) = 0
is exact, since
∂(2 exp(2x) cos(y))/∂y = -2 exp(2x) sin(y)
∂(-exp(2x) sin(y))/∂x = -2 exp(2x) sin(y)
Then
∂f/∂x = 2 exp(2x) cos(y) ==> f(x, y) = exp(2x) cos(y) + g(y)
∂f/∂y = -exp(2x) sin(y) = -exp(2x) sin(y) + dg/dy ==> dg/dy = 0 ==> g(y) = C
==> f(x, y) = exp(2x) cos(y) = C
Given that y = 0 when x = 0, we find that
C = exp(0) cos(0) = 1
so that the particular solution is
exp(2x) cos(y) = 1
• The difference between a polynomial or rational equation and polynomial or rational inequality
Answer:
An equation has an equal sign between two expressions, while an inequality has a ≤ or ≥ sign.
Given limit f(x) = 4 as x approaches 0. What is limit 1/4[f(x)]^4 as x approaches 0?
Answer:
[tex]\displaystyle 64[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Rule [Variable Direct Substitution Exponential]: [tex]\displaystyle \lim_{x \to c} x^n = c^n[/tex]
Limit Property [Multiplied Constant]: [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \lim_{x \to 0} f(x) = 4[/tex]
Step 2: Solve
Rewrite [Limit Property - Multiplied Constant]: [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]: [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)[/tex]Simplify: [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = 64[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
Answer: C. 64
Step-by-step explanation:
Edge 100%
Find the area of a rectangle whose length is 14cm and breadth is 6cm
Answer:
Ellos dan las pistas de algunos problemas se pueden resolver de forma automática, los valores numéricos tienen ninguna importancia en los distintos ejemplos.
Traza 1
Uno de los lados de un rectángulo es 20 cm de largo; un segundo lado del rectángulo es de 0,85 m de largo. Calcular el perímetro y el área del rectángulo.
Traza 2
Calcular el área de un rectángulo cuyas dimensiones son 85 cm de largo y 20 cm respectivamente.
Traza 3
La base de un rectángulo es 20 cm de largo; la área es de 300 cm². Calcular la altura del rectángulo.
Traza 4
La altura de un rectángulo es 15 cm de largo; la área es de 300 cm². Calcula la base del rectángulo.
Traza 5
Un rectángulo tiene la altura que es de 3/8 de la base; la suma de las longitudes de los dos segmentos es 44 cm. Determinar el área del rectángulo y el perímetro.
Traza 6
La base de un rectángulo es de 0,40 m de largo; La altura del rectángulo es 30 cm. Calcular la diagonal.
Traza 7
Un tamaño de un rectángulo es un medio del lado de un cuadrado que tiene el perímetro de 20 cm. Sabiendo que los dos polígonos tienen el mismo perímetro, calcula la medida del tamaño del rectángulo.
Traza 8
La diagonal de un rectángulo es de 50 cm; la base es de 3/4 de la altura. Calcular el perímetro y el área del rectángulo.
Traza 9
La diagonal de un rectángulo mide 50 cm; ella es 5/3 de altura. Calcular el perímetro y el área del rectángulo.
Traza 10
Una mesa rectangular tiene lados de 180 cm y 90 cm respectivamente. Cuál es el perímetro y el área de un mantel que cuelga de 20 cm alrededor de la mesa?
Traza 11
Calcular el área de un rectángulo que tiene la altura 10 cm de largo, sabiendo que la medida de la base es el doble de la altura.
Traza 12
La diferencia entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo
Traza 13
La suma entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo
Traza 14
La suma de la base y la altura de un rectángulo es 50 cm; la base es superior a la altura de 4 cm. Calcular el área del rectángulo.
Traza 15
El semi-perímetro de un rectángulo es 32 cm y una dimensión es de 3/5 de la otra. Calcular el área del rectángulo.
Traza 16
El semi-perímetro de un rectángulo es 30 cm y una dimensión es igual a los sus 2/5. Calcular el área del rectángulo.
Traza 17
Un rectángulo tiene una base de 20 cm y una altura igual a 2/5 de la base. Calcular el perímetro y el área del rectángulo.
Traza 18
Un rectángulo tiene el área de 600 cm² y la base es 20 cm de largo. Cuál es su perímetro ?
Traza 19
Un rectángulo tiene un perímetro de 100 cm y la base es 30 cm de largo. Calcula su área.
Traza 20
Un rectángulo tiene un perímetro de 120 cm. Sabiendo que un tamaño es tres veces la otra, calcula el área del rectángulo.
