The solution to the given differential equation [tex]\frac{dy}{dx} = e^{4x+5y}[/tex] is , [tex]\frac{e^{-5y}}{-5}=\frac{e^{4x}}{4} +c[/tex], where c is constant of integration.
For given question,
We have been given a differential equation [tex]\frac{dy}{dx} = e^{4x+5y}[/tex]
We know that for any real number a, m, n,
[tex]a^{m + n} = a^m \times a^n[/tex]
⇒ dy/dx = [tex]e^{4x}[/tex] × [tex]e^{5y}[/tex]
Separating the variables (x and its differential in one side and y and its differential in another side )
⇒ [tex]\frac{1}{e^{5y}}[/tex] dy = [tex]e^{4x}[/tex] dx
⇒ [tex]e^{-5y}[/tex] dy = [tex]e^{4x}[/tex] dx
Integrating on both the sides,
⇒ [tex]\int e^{-5y}[/tex] dy = [tex]\int e^{4x}[/tex] dx
We know that, [tex]\int e^{ax}\, dx=\frac{e^{ax}}{a} +C[/tex]
⇒ [tex]\int e^{4x}\, dx=\frac{e^{4x}}{4} +C[/tex]
and [tex]\int e^{-5y}\, dy=\frac{e^{-5y}}{-5} +C[/tex]
So the solution is, [tex]\frac{e^{-5y}}{-5}=\frac{e^{4x}}{4} +c[/tex], where c is constant of integration.
Therefore, the solution to the given differential equation [tex]\frac{dy}{dx} = e^{4x+5y}[/tex] is , [tex]\frac{e^{-5y}}{-5}=\frac{e^{4x}}{4} +c[/tex], where c is constant of integration.
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Use method of subtitution, will give brainliest, 20 pts
Answer:
x=3
y = -2
Step-by-step explanation:
2x+5y = -4
y = x-5
We want to use substitution
In the first equation, every time we see y, substitute x-5
2x + 5( x-5) = -4
Distribute
2x + 5x -25 = -4
Combine like terms
7x -25 = -4
Add 25 to each side
7x -25+25 = -5+25
7x = 21
Divide each side by 7
7x/7 = 21/7
x=3
Now we can find y
y = x-5
y = 3-5
y = -2
The answer is x = 3, y = -2 or (3, -2).
We are given that :
2x + 5y = -4y = x - 5Let us substitute the 2nd equation's value of y in the 1st equation.
2x + 5(x - 5) = -42x + 5x - 25 = -47x = 21x = 3Now, substitute for x in the 2nd equation.
y = 3 - 5y = -2determine the quotient of 2/3 divided by 4/5
Clark earns $31 per hour. Calculate his weekly wage if he works 38 hours per week.
Answer:
1178 because 31 dollars an hour for 38 hours you would multiply or times 31 and 38 and get 1178 for total money earned
Is the following number rational or irrational [tex]Is the following number rational or irrational \sqrt{45\\}[/tex]
Samantha and mia each left julia’s house at the same time. mia walked north at 7 kilometers per hour. samantha ran west at 11 kilometers per hour. how far apart were they after one hour? round the answer to the nearest tenth. a right triangle. a point at the angle with measure 90 degrees is labeled julia's house. a line drawn north is labeled 7 kilometers and a line drawn west is labeled 11 kilometers.
Samantha and Mia are 13 km apart from each other.
What is Pythagorean ?A right triangle's squared sides add up to the hypotenuse's squared length, according to the Pythagorean Theorem.
Mia is 7 kilometers north of Julia's home as she walked at a speed of 7 kilometers per hour.
Samantha walked at an average speed of 11 km/h, and she is now 11 kilometers west of Julia's home.
A right-angled triangle is formed by Julia's house, Mia and Samantha's locations after one hour, and the figure's points.
Hypotenuse of the triangle, which measures distance between the females
the Pythagorean theorem,
H² = P² + B²
H² = 7² + 11²
H² = 49 + 121
H = √170
H = 13.038
H = 13km
Between them, there is a 13 kilometer distance.
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3
OYes
O No
Is the following relation a function? (1 point)
x y
1 4
-1 -2
3 10
5 16
Answer: Yes
Step-by-step explanation:
Each value of y maps onto one value of x.
What are the domain and range of g of x equals the square root of the quantity x plus 4?
It is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).
