Answer:
Step-by-step explanation:
To differentiate y = 3x cos(x) + sin(x), we can use the product rule and the chain rule.
Let's start by differentiating the first term, 3x cos(x), using the product rule:
d/dx (3x cos(x)) = 3 cos(x) - 3x sin(x)
Next, we can differentiate the second term, sin(x), using the chain rule:
d/dx (sin(x)) = cos(x)
Putting it all together, we get:
dy/dx = 3 cos(x) - 3x sin(x) + cos(x)
Simplifying the expression, we get:
dy/dx = (4cos(x)) - (3xsin(x))
Therefore, the derivative of y = 3x cos(x) + sin(x) is dy/dx = 4cos(x) - 3xsin(x).
An entrepreneur invests in a new play. The cost includes an overhead of $33,750 plus production costs of $1700 per performance. A sold-out performance brings in $2325 . Assume every performance is sold out, and let x represent the number of sold-out performances.
The entrepreneur's revenue is $2325x, entrepreneur's cost is $33,750 + $1700x and entrepreneur's profit from x sold-out performances is $625x - $33,750
The entrepreneur's revenue from x sold-out performances is given by the formula:
Revenue = (Price per Performance) x (Number of Performances)
Revenue = $2325 x x
Revenue = $2325x
The entrepreneur's cost from x sold-out performances is given by the formula:
Cost = Overhead + (Production Cost per Performance) x (Number of Performances)
Cost = $33,750 + $1700x
The entrepreneur's profit from x sold-out performances is the revenue minus the cost:
Profit = Revenue - Cost
Profit = $2325x - ($33,750 + $1700x)
Profit = $625x - $33,750
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=3sinθ/2cos2θ
Which of the following gives the Cartesian form of the equation above?
Select the correct answer below:
y=2/3x2
2y4(x2+y2)=3x2
2x4(x2+y2)=3y2
y=√3/2x
Answer: correct answer is A 2/3x^2
Step-by-step explanation:Multiply each side of the equation by 2cos2θ to get 2rcos2θ=3sinθ.
Multiply each side of the equation by r to get 2r2cos2θ=3rsinθ. Using the relationships x=rcosθ and y=rsinθ, the equation becomes 2x2=3y.
Divide each side of the equation by 3 and reverse the order of the equation to find that y=2/3x^2
If you can buy one bunch of seedless green grapes for $2, then how many can you buy with $18?
If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.
The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.
In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.
⇒ Number of bunches = ($18)/($2) per bunch,
⇒ Number of bunches = 9 bunches;
Therefore, with $18, you can buy 9 bunches of seedless green grapes.
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4/5 is a real number or imaginary
4/5 is a real number.
What are real numbers?A real number is a value in mathematics that expresses a quantity along a continuous line. Real numbers can be expressed as fractions or decimals and can be positive, negative, or zero.
4/5 is a rational number in this situation, which is a form of real number that may be written as a ratio of two integers. A real number can also be irrational, which means that it cannot be stated as a ratio of two integers and that its decimal representation goes on indefinitely without repeating.
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Which equation is the inverse of 5y+4= (x+3)²+12?
O y = x²+x+1100
y=3± √√5x+ 7/2
O-5-4--(x+3)²--1/
O
O y=-3± √5x+
7
The equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)
Which equation is the inverse of 5y+4= (x+3)²+12?From the question, we have the following parameters that can be used in our computation:
5y+4= (x+3)²+12
Swap x and y in the equation
So, we have
5x + 4= (y + 3)² + 12
When we make the vairiable y the subject, we have
y = -3 ± √(5x - 8)
Hence, the equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)
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solve the equation -16=a- 19
Answer:
a = 3
Step-by-step explanation:
Collect like-terms:
[tex] - 16 = a - 19[/tex]
[tex]a = - 16 + 19[/tex]
[tex]a = 3[/tex]
Answer: 3
Step-by-step explanation: you take 19 from 3 giving you -16
Find the values of the 6 trigonometric functions of angle A.