Traza 21
La diferencia entre el tamaño de un rectángulo es 10 dm. Sabiendo que el perímetro es 100 dm, calcula el área del rectángulo.
Traza 22
Un rectángulo tiene un perímetro de 100 cm. Calcula su área sabiendo que la medida de la base es superior a la de la altura de 10 cm.
Traza 23
En el perímetro de un rectángulo es de 100 cm y la altura es de 20 cm de largo. Calcular el perímetro de un rectángulo equivalente a el mismo y que tiene su base de 40 cm de largo.
Traza 24
Un rectángulo es formado por dos cuadrados congruentes que tienen cada uno el perímetro de 24 cm. Calcular el perímetro y el área del rectángulo.
Traza 25
Un rectángulo es formado por tres cuadrados congruentes con cada lado 20 cm de largo. Calcular el perímetro y el área del rectángulo.
Traza 26
Un rectángulo es formado por dos cuadrados congruentes. Sabiendo que el perímetro del rectángulo es de 180 cm, calcular su área.
Traza 27
Un rectángulo y un cuadrado tienen el mismo perímetro. El lado de un cuadrado de 45 cm y las dimensiones del rectángulo son una 1/2 de la otra. Calcular el área del rectángulo.
Traza 28
Dos rectángulos son equivalentes. Sabiendo que las dimensiones de el primero miden respectivamente 30 cm y 20 cm, y que la base del segundo rectángulo es 40 cm de largo, calcula la diferencia entre los dos perímetros.
Traza 29
Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:
Traza 30
Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:
Traza 31
Un constructor ha comprado un terreno que tiene la planta mostrada en el dibujo y las dimensiones en metros se indican en la figura. Calcula el área y el perímetro de la tierra.
Traza 32
Una parcela de tierra tiene una forma rectangular con unas dimensiones de 50 m y de 30 m de largo. En el interior se ha construido una casa que ocupa una superficie rectangular de longitud 20 m y de 8 m de ancho. Calcular el área de la tierra permanecida libre.
Traza 33
Step-by-step explanation:
Answer:
A= 84cm
Step-by-step explanation:
length x width= area
plug in the given information.
14cm x 6cm = A
A=84
with a length of 14cm and a width of 6cm multiply them for an area of 84cm.
Please helpppppp
ASAPpppppp
Does this graph represent a function?
Answer:
I think it's a function
Step-by-step explanation:
as you can see in the picture curve drawn in a graph represents a function, if every vertical line intersects the curve in at most one point. So I think its a function.
Answer:
yes
Step-by-step explanation:
it's a cubic function having maximum and minimum turning points
it has a point of inflation, y - intercept and x-intercept
A metal rod will be cut into pieces that are each 1/20 meters long. The rod is 4/5 meters long. How many pieces will be made from the rod?
Write your answer in simplest form.
What is the length of segment AC?
Answer:
10 units
Step-by-step explanation:
Point A (3,-1)
Point B (-5,5)
Distance between them,
√{(-5-3)²+(5-(-1))²}
= √{(-8)²+6²}
= √(64+36)
= √100
= 10 units
720 companies 8 companies win what is the probability
Step-by-step explanation:
total outcomes = 720
favourable outcomes =8
=8/720
=0.01111
Does the picture below indicate that:
ZJAC ZDBE?
С DA
J
939
A
B
→E
Yes
No
Pls help
Answer:
No
Step-by-step explanation:
The measure of <JAC is shown to be 93°.
The little square symbol inside <DBE shows that <DBE is a right angle.
The measure of a right angle is 90°.
m<DBE = 90°
Congruent angles are angles with equal measures.
Since the measures of angles JAC and DBE are different, they are not congruent.
Answer: No
Kezang was 5 times as old as his son 10 years ago. After 8 years, Kezang will be twice as
old as his son. What are their present age
!!! HELP ASAP !!! I almost got the problem but the problem was the rounding. I believe I rounded right but it is still incorrect. Can someone please help me on the rounding portion of the question? Thank you for your help!!!
Male bluethroats have a complex song which is thought to be used to attract female birds. Let x denote the duration of a randomly selected song (in seconds) from a male bluethroat. The authors of research on bluethroat song report the mean song duration is 13.8 seconds and the standard deviation of song durations is 11.8 seconds. The authors also noted that the song length distribution is not normal.
