To solve the exact differential equation (5t^2 + 8y) dy + (10yt + 9t^2) = 0, we need to check if it is exact or not. We do so by taking partial derivatives with respect to y and t:
∂/∂y (5t^2 + 8y) = 8
∂/∂t (10yt + 9t^2) = 10y + 18t
Since these partial derivatives are not equal, the equation is not exact. To make it exact, we can multiply the entire equation by a integrating factor, which is given by:
μ = e^(∫(∂/∂t)(10yt + 9t^2) dt) = e^(∫(10y + 18t) dt) = e^(10yt + 9t^2)
Multiplying both sides of the equation by μ, we get:
(5t^2 + 8y)e^(10yt + 9t^2) dy + (10yt + 9t^2)e^(10yt + 9t^2) dt = 0
Now, we can check if this equation is exact:
∂/∂y (5t^2e^(10yt + 9t^2) + 8ye^(10yt + 9t^2)) = 10te^(10yt + 9t^2)
∂/∂t ((10ye^(10yt + 9t^2)) + (9t^2e^(10yt + 9t^2))) = 10ye^(10yt + 9t^2) + 18t^2e^(10yt + 9t^2)
These partial derivatives are equal, so the equation is exact. Therefore, we can find a potential function Φ such that:
∂Φ/∂y = 5t^2e^(10yt + 9t^2) + 8ye^(10yt + 9t^2)
∂Φ/∂t = (10ye^(10yt + 9t^2)) + (9t^2e^(10yt + 9t^2))
Integrating the first equation with respect to y, we get:
Φ = ∫(5t^2e^(10yt + 9t^2) + 8ye^(10yt + 9t^2)) dy = (5t^2/10)e^(10yt + 9t^2) + (4y/10)e^(10yt + 9t^2) + C(t)
where C(t) is an arbitrary constant of integration that depends only on t.
Now, we can differentiate this expression with respect to t and compare it to the second equation:
∂Φ/∂t = (10t/10)e^(10yt + 9t^2) + C'(t)
(10ye^(10yt + 9t^2)) + (9t^2e^(10yt + 9t^2)) = (10t/10)e^(10yt + 9t^2) + C'(t)
Comparing the two expressions, we get:
C'(t) = 10ye^(10yt + 9t^2)
Integrating both sides with respect to t, we get:
C(t) = ∫10ye^(10yt + 9t^2) dt = e^(10yt + 9t^2) + K
where K is another arbitrary constant of integration.
Therefore, the solution to the exact differential equation (5t^2 + 8y) dy + (10yt + 9t^2) = 0 is given by:
(5t^2/10)e^(10yt + 9t^2) + (4y/10)e^(10yt + 9t^2) + e^(10yt + 9t^2) + K = 0
or simplifying:
y = (-5t^2/4) - (1/2)e^(-10yt - 9t^2) - (K/4)e^(-10yt - 9t^2)
where K is an arbitrary constant of integration.
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Let (x) = -x^4 -8x^3 +6x - 2. Find the open intervals on which is concave up (down). Then determine the x-coordinates of all inflection points a f.
The x-coordinates of all inflection points a f of the function[tex]f(x) = -x^4 - 8x^3 + 6x - 2[/tex]are (-4, f(-4)) and (0, f(0)).
To find the intervals of concavity and the inflection points of the function[tex]f(x) = -x^4 - 8x^3 + 6x - 2,[/tex] we need to find the second derivative and analyze its sign.
First, we find the first derivative:
[tex]f'(x) = -4x^3 - 24x^2 + 6[/tex]
Then, we find the second derivative:
[tex]f''(x) = -12x^2 - 48x[/tex]
To determine the intervals of concavity, we need to find where f''(x) is positive or negative.
[tex]f''(x) = -12x^2 - 48x = -12x(x + 4)[/tex]
f''(x) is negative for x < -4 and x > 0, and positive for -4 < x < 0.
Therefore, the function f(x) is concave down on the intervals (-∞, -4) and (0, ∞), and concave up on the interval (-4, 0).
To find the inflection points, we need to find where the concavity changes. This occurs at x = -4 and x = 0.
At x = -4, the function changes from concave down to concave up. Therefore, (-4, f(-4)) is an inflection point.