The values of the trigonometric functions are
1. sin A = 12/13
2. cos A = 5/13
3. Tan A = 12/5
4. cot A = 5/12
5. cosec A = 13/12
6. sec A = 13/5
What are trigonometric functions?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. Examples of these functions are; sin, cos , tan cot, cosec , sec e.t.c
Sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
here the opposite side to angle A is 12 and the adjascent is 5 while the hypotenuse is 13.
Therefore,
1. sin A = 12/13
2. cos A = 5/13
3. Tan A = 12/5
4. cot A =1/tan A = 5/12
5. cosec A = 1/sin = 13/12
6. sec A = 1/cos = 13/5
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[tex]x-\sqrt{x} +4-2\sqrt{x+3} =0\\[/tex]
The solution of the equation x - √x + 4 - 2√(x+3) =0 is given by x ≈ 0.449 or x = 2.
The expression is equal to,
x - √x + 4 - 2√(x+3) =0
By rearranging the terms and simplifying the expression as follows,
x - √x + 4 - 2√(x+3) = 0
⇒x + 4 = √x + 2√(x+3)
Square both sides to eliminate the square root,
⇒ (x + 4)² = (√x + 2√(x+3))²
⇒ x² + 8x + 16 = x + 4(x+3) + 4√x√x+3
⇒x² + 8x + 16 -x -4x -12 = 4√x√x+3
⇒ x² + 3x + 4 = 4√x√x+3
⇒x² + 3x + 4 = 4√x√(x+3)
⇒ x² + 3x + 4 = 4√(x²+3x)
Squaring both sides again gives,
⇒ (x² + 3x + 4)² = 16(x²+3x)
Expanding the left side gives,
x⁴ + 6x³ + 17x² + 24x + 16 = 16x² + 48x
Simplifying and rearranging the terms,
x⁴ + 6x³ + x² - 24x + 16 = 0
Factor this equation as follows,
(x² + 4x - 2)(x² + 2x - 8) = 0
The solutions are,
x²+ 4x - 2 = 0 or x² + 2x - 8 = 0
Solve each quadratic equation using the quadratic formula,
For x² + 4x - 2 = 0
x = (-4 ± √(4² - 4(1)(-2))) / (2(1))
⇒ x = (-4 ± √24) / 2
Simplifying the expression under the square root gives,
⇒ x = (-4 ± 2√6) / 2
⇒ x = -2 ± √6
For x² + 2x - 8 = 0
x = (-2 ± √(2² - 4(1)(-8))) / (2(1))
⇒x = (-2 ± √36) / 2
Simplifying the expression under the square root gives,
⇒ x = (-2 ± 6) / 2
⇒ x = -4 or x = 2
Discard the negative solution -2-√6 and -4
As it would lead to a negative value under the square root.
The final solutions are,
x ≈ 0.449 or x = 2
Therefore, the solution of the given equation is equal to x ≈ 0.449 or x = 2.
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The above question is incomplete , the complete question is:
Solve for x.
x - √x + 4 - 2√(x+3) =0
Which term of the sequence 1/4;-1;-21/4;...is equal to -131/2
11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).
Step-by-step explanation:
the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the
Identify the pairs of supplementary angles.
Choose all that apply.
A. RQS and SQR
B. SQT and SQR
C. TQP and RQP
D. SQR and RQP
E. PQR and RQP
F. SQT and TQP
G. TQP and PQT
H. SQR and TQP
The pairs of supplementary angles are;
B. <SQT and <SQR
C. <TQP and <RQP
D. <SQR and <RQP
F. <SQT and <TQP
What are supplementary angles?Two or more angles are referred to as supplementary angles if they add up to 180^o. Therefore the sum of angles is equal to the sum of angles on a straight line.
