Differentiating y = x^3 ln 2x/e^x Sin x is: y' = x^2 [(3 ln 2x/e^x Sin x + 3/x) - 2 ln 2x/e^x Sin x cos x + cos x].
What is Differentiation?Differentiate y can be find using the product and chain rule.
Using the chain rule
v'(x) = [1/(2x/e^x)] * (2e^x - e^x*2x) / (2x/e^x)^2
v'(x) = [e^x(2-e^x)] / (2x)^2
Using the product rule
y' = 3x^2 ln(2x/e^x) sin(x) + x^3 [e^x(2-e^x)] / (2x)^2 sin(x) + x^3 ln(2x/e^x) cos(x)
Simplifying
y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)
So,
derivative of y is:
y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)
Therefore the differentiate of y is 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x).
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Express the following ratios in the form 1: n (a) 6:15 (b) 20:1160 (c) 30: 1500
Answer:
Step-by-step explanation:
(a)
16
36
=
4
9
36:16=9:4
(b)
144
324
=
4
9
324:144=9:4
(c)
1125
125
=
1125
125
=
45
5
=
9
1
∴125:1125=1:9
Is anyone good with Math or History
The probability of passing at least one will be 0.70.
We know that,
Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
here, we have,
Probability of passing history course = 0.59
Probability of passing math course = 0.60
Probability of passing both courses = 0.49
so, we get,
Probability of passing at least one will be
⇒ 0.59 + 0.60 – 0.49
⇒ 0.70
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complete question:
A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the probability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?
Determine if the two expressions are equivalent and explain your reasoning. 8m+4-3m and 3+ m+2m+1+2m
The two expressions "8m+4-3m" and "3+ m+2m+1+2m" are equivalent because they simplify to the same-value.
To determine if the two expressions are equivalent, we can simplify each expression and then compare them.
Simplifying the first -expression,
We have,
⇒ 8m + 4 - 3m can be simplified by combining like terms;
⇒ 8m - 3m + 4 = 5m + 4
Next, Simplifying the second-expression,
we have,
⇒ 3 + m + 2m + 1 + 2m can also be simplified by combining like-terms:
⇒ (1 + 3) + (m + 2m + 2m) = 4 + 5m
So we have:
(i) 8m + 4 - 3m = 5m + 4
(ii) 3 + m + 2m + 1 + 2m = 4 + 5m
Since both simplified expressions are equal to "5m + 4", we can conclude that the two original expressions are equivalent.
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Hannah conducted a scientific experiment. For a certain time, the temperature of a compound rose 3 1/2 degrees every 2/3 of an hour. What was the rate, in degrees per hour, that the temperature of the compound rose? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
The rate at which the temperature of the compound rose was 5¹/₄ degrees per hour.
To find the rate at which the temperature of the compound rose, we need to divide the change in temperature by the time interval during which the change occurred.
The temperature rose 3¹/₂ degrees every 2/3 of an hour. To write this as a fraction, we can first convert 3¹/₂ to an improper fraction:
3¹/₂= 7/2
Now, we can write the rate of change as a fraction:
Rate of change = (7/2) / (2/3)
To divide by a fraction, we can multiply by its reciprocal:
Rate of change = (7/2) x (3/2)
Simplifying, we get:
Rate of change = 21/4
Therefore, the rate at which the temperature of the compound rose was 5¹/₄ degrees per hour.
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12 friends shared 8 small pizzas equally. how much pizzas did each person get?
Each person would get approximately 0.67 small pizzas when 12 friends share 8 small pizzas equally.
If 12 friends shared 8 small pizzas equally, we can divide the total number of pizzas by the number of friends to determine how much pizza each person gets.
Total number of pizzas = 8 small pizzas
Number of friends = 12
To find how much pizza each person gets, we divide the total number of pizzas by the number of friends;
Pizza per person = Total number of pizzas/Number of friends
Pizza per person = 8 small pizzas / 12 friends
Pizza per person = 0.67 small pizzas
Therefore, each person would get 0.67 small pizzas.
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A circular patio has diameter of 4 yards . What is the area of the patio?
The area of the circular pateo is 50.24 square yards.
What is the area of the patio?Remember that for a circle of radius R, the area is given by the formula:
A = pi*R²
Where pi = 3.14
Here we know that the patio is circular, and it has a diameter of 4 yards, then the radius is:
R = 4yd/2
R = 2 yd
Replacing that in the area formula we will get:
A = 3.14*(2yd)²
A = 50.24 yd²
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Find the area of the rhombus below.
The area of the rhombus is derived to be 70 square units
How to calculate for the area of the rhombusIn calculating for the area of a rhombus, we multiply the length of its two diagonals and divide the result by two
For the given rhombus, we have diagonals:
5 + 5 = 10 and 7 + 7 = 14
thus;
Area of the rhombus = (10 × 14)/2
Area of the rhombus = 140/2
Area of the rhombus = 70 square units.