At x = 0, the function changes from concave up to concave down. Therefore, (0, f(0)) is also an inflection point.
Thus, the inflection points of f(x) are (-4, f(-4)) and (0, f(0)).
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According to these three facts, which statements are true? Circle D has center (2, 3) and radius 7. Circle F is a translation of circle D, 2 units right. Circle F is a dilation of circle D with a scale factor of 4. Select each correct answer. Responses Circle F and circle D are similar. Circle , F, and circle , D, are similar. The radius of circle F is 28. The radius of circle , F, is 28. The center of circle F is (0, 3). The center of circle , F, is , begin ordered pair 0 comma 3 end ordered pair,. Circle F and circle D are congruent. Circle , F, and circle , D, are congruent
Answer:
The answer to your problem is:
The radius of circle F is 28.
Circle F and circle D are similar.
Step-by-step explanation:
How to find the radius:
A = π × [tex]r^{2}[/tex]
But the radius of a circle from diameter. If you can recall the diameter d, the radius is r = d / 2.
By looking at our facts we can actually see ( if we use the comparing method ) that the circles, F & D are very much similar.
Thus the answer to your problem is:
The radius of circle F is 28.
Circle F and circle D are similar.
Deshaun needs to read 3 novels each month. Let N be the number of novels Deshaun needs to read in M months. Write an equation relating N to M. Then use this equation to find the number of novels Deshaun needs to read in 19 months.
1. An equation representing the number (N) of novels Deshaun needs to read in M months is N = 3M.
2. Based on the above equation, Deshaun needs to read 57 novels in 19 months.
What is an equation?An equation is a mathematical statement that shows the equality or equivalence of mathematical expressions.
While mathematical expressions combine variables with numbers, constants, and values using mathematical operands, equations use the equal symbol (=) in addition.
The number of novels Deshaun needs to read per month = 3
The number of months involved = 19 months
Let the number of novels Deshaun needs to read in M months = N
Let the number of months involved = M
Equation:N = 3M
N = 57 (3 x 19)
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Match each equation to the situation it represents. Situation Leilah has not yet studied 600 of her 2400 flashcards. She studies 40 new cards each day. Stetson rents studio space for $600 a month for music lessons. He charges his students $40 per hour and earned a profit of $2400 this month. A kit contains 600 letter tiles and 40 number tiles. Each tile has the same mass, and the kit has a total mass of 2400 g. Equation 40x600 2400 2400 40x = 600 (600 +40) x = 2400
Each equation should be matched to the situation it represents as follows;
"Leilah has not yet studied 600 of her 2400 flashcards. She studies 40 new cards each day." ⇒ 2400 - 40x = 600
"Stetson rents studio space for $600 a month for music lessons. He charges his students $40 per hour and earned a profit of $2400 this month." ⇒ 40x - 600 = 2400
"A kit contains 600 letter tiles and 40 number tiles. Each tile has the same mass, and the kit has a total mass of 2400 g." ⇒ (600 + 40)x = 2400.
How to write a linear function to represent each of the equations?In this scenario and exercise, the independent variable (domain or input value) would be represented by the variable x, and then each of the situations described by the word sentence (problem) would be translated into an algebraic equation or linear function as follows;
Since Leilah studies 40 new cards per day, but hasn't studied 600 of her 2400 flashcards yet, a linear function to model or represent this situation is given by;
2400 - 40x = 600
The rent for Stetson's studio space is $600 per month and he charges his students $40 each hour while earning a profit of $2400 this month, a linear function to model or represent this situation is given by;
40x - 600 = 2400
Since this kit with a total mass of 2400rams contains 600 letter tiles and 40 number tiles, and each of the tiles have the same mass, the required linear function is given by;
(600 + 40)x = 2400.
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What is the circumference of the circle with a radius of 1.5 meters? Approximate using π = 3.14.
9.42 meters
7.07 meters
4.64 meters
4.71 meters
Answer:
9.42 meters
Step-by-step explanation:
radius= 1.5
double the radius to get the diameter
diameter= 3
to find the circumference the equation is π × d
3.14 × 3= 9.42
circumference= 9.42
Answer: B
The guy above is wrong! The correct answer is 7.07, and I double checked with a circumference calculator.
Step-by-step explanation:
-To find the circumference of a circle, you can use the formula C = πd.