Thus, the pair of supplementary angles in the given diagram are;
B. <SQT and <SQR
C. <TQP and <RQP
D. <SQR and <RQP
F. <SQT and <TQP
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Given the definitions of f(x) and g(x) below,
find the value of (gof)(-7).
f(x)
13
g(x) = 2x² - 6x – 10
=
- 2x
The composition of functions is solved and gof ( -7 ) = 1,286
Given data ,
Let the first function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = 13 - 2x
Let the second function be represented as g ( x )
Now , the value of g ( x ) is
g ( x ) = 2x² - 6x - 10
Now , g o f ( x ) = 2 ( 13 - 2x )² - 6 ( 13 - 2x ) - 10
On simplifying , we get
g o f ( x ) = 2 ( 169 + 4x² - 52x ) - 78 + 12x - 10
g o f ( x ) = 250 + 8x² - 92x
Now , the composition of function is
g o f ( -7 ) = 8 ( -7 )² - 92 ( -7 ) + 250
g o f ( -7 ) = 392 + 894
g o f ( -7 ) = 1,286
Hence , the function is g o f ( -7 ) = 1,286
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How many liters each of a 50% acid solution and a 60% acid solution must be used to produce 60 liters of a 55% acid solution? (Round to two decimal places if necessary.)
To produce 60 liters of a 55% acid solution, we need 18 liters of a 50% acid solution and 42 liters of a 60% acid solution.
Let x be the number of liters of the 50% acid solution needed, and y be the number of liters of the 60% acid solution needed.
We can set up two equations based on the amount of acid and the total volume:
0.50x + 0.60y = 0.55(60)
x + y = 60
Simplifying the first equation:
0.50x + 0.60y = 33
5x + 6y = 330 (multiplying both sides by 10)
We can solve for one variable in terms of the other in the second equation, and substitute into the first equation:
y = 60 - x
5x + 6(60 - x) = 330
Simplifying:
x = 18
So we need 18 liters of the 50% acid solution, and:
y = 60 - x = 42
So we need 42 liters of the 60% acid solution.
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Which of the polar coordinates given below correctly describes the point A on the graph shown here? Select all correct answers.
Select all that apply:
(5,5π4)
(5,7π4)
(5,−3π4)
(−5,π4)
(−5,5π4)
(−5,−7π4)
Answer:
(5,5π/4)
(5,−3π/4)
(−5,π/4)
(−5,−7π/4)
Step-by-step explanation:The correct answer is:
r = 5 units (distance from the pole)
θ = 5π/4 radians (angle measured counterclockwise from the ray θ = 0)
Note: The polar coordinates for point A on the given graph are r = 5 and θ = 5π/4. The r-value represents the distance from the pole to the point, and the θ-value represents the angle measured counterclockwise from the reference ray θ = 0.
I’ll give brainliest Write an inequality that represents this situation below.
Your suitcase for vacation will fit at most 11 outfits you already have 5 packed
Answer:
An inequality that represents this situation is:
x + 5 ≤ 11
where x is the number of outfits you can pack in addition to the 5 you already have.
Step-by-step explanation:
i got a what if If you have 6 outfits packed already, then the inequality becomes:
x + 6 ≤ 11
where x is the number of outfits you can pack in addition to the 6 you already have. happy to help
i need help with this lol
The trio of sides that will make a right triangle are the ones in the first option:
5, 12, and 13.
Which set would make a right triangle?Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longest side.
So for example, for the first option we would have:
5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169
The equation is true, thus, these sides make a right triangle.
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What side-angle relationship is given in the following triangle?
A. ASA
B. AAA
C. SSS
D. SAS
Without more information or a diagram, it's not possible to definitively determine which side-angle relationship (ASA, AAA, SSS, SAS) the triangle fits. These acronyms represent different combinations of sides and angles known in a triangle.