What are the domain and range of a function?The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f(x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.To find the domain and range:
The given function in the problem is: [tex]g(x)=\sqrt{x+4}[/tex]Because the square root function does not exist for negative numbers, the domain is denoted by: [tex]x+4[/tex] ≥ [tex]0[/tex] → [tex]x[/tex] ≥ [tex]-4[/tex]Therefore, it is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).The range of the square root function is [tex]x[/tex] ≥ [tex]0[/tex], which remains the same as there are no vertical translations.Therefore, it is discovered using its notion that the domain and range of the function are given by (C) D: [–4, ∞) and R: [0, ∞).
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The complete question is given below:
What are the domain and range of g of x equals the square root of the quantity x plus 4?
(A) D: [4, ∞) and R: [0, ∞)
(B) D: (–4, ∞) and R: (–∞, 0)
(C) D: [–4, ∞) and R: [0, ∞)
(D) D: (4, ∞) and R: (–∞, 0)
5 yd
5 yd
8 yd
5 yd
14 yd
3 yd
9 yd
6 yd
Pleasee help rn
Given the function w(x) = 9x + 8, evaluate w(5). Explain all steps.
The value of the function w(5) is 53
How to evaluate the function?The function is given as:
w(x) = 9x + 8
The expression w(5) implies that the value of x is 5
i.e. x = 5
Substitute the known values in the above equation
w(5) = 9 * 5 + 8
Evaluate the product
w(5) = 45 + 8
Evaluate the sum
w(5) = 53
Hence, the value of the function w(5) is 53
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This pattern follows the rule add 14. What other features do you observe?
13, 27, 41, 55
please help meeeeee
The above pattern follows an arithmetic sequence with a common difference of 14 and first term of 13
How to solve a pattern?The pattern can be represented as follows:
13, 27, 41, 55
The first term of the sequence is 13 and the common difference is 14.
The above pattern is an arithmetic sequence.
Therefore, the following can be used to find the nth term.
nth term = a + (n - 1)d
where
n = number of termd = common differencea = first termTherefore,
a = 13
d = 27 - 13 = 14
Let's find the next term
5th term = 13 + (5 - 1)14
5th term = 13 +(4)14
5th term = 13 + 56
5th term = 69
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On the day after my birthday this year, I can truthfully say: "The day after tomorrow is Monday". On which day is my birthday?
Answer: Friday
Step-by-step explanation:
What is the surface area of a rectangular prism that has a length of 12 mm, a width of 15 mm, and a height of 16 mm?
Given the domain {-4, 0, 5}, what is the range for the relation 12x 6y = 24? a. {2, 4, 9} b. {-4, 4, 14} c. {12, 4, -6} d. {-12, -4, 6}
The domain of the function 12x + 6y = 24 exists {-4, 0, 5}, then the range of the function exists {12, 4, -6}.
How to determine the range of a function?Given: 12x + 6y = 24
Here x stands for the input and y stands for the output
Replacing y with f(x)
12x + 6f(x) = 24
6f(x) = 24 - 12x
f(x) = (24 - 12x)/6
Domain = {-4, 0, 5}
Put the elements of the domain, one by one, to estimate the range
f(-4) = (24 - 12((-4))/6
= (72)/6 = 12
f(0) = (24 - 12(0)/6
= (24)/6 = 4
f(5) = (24 - 12(5)/6
= (-36)/6 = -6
The range exists {12, 4, -6}
Therefore, the correct answer is option c. {12, 4, -6}.
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A 6 character computer password is made up of 4 numbers followed by 2 letters. How many different passwords are possible?
Answer: 6,760,000
Step-by-Step Explanation:
WS=
Help me please thanks so much :) I appreciate it
Answer:
Step-by-step explanation:
3 units
Answer:
3 units.
Step-by-step explanation:
Opposite sides of a parallelogram are equal in length,
So side OD = side WS.
We see from the diagram that OD is 3 units long so
WS = 3 also.
An airport parking lot charges a basic fee of $2 plus $1 per half-hour parked. what is the total charge from parking in the lot for 72 hours? a. $144 b. $146 c. $74 d. $72 please select the best answer from the choices provided a b c d
Using a linear function, the total charge from parking in the lot for 72 hours is of:
b. $146.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Both the basic fee, which is the y-intercept, and the hourly fee, which is the slope, are of $2, hence the cost of parking x hours is given by:
C(x) = 2x + 2
Hence the cost for parking 72 hours is:
C(72) = 2 x 72 + 2 = 2 x 73 = $146.
Which means that option b is correct.