-By using this formula the answer found is 7.07
This is 100% the right answer, trust me.
Brainliest?
Medical records at a doctor’s office reveal that 12% of adult patients have seasonal allergies. Select a random sample of 100 adult patients and let p^ = the proportion of individuals in the sample who have allergies.
(a) Calculate the mean and standard deviation of the sampling distribution of p^.
(b) Interpret the standard deviation from part (a).
(c) Would it be appropriate to use a normal distribution to model the sampling distribution of p^ ? Justify your answer
The mean of the sampling distribution is 0.12 and the standard deviation is 0.033
(a) The mean of the sampling distribution of p^ is equal to the population proportion, which is p = 0.12. The standard deviation of the sampling distribution of p^ is given by the formula:
σ = sqrt[(p(1-p))/n]
where n is the sample size. Plugging in the values, we get:
σ = sqrt[(0.12)(0.88)/100] = 0.033
Therefore, the mean of the sampling distribution is 0.12 and the standard deviation is 0.033.
(b) The standard deviation from part (a) represents the amount of variability we expect to see in the sampling distribution of p^ due to chance.
It tells us how much we would expect p^ to vary from sample to sample, if we were to repeat the sampling process many times.
(c) Yes, it would be appropriate to use a normal distribution to model the sampling distribution of p^, because the sample size n is large enough (n=100) for the Central Limit Theorem to apply.
According to the Central Limit Theorem, the sampling distribution of p^ will be approximately normal with mean p and standard deviation σ/sqrt(n), as long as the sample size is sufficiently large.
In this case, the sample size is large enough, so we can use a normal distribution to model the sampling distribution of p^.
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Evaluate the integral (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.) 3 V x2 +8514 dx = Shule) 32+2). 10/8+) 6 + + *(x+8) corec
To evaluate the integral ∫(3/(√(x² + 8514))) dx, we can use the substitution u = x² + 8514 and du/dx = 2x, which gives us:
∫(3/(√(x² + 8514))) dx = (3/2)∫(1/√u) du
= (3/2) * 2√u + C
= 3√(x² + 8514) + C
Note that we absorbed the arbitrary constant into C as much as possible.
It seems that your question contains some typos and unclear expressions. However, I can help you evaluate a definite integral that includes fractions and an arbitrary constant.
Consider the integral:
∫(3√(x² + 8514) dx)
To solve this integral, let's perform a substitution:
u = x² + 8514
du = 2x dx
Now, we can rewrite the integral as:
(3/2) ∫(√u du)
Now, we can integrate:
(3/2) ∫(u^(1/2) du) = (3/2) * (2/3) * u^(3/2) + C
Now, substitute u back with the original expression:
(3/2) * (2/3) * (x² + 8514)^(3/2) + C = (x² + 8514)^(3/2) + C
So, the evaluated integral is:
(x^2 + 8514)^(3/2) + C
Where C is the arbitrary constant.
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Paula works part time ABC Nursery. She makes $5 per hour watering plants and $10 per hour sweeping the nursery. Paula is a full-time student so she cannot work more than 12 hours each week but must make at least $60 per week.
Part A: Write the system of inequalities that models this scenario.
Part B: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set.
The system of inequalities that models this scenario are:
x + y ≤ 12 (she is unable to work more than 12 hours each week)5x + 10y ≥ 60 (she need to make at least $60 per week)What is the system of inequalities?Part A: Based on the question, we take x be the number of hours that Paula spends watering plants and also we take y be the number of hours she spends sweeping the nursery. Hence system of inequalities equation will be:
x + y ≤ 12 (she is unable to work more than 12 hours each week)
5x + 10y ≥ 60 (she need to make about $60 per week)
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two cards are drawn from a deck of 52 playing cards. the first card is not replace before the 2nd card is drawn. what is the probabilty of drawing a king and another king?
A. 3/676
B. 1/221
C. 1/169
D. 2/169
Answer:
1/221.
Step-by-step explanation:
Probability(first card is a King) = 4/52 = 1/13 (as there are 4 kings in the pack).
Now there are 51 cards left in the pack, 3 of which are Kings, so:
Probability(second card is a King) = 3/51 = 1/17.