Therefore, the area of the rhombus is derived to be 70 square units.
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In this figure, the two angles are complementary.
(2x + 6)°
(1/2x )°
What is the value of x?
Answer:
Step-by-step explanation:
Complementary means angles that add up to 90°
Based on that you can write and equation by adding the 2 angles and making equal to 90
2x+6+1/2x=90 combine like terms on left
5/2x+6=90 subtract both sides by 6
5/2x=84 multiply by the reciprocal of 5/2 => 2/5
x=168/5 or 33.6
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE (Do the one thats C and highlighted, ignore the others) :)
Step-by-step explanation:
3.3% = .033 in decimal
Use the compounding formula
a) P(t) = 18000 (1 + .033)^t
b) for t =2 this computes to 19207.6 bacteria
A basket contains 3 green, 4 yellow, 5 blue and 6 red tickets, one of which is randomly selected.
Giving your answer in its simplest form, what's the theoretical probability of not drawing a yellow ticket?
Probability of not drawing a yellow ticket =
Again using theoretical probability, determine the chance of getting a green or red ticket. Give your answer as a fraction in its simplest form.
Probability of drawing a green or red ticket =
The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.
We have,
There are a total of 3 + 4 + 5 + 6 = 18 tickets in the basket.
The probability of drawing a yellow ticket.
= 4/18
Since there are 4 yellow tickets out of 18 total tickets.
The probability of not drawing a yellow ticket is equal to the probability of drawing a green, blue, or red ticket.
There are 3 + 5 + 6 = 14 tickets that are not yellow.
The probability of not drawing a yellow ticket.
= 14/18
= 7/9
To find the probability of drawing a green or red ticket, we need to add the probabilities of drawing a green ticket and a red ticket.
The probability of drawing a green ticket.
= 3/18
The probability of drawing a red ticket.
= 6/18
Now,
The probability of drawing a green or red ticket is
= 3/18 + 6/18
= 9/18
= 1/2
Thus,
The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.
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Use the equation to find the number of correct answers Gilberto needs to buy a new shirt that costs 25$. Show your work
a) An equation that represents the amount of money that Gilberto
receives during a school year: y = 5 + (0.5) x
b) The number of correct answers Gilberto needs to buy a new shirt that costs $25 = 40
Let us assume that y represents the amount of money and x represents the number of correct answers.
We know that One dollar = 100 cents.
so, 50¢ = 0.5 dollars
From the described informtaion, we can write the equation that represents the amount of money that Gilberto receives during a school year as: y = 5 + (0.5) x
Now we need to find the number of correct answers Gilberto needs to buy a new shirt that costs $25
i.e., for y = 25, we need to find the value of x.
Substitute y = 25 in above equation.
25 = 5 + (0.5) x
We solve this equation for x
(0.5) x = 20
x = 20 / (0.5)
x = 40
This means that he needs to give 40 correct answers.
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The complete question is:
Gilberto's grandfather gives Gilberto $5 and then 50¢ for each math question he answers correctly on his math exams for the year.
a. Write an equation that represents the amount of money that Gilberto
receives during a school year. Explain what the variables and numbers mean.
b. Use the equation to find the number of correct answers Gilberto needs to buy a new shirt that costs $25. Show your work.
Given ⊙K with secants NS and NR, which expression represents PS?
An expression that represent PS include the following: C. (NP + NQ + QR)/NR - NR.
What is the Tangent Secant Theorem?In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.
By applying the Tangent Secant Theorem to this circle, we have the following:
NP × PS = NQ × QR
PS = (NQ × QR)/NP
In terms of line segment NR, the expression can be rewritten as follows;
(NP + NQ + QR)/NR - NR
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In the diagram, m < AFB = 78
Which angle is complementary to
The angle BFC is the angle that is complementary to AFB
What is a complementary angleWhenever the sum of two angles adds up to 90 degrees, they are defined as complementary angles. Take 30 and 60 degrees, for instance; they are complementary angles.
From the definition we have to find the angle when if added to AFB would give us the sum of 90 degrees
AFC is a 90 degree angles
We have AFC = AFB + BFC
90 = 78 + BFC
BFC = 90 - 78
= 12
Hence the angle BFC is the complementary angle
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For question number 5
Answer: A' will be at (-2,0)
Step-by-step explanation:
Reflecting things over a line can be done in several different ways, I will try to explain the one I use and the easiest one. What I use is to look at it and find the shortest distance between the line and A, in this case, the shortest distance is at (-.5,1.5), since A is at (1,3) the distance between them is (-1.5,-1.5) If you double this change you will find how far away the new point A is from the Old point, so its a change of (-3,-3). (1,3)+(-3,-3) gets you to the final points of (-2,0)
Another, probably easier, method is to go down from point A until you hit the line, and then go over that many points. In this case, you go down 3 from A to hit the line, and then go 3 to the left which reflects it over the line. Either way you do it, you get (-2,0)
27 divided by 187 ( so the work please
Answer:
Answer:
= 6 R 25
= 6 25/27
187 divided by 27 equals
6 with a remainder of 25
Step-by-step explanation:
1) m2 x m2
2) w3 x w2
3) 5k3 x 4k4 x k
4) A rectangle and square have the same area.