Required:
a. Let = average song duration (in seconds) for a sample of 36 male bluethroat songs. Is this distribution of the sample mean song duration " normally distributed" ?
b. Find the probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds. Draw, label, and shade a graph to illustrate your result.
Answer:
a) Sample size larger than 30, so by the Central Limit Theorem, yes.
b) 0.8199 = 81.99% probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds. The sketch is given at the end.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean song duration is 13.8 seconds and the standard deviation of song durations is 11.8 seconds.
This means that [tex]\mu = 13.8, \sigma = 11.8[/tex]
Sample of 36
This means that [tex]n = 36, s = \frac{11.8}{\sqrt{36}} = 1.9667[/tex]
a. Let = average song duration (in seconds) for a sample of 36 male bluethroat songs. Is this distribution of the sample mean song duration " normally distributed" ?
Sample size larger than 30, so by the Central Limit Theorem, yes.
b. Find the probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds. Draw, label, and shade a graph to illustrate your result.
This is 1 subtracted by the p-value of Z when X = 12. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{12 - 13.8}{1.9667}[/tex]
[tex]Z = -0.915[/tex]
[tex]Z = -0.915[/tex] has a p-value of 0.1801.
1 - 0.1801 = 0.8199
0.8199 = 81.99% probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds.
Sketch:
I have completed everything except for the last box. Can someone please help me on the last box? Thank you for your help!
Answer:
[tex]2.5\%[/tex]
Step-by-step explanation:
From the Empirical Rule, 95% of the data shown falls between 63 and 95. The other 5% is evenly distributed to each side (since the distribution is bell-shaped), hence there being [tex]\boxed{2.5\%}[/tex] of scores less than 63.
The directions say to give the approximate percentage which is vague. You may have to input [tex]3\%[/tex] if it does not accept [tex]2.5\%[/tex].
1. Define the following: Odds ratio Relative risk 2. Describe how to calculate the Odds ratio and provde the formula. 3. Describe how to calculate the Relative Risk and provide the formula.
Answer and Explanation:
Odds ratio is the odds that an outcome would happen given a level of exposure in comparison to the occurrence of that outcome without exposure. Odds ratio is calculated by dividing odds of event occurring with exposure(the first group) by odds of event(usually disease) occurring without exposure. Odds is different from probability(denoted p/1-p). While probability is the number of favorable events divided by total number of events, odds is number of favorable events/number of unfavorable events.
Relative risk, also measuring relationship between exposure and outcome, is the ratio of the probability that an outcome would occur without exposure and probability that an outcome would occur with exposure.
38)
A man completes a job in 5 days working 8 hours a day. How many days will he take to complete the same job working 2 hours overtime per day in addition?
Answer:
dbcjchdiskcnbcksksnnckdkxnn
the expression -6x-7(4+3) is equivalent to?
Answer:
x(12y+4)
2 0 l e t t e r s
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. P(X > 3), n = 5, p = 0.2
Answer:
0.0064
0.00032
Step-by-step explanation:
Given the details:
P(X > 3), n = 5, p = 0.2
The binomial distribution is related using the formula:
P(x = x) = nCx * p^x * q^(n-x)
q = 1 - p = 1 - 0.2 = 0.8
P(X > 3) = p(x = 4) + p(x = 5)
P(x = 4) = 5C4 * 0.2^4 * 0.8^1 = 5 * 0.2^4 * 0.8^1 = 0.0064
P(x = 5) = 5C5 * 0.2^5 * 0.8^0 = 1 * 0.2^5 * 0.8^0 = 0.00032
Is the following shape a square? How do you know?
.8
C.
A
0
O A. No, the opposite sides are not parallel.
B. Yes, the opposite sides are parallel, and all sides are the same
length
O C. No, the sides are not congruent.
D. Yes, the adjacent sides are perpendicular, and all sides are the
same length
PLEASEEEE HELPPPPPPP!!!!!
To find S or T add them together:
3/5 + 1/3
Rewrite the fractions to have a common denominator
9/15 + 5/15 = 14/15
Answer: 14/15
Step-by-step explanation:
Here is your answer . Hope it helps.
f(x)=-2x^2+x-5 find f(-6)
f(x) = 2x² + x - 5
f(-6) = 2(-6)² + (-6) -5
=> f(-6) = 2(36) -11
=> f(-6) = 72 - 11
=> f(-6) = 61
Could someone help me solve this please.
Answer: maybe 20 % at least because it might me adding
Omar keeps his sneaker collection carefully arranged on the floor of his closet. 8 pairs of
sneakers fit perfectly side-by-side from one end of the closet to the other. The closet is 60
inches wide.