These 2 events are independent so we multiply the probabilities:
Required probability =
1/13 * 1/17
= 1/221.
Please help asap I need this until tmr
The following table shows the weight of a cat in pounds and the corresponding number of cans of cat food to be given each day.
To complete the table, we need to use the information that the directions on the small cans of cat food say to feed a cat 1 can of food each day for every 4 pounds of body weight.
For example, for a cat weighing 4 pounds, we need to give 1 can of food each day.
For a cat weighing 5 pounds, we need to give more than 1 can but less than 2 cans of food each day.
To find the exact number of cans, we can use the formula:
cans per day = weight in pounds / 4
Substituting the given values, we get:
cans per day = 5 / 4
cans per day = 1.25
Therefore, for a cat weighing 5 pounds, we need to give 1.25 cans of food each day. We can round this to the nearest tenth to get 1.3 cans per day.
Similarly, we can use the formula to complete the rest of the table:
KIT-E-KAT weight in pounds cans per day
4 1
5 1.3
6 1.5
7 1.8
8 2
9 2.3
10 2.5
11 2.8
12 3
13 3.3
14 3.5
15 3.8
Therefore, the completed table shows the weight of a cat in pounds and the corresponding number of cans of cat food to be given each day.
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Savannah recorded the average rainfall amount, in inches, for two cities over the course of 6 months. Show your work
City A: {2.5, 3, 6, 1.5, 4, 1}
City B: {4, 7, 3.5, 4, 3.5, 2}
What is the mean monthly rainfall amount for each city?
What is the mean absolute deviation (MAD) for each city? Round to the nearest tenth.
What is the median for each city?
Hello, I am Alyssa Ann Verrett.
Put the numbers in order:
City A: {2, 3.5, 4, 4, 5, 5.5}
City B: {3.5, 4, 5, 5.5, 6, 6}
a)
The mean monthly rainfall amount for city A: 4 in;
The mean monthly rainfall amount for city B: 5 in;
b)
The MAD monthly rainfall amount for city A: 0.8 in;
The MAD monthly rainfall amount for city B: 0.8 in;
c)
The median monthly rainfall amount for city A: 4 in;
The median monthly rainfall amount for city A: 5.25 in;
Step-by-step explanation:
a) The general definition of mean of a set X is:
mean = (x₁ + x₂ + x₃ + ... xₙ)/n
For City a:
mean = (4+3.5+5+5.5+4+2)/6 = 4
For City b:
mean = (5+6+3.5+5.5+4+6)/6 = 5
b) The general definition of mean absolute deviation of a set X is:
MAD = (|x₁-mean| + |x₂-mean| + |x₃-mean| + ... + |xₙ-mean|)/n
For City a:
MAD = ( |4-4| + |3.5-4| + |5-4| + |5.5-4| + |4-4| + |2-4| )/6 = (0 + 0.5 + 1 + 1.5 + 0 + 2)/6 = 5/6 =0.8
For City b:
MAD = ( |5-5| + |6-5| + |3.5-5| + |5.5-5| + |4-5| + |6-5| )/6 = (0 + 1 + 1.5 + 0.5 + 1 + 1)/6 = 5/6 = 0.8
c) The general definition of median depends on the quantity of elements in the set X and it represents the middlemost value of the set:
When the quantity is odd:
median= x₍ₙ₊₁₎/₂
When the quantity is even:
median= (xₙ/₂ + x ₙ₊₂/₂) /2
For City A:
median = 2, 3.5, 4, 4, 5, 5.5 = (4 + 4) / 2 = 4
For City B:
median = 3.5, 4, 5, 5.5, 6, 6 = (5 + 5.5) / 2 = 5.25
Carlotta purchased a whole life insurance policy with an annual premium of $780. In the first year, 60% of the annual premium is allocated to the insurance component and 40% to the investment component. The investment earns 2. 2% interest, compounded annually. How much will Carlotta have in the investment portion of her policy after the first year? Round to the nearest cent.
Omg help me please
After the first year, Carlotta will have $124.80 in the investment portion of her policy.
This is calculated by taking 40% of her annual premium
($780 x 0.40 = $312),
2.2% ($312 x 0.022 = $6.84).
So the total amount in the investment portion is
$312 + $6.84 = $318.84, rounded to the nearest cent, which is $124.80.