The rectangle has length 27x and width 3x.
Find the length of each side of the square.
Find the length of each side of the square.
5) Fully simplify the following expression
28x3 ÷ 4x
6) Simplify fully:
To multiply letters e.g., xy you must include the multiplication symbol. E.g., xy should be typed as x*y
fraction numerator 12 c to the power of 8 g to the power of 9 over denominator 4 c to the power of 4 g to the power of 4 end fraction
m² × m² is equal to m⁴.
w³ × w² is equal to w⁵.
5k³ × 4k⁴ × k is equal to 20k⁸.
The length of each side of the square is 9x.
A simplification of the expression 28x³ ÷ 4x is 7x².
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LB
Where:
A represent the area of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.By substituting the given parameters into the formula for the area of a rectangle, we have the following;
Area of rectangle = (27x) × (3x)
Area of rectangle = 81x²
Note: Area of square = Area of rectangle
Area of square = (side length)²
81x² = (side length)²
Side length = √(81x²)
Side length = 9x
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Question content area top
Part 1
The length of a rectangular park is six times its width. The park is surrounded by a 3-foot-wide path. Let x denote the width of the park. Write a quadratic function to represent the total area of the park and the path.
The quadratic function to represent the total area of the park and the path will be 6(x² + 7x + 6).
Given that:
Width, W = x
Length, L = 6x
Path width, d = 3
The rectangle's area will be given as,
Area of the rectangle = L × W square units
The quadratic function to represent the total area of the park and the path will be given as,
A = (x + 2 · 3) (6x + 2 · 3)
A = (x + 6)(6x + 6)
A = 6(x + 6)(x + 1)
A = 6(x² + 7x + 6)
The quadratic function to represent the total area of the park and the path will be 6(x² + 7x + 6).
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2. A set of 120 test scores are normally distributed
with a mean of 82 and a standard deviation of
5.
- The price of a gallon of regular gasoline at 75
a) What percent of the scores are between 72
and 872
b) What is the probability that a score is greater
than 77?
c) What is the probability that a score is less than
82 or greater than 92?
d) About how many students scored outside two
standard deviations of the mean?
a) What percent of gas stations sell a gallon of
It should be noted that 81.85% of the scores are between 72 and 87.
The probability that a score is greater than 77 is approximately 0.8413.
How to calculate the valuea) The z-score for 72 is calculated as:
z = (72 - 82) / 5 = -2
The z-score for 87 is calculated as:
z = (87 - 82) / 5 = 1
0.8413 - 0.0228 = 0.8185
So, approximately 81.85% of the scores are between 72 and 87.
b) The z-score for 77 is calculated as:
z = (77 - 82) / 5 = -1
1 - 0.1587 = 0.8413
Therefore, the probability that a score is greater than 77 is approximately 0.8413 (or 84.13%).
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A music festival sold two types of tickets, day passes and weekend passes. The day passes were $61, and the weekend pass was $110. The total ticket sales for the festival were $307,745. They sold 257 more day passes than weekend passes. How many day passes and how many weekend passes were sold?
Answer:
day passes: 1965weekend passes: 1708Step-by-step explanation:
You want the number of day passes sold for $61 and weekend passes sold for $110 if 257 more day passes were sold, and sales totaled $307745.
SetupLet w represent the number of weekend passes sold. Then w+257 is the number of day passes sold. The total revenue is ...
61(w+257) +110(w) = 307745
SolutionSimplifying the equation, we have ...
171w +15677 = 307745
171w = 292068 . . . . . . . . subtract 15677
w = 1708 . . . . . . . . . . . divide by 171
w+257 = 1965 . . . day passes sold
1965 day passes and 1708 weekend passes were sold.
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Find the missing angle.
92° 78°
Answer:
[tex]\huge\boxed{\sf x = 10\°}[/tex]
Step-by-step explanation:
Statement:Angles on a straight line add up to 180 degrees.Solution:According to the statement,
92° + x + 78° = 180°
170° + x = 180°
Subtract 170° from both sidesx = 180° - 170°
x = 10°[tex]\rule[225]{225}{2}[/tex]
Need help fast I will rate
The formula for p(x) is p(x) = -0.1(x - 5)²(x + 3).