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An observer (o) spots a plane (p) taking off from a local airport and flying at a 29° angle horizontal to her line of sight and located directly above a tower (t). the observer also notices a bird (b) circling directly above her. if the distance from the plane (p) to the tower (t) is 6,000 feet, how far is the bird (b) from the plane (p)? round to the nearest whole number. two parallel lines bp and ot with a transversal running through p and o. dotted red line from p to t and from b to o. angle pot is 29 degrees. the length of pt is 6000. the length of bp is x. 6,857 feet 10,824 feet 12,371 feet 22,063 feet
The distance between the bird and the aircraft is 10824 feet.
What is right angled triangle?Any triangle with one angle at a right angle or two perpendicular sides is referred to as a right triangle, right-angled triangle, orthogonal triangle, or more formally, a rectangle triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
What is Tangent?The straight line that "just touches" the curve at a certain point is known as the tangent line to a plane curve. It was described by Leibniz as the line connecting two points on the curve that are endlessly near to one another.
According to the given information:Angle of elevation = 29°
Length of plane to the tower = 6000 feet
So, it forms a right angled triangle.
So, we will use "Tangent":
tan29° = AB/CB
.55 = 6000/CB
CB = 6000/0.55
CB = 10824ft
Consider, ΔABC,
Hence, The distance between the bird and the aircraft is 10824 feet.
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Can someone help please?
[tex]r = \frac{15}{7} [/tex]
the weights of cars passing over a bridge have a mean of 3550 pounds and standard deviation of 870 pounds. assume that the weights of the cars passing over the bridge are normally distributed. use a calculator to find the approximate probability that the weight of a randomly selected car passing over a bridge is between 2800 and 4500
Answer:
Using the usual notations and formulas,
Using the usual notations and formulas,mean, mu = 3550
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculate
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)Probability that a car randomly selected is greater than 3000
Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)Probability that a car randomly selected is greater than 3000=1 - P(X < 3000) = 1 - 0.2636 (to 4 decimals) =0.7364 (to 4 decimals)
Please help with this question on a acellus thanks!
Using the law of sines, it is found that the measure of angle x is given as follows:
x = 69.9º.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is a.The length of the side opposite to angle B is b.The length of the side opposite to angle C is c.The lengths and the sine of the angles are related as follows:
sin(A)/A = sin(B)/B = sin(C)/C
Considering the given triangle, the following relation can be established:
sin(x)/11 = sin(28º)/x
Hence, applying cross multiplication:
sin(x) = 2sin(28º)
sin(x) = 0.938943126
x = arcsin(0.938943126)
x = 69.9º.
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HELP ASAp!!! Will give brainlest. Find all solutions of the equation in the interval
Answer:
7/6π, 1/6π
Step-by-step explanation:
We know that tan is sine/cosine, so cot is cosine/sine.
In this case, we know cotθ = √3
As the number is positive, using the unit circle, we now can say that the two solutions are in quadrants I and III.
Taking a look at the unit circle, we can finalize our answer.
What is the sum of the geometric sequence -3, 18, -108,
if there are 8 terms?
Step-by-step explanation:
using gp formula
tn=ar^n-1
which our a which is the first term is = -3
our r which is t2/t1=-6
t8=(-3)(-6)^8-1
=(-3)(-6)^7
=(-3)(-279936)
=839808
Last one for the night lol thanks again
Answer:
[tex]BC=24[/tex]
Step-by-step explanation:
We know that in an isosceles triangle if two angles are congruent then the opposite sides of the angle must also be congruent.
Therefore [tex]AC=AB[/tex]
Then we can create an equation and solve for x
[tex]x+8=2x-1\\x+9=2x\\9=x[/tex]
Now that we have x we just need to substitute it for [tex]BC[/tex]
[tex]BC=3x-3\\BC=3(9)-3\\BC=27-3\\BC=24[/tex]
Wynn is 24 years old and has decided to reduce the number of cups of coffee he buys by 2 cups per day. One cup of coffee typically costs $2.50. Assuming 30 days in a month, if he chooses to invest this money at the end of every 6 months into an investment paying 5.50% compounded semi-annually, how much will he have when he turns 69?
The total amount he would have at 69 is $343,347.81.
What is the total amount saved?The formula that can be used to determine the future value of the deferred annuity is:
Future value = annuity factor x monthly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 5.5 /2 = 2.75%n = number of payments = 2 x (69 - 24) = 90Amount he would save every 6 months:
amount saved per day = $2.50 x 2 = $5Amount saved per month : $5 x 30 = $150 Amount saved every 6 months = $150 x 6 = $900Future value : 900 x {[(1.0275^90) - 1] / 0.275}= $343,347.81
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sketch the graph: y=1/3x+2
The slope of the line is 1/3and the y-intercept is at the (0, 2) as shown in the graph below.