The whole life insurance policy that Carlotta purchased has both an insurance component and an investment component. In the first year, 60% of the annual premium is allocated to the insurance component, which means that $468 of her $780 premium goes towards the cost of the insurance.
The remaining 40% is allocated to the investment component, which is what Carlotta will earn interest on.
At a rate of 2.2%, compounded annually, the investment portion of Carlotta's policy earns $6.84 in interest after the first year. This is added to the $312 that was allocated to the investment portion, giving a total of $318.84.
This means that Carlotta has $124.80 in the investment portion of her policy after the first year. It's important to note that this amount will continue to grow over time as Carlotta pays her premiums and earns interest on her investment.
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Events D and E are independent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true?
(A) P(E) = 0.12
(B) P(E) = 0.4
(C) P(D or E) = 0.28
(D) P(D or E) = 0.72
(E) P(D or E) = 0.9
The probability that is true is P(D or E) = 0.72.
Option D is the correct answer.
We have,
We can start by using the formula:
P(D and E) = P(D) x P(E)
Since D and E are independent events, their probabilities multiply to give the probability of both events happening together.
Plugging in the given values.
0.18 = 0.6 x P(E)
Solving for P(E).
P(E) = 0.18 / 0.6 = 0.3
So option (A) is not correct.
To find P(D or E), we can use the formula:
P(D or E) = P(D) + P(E) - P(D and E)
Plugging in the given values.
P(D or E) = 0.6 + 0.3 - 0.18 = 0.72
Thus,
P(D or E) = 0.72 is true.
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5u–u+3u=14
help! me please
Answer:
u = 2
Step-by-step explanation:
Please help I need it ASAP, also needs to be rounded to the nearest 10th
The length of segment BC is given as follows:
BC = 47.2 km.
What is the law of cosines?The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.
The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:
c² = a² + b² - 2ab cos(C)
The parameters for this problem are given as follows:
a = 27.8, b = 24.7, C = 129.1
Hence the length of segment BC is given as follows:
(BC)² = 27.8² + 24.7² - 2 x 27.8 x 24.7 x cosine of 129.1 degrees
(BC)² = 2249.0497
[tex]BC = \sqrt{2249.0497}[/tex]
BC = 47.2 km.
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What is the area of a regular hexagon with side length of 12. 7 and apothem length of 11?
PLEASE HELP!
The area of the regular hexagon with a side length of 12.7 and apothem length of 11 is approximately 416.61 square units.
To find the area of a regular hexagon, you can use the formula , where A is the [tex]A =\frac{3\sqrt{3} }{2} (s^{2} )[/tex]area, s is the length of one side, and √3 is the square root of 3.
However, since the apothem length is given, you can also use the formula , where ap is the apothem length and p is the perimeter of the hexagon.
First, let's find the perimeter of the hexagon. Since a hexagon has six sides, the perimeter will be 6 x 12.7 = 76.2.
Next, we can use the apothem length of 11 and the side length of 12.7 to find the length of the radius of the circle inscribed in the hexagon. This is because the apothem is the distance from the center of the hexagon to the midpoint of any side, and the radius is the distance from the center to any vertex.
Using the Pythagorean theorem, we can find the radius:
[tex]r^2 = ap^2 + (\frac{s}{2} )^{2}[/tex]
[tex]r^2 = 11^2 + (\frac{12.2}{7} )^{2}[/tex]
[tex]r^2 = 121 + 40.1225[/tex]
[tex]r^2 = 161.1225[/tex]
[tex]r = \sqrt{161.1225}[/tex]
[tex]r = 12.69[/tex]
Now that we know the radius, we can use the formula for the area of a regular polygon in terms of the radius: A = (1/2) x r x ap x n, where n is the number of sides (which is 6 for a hexagon).
Plugging in the values we have:
[tex]A = \frac{1}{2} (12.69)(11)(6)[/tex]
[tex]A = 416.61[/tex]
Therefore, the area of the regular hexagon with a side length of 12.7 and apothem length of 11 is approximately 416.61 square units.
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Consider ABC.
What is the length of AC
A. 32units
B.48units
C.16units
D.24units
Describe the effect that each transformation
below has on the function (x)= x\,
where a > 0.
g(x) = |x-a|
h(x) = |x|-a
Graph of g(x) translated right direction and h(x) translated downwards direction with respect to f(x).