How wide is each pair of sneakers?
Answer:
7.5 inches wide. I wasnt wrong. for a second i thought it was asking for the width of each individual sneaker.
Answer:
each pair of sneakers are 7.5 inches wide
Where did this part came from how did this value came from
Answer:
Sin (theta) has the same value for the both value of theta, so both applies.
Answered by GAUTHMATH
PLEASE ANSWER!!
What is the remainder for the synthetic division problem below?
2/ 3 1 2 -7
A. 25
B. 17
C. -29
D. -39
A: 25.
Explanation: Check the attached image.
For synthetic division, you just need to multiply the 1st number of the polynomial by the divisior, and then, add it up to the next number; then, the coefficient will be multiplied by the divisor, and so on and so forth until you reach the last number... that last coefficient at the end is the reminder that you've been asked for
Evaluate the following expressions using the chip method. SHOW ALL WORK!!!
Answer:
a. -7 b. -20c. 7Step-by-step explanation:
a. -9+2, in this case, it is -7 because you take the bigger number and subtract it by the lower number. If the bigger number is negative your answer will be negative, if the bigger number is positive it will be positive it is just really a basic subtraction problem just add the sign.b. In multiplication +++=+ ++-=- and a -+-=+ do your problem without thinking about the signs and then add the signs with the formula I showed you.c. ---=+Hope this helps :)!
If the number of observations for each sample is 150 units, what is the 3-sigma upper control limit of the process
Complete Question
Complete Question is attached below
Answer:
[tex]UCL= 0.25[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size[tex]n=150[/tex]
Sample Variants [tex]s=7[/tex]
Sigma control limits [tex]Z = 3[/tex]
Therefore
Total number of observations is Given as
[tex]T_o=n*s[/tex]
[tex]T_o=150 *7[/tex]
[tex]T_0=1050[/tex]
Generally
Summation of defectivee
[tex]\sum np=23+34+15+30+25+22+18[/tex]
[tex]\sum np= 167[/tex]
Generally the equation for P-bar is mathematically given by
[tex]P-bar=\frac{\sum np}{T_o}[/tex]
[tex]P-bar=\frac{167}{1050}[/tex]
[tex]P-bar=0.16[/tex]
Therefore
[tex]Sp=\sqrt{\frac{P-bar(1-P-bar)]}{ n}}[/tex]
[tex]Sp=\sqrt{\frac{[0.159(1-0.159)]}{150}}[/tex]
[tex]Sp=0.03[/tex]
Generally the equation for 3-sigma upper control limit of the process is mathematically given by
[tex]UCL = P-bar + Z*Sp[/tex]
[tex]UCL= 0.16 + 3*0.03[/tex]
[tex]UCL= 0.25[/tex]
I’m new and i need help!!
Please help me of you know the answers.
Answer:
2, x, 2x
Step-by-step explanation:
A) 2
They are even numbers, so it is going to be 2.
B) x
It is going to only be x because the exponents are even and odd.
C) 2x
It is going to be 2x because the numbers are even but the exponents are even and odd.
Hope this helps.
Choose ALL of the following functions that represent exponential decay. f(x) = 5(2/3)^x
Answer:
exponential decay
Step-by-step explanation:
The function is in the form
y = ab^x where a is the initial value and b is the growth or decay rate
If b >1 then it is growth
b < 1 then it is decay
f(x) = 5(2/3)^x
a = 5
b = 2/3
2/3 <1 so it is decay
Two buses leave towns 576 kilometers apart at the same time and travel toward each other. One bus travels 12
h
slower than the other. If they meet in 3 hours, what is the rate of each bus?
km
Rate of the slower bus:
Rate of the faster bus:
Answer:
Rate of slower bus; 90 km/h
Rate of faster bus; 102 km/b
Step-by-step explanation:
We know that formula do distance is;
Distance = speed/time
We are told that One bus travels 12h slower than the other.
Let speed of slower bus be x.
Thus;
Speed of faster bus = x + 12
Speed of slower bus = x
After 3 hours, distance by faster bus = 3(x + 12)
Speed of slower bus = 3x
Since the towns are 576 km apart, then;
3(x + 12) + 3x = 576
Divide through by 3 to get;
x + 12 + x = 192
2x + 12 = 192
2x = 192 - 12
2x = 180
x = 180/2
x = 90 km/h
Faster bus speed = 90 + 12 = 102 km/h