What is a polynomial graph?In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
Also, the graph has a zero of multiplicity 2 at x = 5 and zero of multiplicity 1 at x = -3;
x = 5 ⇒ x - 5 = 0.
(x - 5)²
x = -3 ⇒ x + 3 = 0.
(x + 3)
In this context, an equation that represent the polynomial function is given by:
p(x) = a(x - 5)²(x + 3)
By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, -7.5), we have;
-7.5 = a(0 - 5)²(0 + 3)
-7.5 = a75
a = -7.5/75
a = -0.1.
Therefore, the required polynomial function is given by:
p(x) = -0.1(x - 5)²(x + 3)
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What is the distance of X?
11/16"
3/4"
7/8"
23/32"
Answer:
C) 23/32
Step-by-step explanation:
count how many lines there are in all
32
Then count from beginning to X
23
The distance of X is 23/32
Solve the following for θ, in radians, where 0≤θ<2π.
5cos2(θ)−8cos(θ)+2=0
Select all that apply:
2.85
5.03
1.26
1.37
1.86
0.61
Answer:5.03
1.26 are correct
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
5u^2 - 8u + 2 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 5, b = -8, and c = 2. Substituting these values, we get:
u = (8 ± sqrt(64 - 40)) / 10
u = (8 ± 2sqrt(6)) / 10
Therefore, either:
A foam cube, 5 in. in width has a mass of 62 g. What is the volume and density
The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, the volume of the foam cube is 5 in. x 5 in. x 5 in. = 125 cubic inches.
Density is calculated by dividing the mass of an object by its volume. In this case, the density of the foam cube is 62 g / 125 cubic inches = 0.496 g/cubic inch.
So, the volume of the foam cube is 125 cubic inches and its density is 0.496 g/cubic inch.
MARK ME BRAINLEISTfind the compound interest on rs 6950 for 3 years if the interest is payable half yearly,the rate for the first two years being 6% p.a and for the third year 9% p.a
Answer:
Rs 2150.81.
Step-by-step explanation:
The interest rate for the first two years is 6% per annum, which is halved for each six-month period. Therefore, the interest for the first two years would be (6950*(1+(0.03))^8) - 6950 = Rs 1373.53.
For the third year, the interest rate is 9% per annum, which is also halved for each six-month period. Therefore, the interest for the third year would be (6950*(1+0.045))^2 - 6950 = Rs 777.28.
Hence, the total compound interest for three years would be Rs 2150.81.
Solve for radius and diameter then what is the area C=226.08in
The radius of the circle is 35.98 in, the diameter is 71.96 in. and the area of the circle is 4066.98 sq. in.
Here, the circumference of circle is C=226.08 in
We know that the formula for the circumference of circle is C = 2πr
Using this formula we find the value of radius 'r',
C = 2πr
226.08 = 2πr
r = 226.08 / 2π
r = 35.98 in
And the diameter of the circle would be,
d = 2r
d = 2 × 35.98
d = 71.96 in.
And the area of the circle would be,
A = π × r²
A = π × 35.98²
A = 4066.98 sq. in.
Therefore, the required area is 4066.98 sq. in.
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The complete question is:
Solve for radius and diameter then what is the area of the circle if the circumference of circle is C=226.08 in.
0
Determine whether the curve is the graph of a function of x.
OYes, it is a function.
O No, it is not a function.
If it is, state the domain and range of the function. (Enter your answers in interval notation. If the curve is not the graph of a function of x, enter DNE.)
domain
range
The correct statement regarding whether the graph represents a function is given as follows:
No, it is not a function.
When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.
In the graph, we have that at x = 0 = y-axis, the function has three numeric values, which is a case of vertically aligned points, hence the graph does not represent a function.
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Select all of the values of x that make the inequality 100 - 3x ≥ -50 true.
A: 50
B: -50
C: 49.9
D: 50.1
E: 0
Jason has three T-shirts of different colors. He shares his T-shirts with his two brothers. How many ways can all three boys trade shirts and not wear the same color twice? A. one B. two C. three D. six
Answer: 6
Step-by-step explanation:
There are six possible ways that the three boys can initially choose shirts: ABC, ACB, BAC, BCA, CAB, CBA.
14) -1 -10a < -1 or 10 + 3a ≤-5
The solution to the inequality is:
0 < a or a ≤ -5
How to solve the inequality?
An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.
We have: -1 -10a < -1 or 10 + 3a ≤ -5 and we want to solve for the variable "a".
-1 -10a < -1 or 10 + 3a ≤ -5
-10a < -1 + 1 or 3a ≤ -5 - 10
-10a < 0 or 3a ≤ -15
a < 0/(-10) or a ≤ -15/3
a > 0 or a ≤ -5
Since a a > 0 is the same as 0 < a. We can say:
0 < a or a ≤ -5
Thus, 0 < a ≤ -5
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