The given functions are;
f(x) = |x| where a > 0
g(x) = |x-a|
h(x) = |x|-a
Plot the graph of f(x)
We get vertex point (0, 0)
Now plot the graph of g(x) = |x-a|
This graph is translated towards right direction by a unit with respect to f(x)
Now plot the graph of h(x) = |x|-a
This graph is translated downwards with respect to f(x) by a unit.
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Help me please I dont know the value to y
Answer:
y=9
Step-by-step explanation:
The opposite angles of 2 intersecting lines are equal.
11y-36⁰=63⁰
11y=63⁰+36⁰
11y=99⁰
y=9
Hope this helps!
Maria records random speeds from three different Internet providers in the table. ProviderDownload Speed (megabits per second)CityNet3. 6, 3. 7, 3. 7, 3. 6, 3. 9Able Cable3. 9, 3. 9, 4. 1, 4. 0, 4. 1Tel-N-Net3. 9, 3. 7, 4. 0, 3. 6, 3. 8 Which company offers the fastest mean downloading speed?  00:00 CityNet  00:00 Able Cable  00:00 Tel-N-Net  00:00 Impossible to determine from the information given
Able Cable offers the fastest mean downloading speed among the three providers with a speed of 4.0 Mbps.
How to determine the fastest internet provider?We can calculate the mean (average) download speed for each provider and compare them to determine which company offers the fastest mean downloading speed.
Based on the given data, the mean download speed for each provider is:
City Net: (3.6 + 3.7 + 3.7 + 3.6 + 3.9) / 5 = 3.7 megabits per second (Mbps)
Able Cable: (3.9 + 3.9 + 4.1 + 4.0 + 4.1) / 5 = 4.0 Mbps
Tel-N-Net: (3.9 + 3.7 + 4.0 + 3.6 + 3.8) / 5 = 3.8 Mbps
Therefore, Able Cable offers the fastest mean downloading speed among the three providers with a speed of 4.0 Mbps.
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3x − 15y = 11 in slope intercept form
Answer:
To convert the equation 3x - 15y = 11 into slope-intercept form, we need to solve for y.
First, we'll subtract 3x from both sides:
-15y = -3x + 11
Next, we'll divide both sides by -15:
y = (3/15)x - (11/15)
Simplifying the fraction:
y = (1/5)x - (11/15)
This is the slope-intercept form, where the slope is 1/5 and the y-intercept is -11/15.
The monomial -3xy2z(-2x2yz) has degree of:
The degree of the monomial expression -3xy²z(-2x²yz) is derived to be equal to 8.
What is a monomialA monomial is a type of algebraic expression that consists of only one term. It is an expression in which the variables and their exponents are multiplied together, with no addition or subtraction involved. The degree of a monomial is the sum of the exponents of its variables.
Given the monomial:
-3xy²z(-2x²yz)
We can simplify it by multiplying the coefficients and adding the exponents of the variables:
-3(-2)x^(2+1) y^(2+1) z^(1+1)
= 6x³y³ z²
Therefore, the degree of the given monomial expression is: 3 + 3 + 2 = 8.
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Earth's distance from the sun is 1. 496 x 108 km. Saturn's distance from the sun is 1. 4246 x 10 km. How many times further from the sun is Saturn? Explain how you arrived at your answer.
Saturn is approximately 9.52 times further from the sun than Earth.
To find out how many times further from the sun Saturn is compared to Earth, we need to divide Saturn's distance from the sun by Earth's distance from the sun.
First, let's correct the distances given:
- Earth's distance from the sun: 1.496 x 10^8 km
- Saturn's distance from the sun: 1.4246 x 10^9 km (I assume you missed the exponent)
Now, let's calculate the ratio:
Ratio = (Saturn's distance) / (Earth's distance)
Ratio = (1.4246 x 10^9 km) / (1.496 x 10^8 km)
To make the calculation easier, let's factor out the common exponent (10^8):
Ratio = (1.4246 x 10) / (1.496)
Ratio ≈ 9.52
So, Saturn is approximately 9.52 times further from the sun than Earth.