Graph of a linear functionA linear function is a function that has a leading degree of 1. The standard equation for a linear function is expressed as:
y = mx + b
where
m is the slope which is equal to the rate of change of y coordinate to x-coordinates.
b is the y-intercept
Given the following equation
y= 1/3x + 2
The slope of the line is 1/3 and the y-intercept is at the(0,2) as shown in the graph below.
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What is the product of –3 and 5?
17. In a spelling competition, school X had 12 more participants than school Y and 18 fewer participants than school Z. The ratio of the number of boys to the number of girls in school X, Y and Z were 1:2, 1:5 and 2: 1 respectively. There were 50 more girls than boys in total from the 3 schools. How many participants from the 3 school were there in all?
There were 204 participants from the three schools
How to determine the number of participants?The given parameters are:
X = 12 + Y
X = Z - 18
Girls = Boys + 50
The ratios of the number of boys to girls in the schools are:
1 : 2
1 : 5
2 : 1
This means that:
School X: Boys = 1/3 and Girls = 2/3School Y: Boys = 1/6 and Girls = 5/6School Z: Boys = 2/3 and Girls = 1/3So, we have:
Boys = 1/3X + 1/6Y + 2/3Z
Girls = 2/3X + 5/6Y + 1/3Z
Substitute the above equations in Girls = Boys + 50
2/3X + 5/6Y + 1/3Z = 1/3X + 1/6Y + 2/3Z + 50
Evaluate the like terms
1/3X + 2/3Y - 1/3Z = 50
Multiply through by 3
X + 2Y - Z = 150
So, we have:
X = 12 + Y
X = Z - 18
X + 2Y - Z = 150
Substitute X = 12 + Y in X = Z - 18 and X + 2Y - Z = 150
12 + Y = Z - 18 ⇒ Y - Z = 30
12 + Y + 2Y - Z = 150 ⇒ 3Y - Z = 138
Subtract Y - Z = 30 from the equation 3Y - Z = 138 to eliminate Z
2Y = 108
Divide by 2
Y = 54
Substitute Y = 54 in X = 12 + Y
X = 12 + 54
X = 66
Substitute X = 66 in X = Z - 18
66 = Z - 18
Solve for Z
Z = 66 + 18
Z = 84
So, the total number of participants from the 3 schools is
Total = X + Y + Z
This gives
Total = 66 + 54 + 84
Evaluate the sum
Total = 204
Hence, there were 204 participants from the three schools
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What is the period of y=−5 cos( 8 π x)+3? Give an exact value. units PLEASE MAKE IT QUICK
Answer:
Maximum/Minimum Value: (0,−2) is a local minima (1/8,8) is a local maxima
Explanation: Use the derivative to find the maximum and minimum
Answer:
Period = ¹/₄
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function:
f(x) = A cos(B(x + C)) + D
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftGiven function:
[tex]y=-5 \cos (8 \pi x)+3[/tex]
Comparing the given function with the standard form:
A = 5B = 8πC = 0D = 3[tex]\implies \sf Period=\dfrac{2 \pi}{B}=\dfrac{2 \pi}{8 \pi}=\dfrac{1}{4}[/tex]
Therefore, the period of the given function is ¹/₄.
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A shop is having a 10% off sale. Find the sale price of a cap which normally costs $12?
Answer: $10.8
Step-by-step explanation: To do this, we need to find 90% of $12 because the cap is 10% off. We can do this by multiplying 12 by 0.9. 12 x0.9 = 10.8.
Can anyone tell me how you could describe this answer to the equation?
[tex]f(x)=\frac{5x}{x-25}[/tex]
The end behavior of the given polynomial is that as x → -∞ or x → ∞, then, f(x) → 5
What is the end behavior of the Polynomial?We are given the polynomial;
f(x) = 5x/(x - 25)
Now, we want to find the limits as x → ±∞. Let us rearrange the given polynomial to get; f(x) = 5/(1 - (25/x))
Thus, applying limits we have;'
lim x → ±∞ [5/(1 - (25/x))]
From algebraic limit laws we know that;
If f(x) = k, then;
lim x → +∞ [f(x)] = k
Also, lim x → -∞ [f(x)] = k
Thus, applying limits at infinity to our polynomial gives;
lim x → ±∞ [5/(1 - (25/x))] = 5/(1 - 0) = 5
This is because lim x → ∞ for 1/x is 0.
Thus, f(x) has horizontal asymptotes at y = 5
Thus, we conclude that the end behavior is that as x → -∞ or x → ∞, then, f(x) → 5
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