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in 2018, coolville, california had a population of 72,000 people. in 2020, the population had dropped to
70,379. city officials expect the population to eventually level off at 60,000.
a. what kind of function would best model the population over time? how do you know?
b. write an equation that models the changing populaion over time.
a. The function that would best model the population over time is Exponential decay
b. write an equation that models the changing population over time P(t) = [tex]72,000 * e^(-0.035t)[/tex]
a. Exponential rot (Exponential decay) work would best demonstrate the populace over time.
Usually, the populace has diminished from 72,000 to 70,379 in fair 2 years, which could be a generally brief time period. Also, city authorities anticipate the populace to level off at 60,000, which is a sign of exponential rot.
b. The exponential rot work can be composed as:
P(t) = P0 *[tex]e^(-kt)[/tex]
Where P(t) is the populace at time t, P0 is the starting populace, e is the scientific steady around rise to 2.718, and k is the rot consistent.
Utilizing the given data, able to substitute the values:
P(0) = 72,000 (populace in 2018)
P(2) = 70,379 (populace in 2020)
To illuminate for k, able to utilize the equation:
k = ln(P0/P(t))/t
k = ln(72,000/70,379)/2
k ≈ 0.035
Subsequently, the condition that models the changing populace over time is:
P(t) = [tex]72,000 * e^(-0.035t)[/tex]
where t is the time in a long time since 2018.
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HELP PLEASE!! the function f(x)has a vertical asymptote at x=[blank]
Answer:
Step-by-step explanation:
Solution: -4
The graph gets closer and closer to the line x=-4 but never touches it.
Write each of teh following expressions without using absolute value.
|y-x|, if y>x
The expression |y-x| without absolute value is simply: y-x
In mathematics, the absolute value refers to the magnitude or numerical value of a real number without considering its sign. It gives the distance of the number from zero on the number line. The absolute value of a number x is denoted by |x| and is defined as follows:
If x is positive or zero, then |x| = x.
If x is negative, then |x| = -x (the negative sign is removed).
Since y > x, the difference (y-x) will be positive. The absolute value of a positive number is the number itself. Therefore, the expression |y-x| without absolute value is simply: y-x
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Calculate the bearing of U from T. U N 32° T
The bearing of U from T in the image is 32 degrees South by West of T
What is Bearing?In mathematics, bearings refer to the direction of an object or location in relation to two points. It is determined by the angle between the line joining them and that of the north.
Measured typically in degrees, it follows a cardinal system where 0° or 360° signifies North; East stands for 90°, South denotes at 180° while West represents 270°.
Thus, it can be seen that the bearing of U from T in the image is 32 degrees South by West of T
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This magic grid contains number sequences that increase in steps. What is the missing number? A 16 B 8 C 4 D 12 E 20
Answer:
12
Step-by-step explanation:
The numbers increase by 4 on each row.
Find the divergence of vector fields at all points where they are defined
div ( (2x^2 - sin(xz)) i + 5j - (sin (Xz)) k)
The divergence of vector fields at all points where they are defined ar 4x - 2xcos(xz) for all points in R3.
The divergence of the given vector field F = (2x^2 - sin(xz)) i + 5j - (sin (xz)) k can be found using the formula for divergence:
div(F) = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z)
Here, Fx = (2x² - sin(xz)), Fy = 5, and Fz = -sin(xz). Taking the partial derivatives, we get:
∂Fx/∂x = 4x - zcos(xz)
∂Fy/∂y = 0
∂Fz/∂z = -xcos(xz)
Therefore, the divergence of F is:
div(F) = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z) = 4x - zcos(xz) - xcos(xz) = 4x - 2xcos(xz)
The divergence of F is defined for all points where F is defined, which is the entire 3-dimensional space. So, the divergence of F is 4x - 2xcos(xz) for all points in R3.
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in right triangle abc, mzb + m2c. let sinb = r and cos b = s. what is sinc-cosc?
The value of the trigonometric expression sin c - cos c is: s - r
How to solve Trigonometric Ratios?The three most common trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
We are given that:
sinb = r and cos b = s
Thus, from the diagram attached, we can see that:
sin B = rh/h = r
cos B = sh/h = s
Thus, using trigonometric ratios, we can equally say that:
cos C = rh/h = r
sin C = sh/h = s
Thus:
sin c - cos c = s - r
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