Explanation:Given the question, it's clear that we are discussing a concept in Geometry - the side-angle relationships in a triangle. However, without more information or an accompanying diagram, it isn't possible to definitively determine which of the side-angle relationships (ASA, AAA, SSS, SAS) the triangle fits. These acronyms represent different combinations of side and angle information known about a triangle. For example, ASA means that we know two Angles and the Side between them. SAS relates to knowledge of two Sides and the Angle between them, and so forth. More information or a visual representation would allow a more conclusive answer.
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Pythagorean triples are given by these formulas:
(2²-37, 2zy, z²+37²)
The hypotenuse of a right triangle is 29. The lengths of the legs are whole numbers. List your answers in increasing
order.
The lengths of the two legs are
and
The lengths of the two legs of the right triangle are 58 and 839, in increasing order.
We have,
The formula given is incorrect.
The correct formula for Pythagorean triples with a given integer z is:
(z² - 1², 2z, z² + 1²)
Using this formula, we can find the two legs of the right triangle with hypotenuse 29 as follows:
z² + 1² = 29²
z² + 1 = 29²
z² = 29² - 1
z² = 840
z = √840
z = 28.98
Since z must be an integer, we can try integer values close to 28.98 to find one that works.
Trying z = 29,
a = z² - 1² = 840 - 1 = 839
b = 2z = 58
c = z² + 1² = 840 + 1 = 841
Therefore,
The lengths of the two legs of the right triangle are 58 and 839, in increasing order.
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Triangle 1 undergoes four different transformations.
The results of these transformations are shown.
1
4
2
5
3
Which statement best describes one of these
transformations?
Triangle 1 is rotated to result in triangle 2.
O Triangle 1 is dilated to result in triangle 3.
O Triangle 1 is reflected to result in triangle 4.
Triangle 1 is stretched to result in triangle 5.
time tables on the map mannnnn
Use the image to determine the direction and angle of rotation. Graph of triangle ABC in quadrant 1 with point A at 1 comma 3. A second polygon A prime B prime C prime in quadrant 4 with point A prime at 3 comma negative 1. 90° clockwise rotation 180° clockwise rotation 180° counterclockwise rotation 90° counterclockwise rotation
L={d,e,g} J ={b,c,h} what is the union of L and J
Step-by-step explanation:
well, the combination of all set elements.
FYI : if some elements appear in both sets, we only use these once for the result set (this is not the case here, but it might be in other questions).
the combination of both sets is then
{b, c, d, e, g, h}
which of the following equations demonstrates the Associative Property of Multiplication?
18(27 • 3) = 18(3 • 27)
8(9 + 2) = 64 + 16
12(17 • 23) = (12 • 17) • 23
18(27 • 3) = 18(81)
Answer:
12 • (17 • 23) = (12 • 17) • 23
Factorise fully 5a + 15ab
Answer:
Therefore, the fully factorised form is 5a(1 + 3b).
Step-by-step explanation:
5a + 15ab as 5a(1 + 3b) by taking out the common factor of 5a from both terms.
i need help with math
The relationship between the distance that birds fly in relation to the time they do so, is positive.
There are about 3 outliers but for the most part, the relationship is positive.
How to describe the relationship ?The graph which shows the distance that birds fly in relation to the time they do, shows that there is a positive relationship because as the time increases, the distance that the birds have flown also increases.
There are some outliers such as the bird that flew 1 mile in 7 hours but in general, as the time increases, the distance increases as well. There are two clusters of distance as well.
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Select all the correct answers. What are the solutions to this equation? 2 x 2 = - 10 x + 12 x = - 6 x = - 2 x = 1 x = - 3 x = 6
Answer:
The correct solutions to the equation 2x^2 = -10x + 12 are x = -2 and x = 3.
Step-by-step explanation:
A police car is chasing a speeding car on a right-angled intersection such that former is approaching to the intersection, while the latter is moving away from it. At the point where the police car is at 80 mph and it is 44 yards from the intersection, the police radar detected that the distance between them is increasing at 45 mph, while the other car is 117 yards away from the intersection. What is the rate of the speeding car?
The rate of the speeding car is 0.493.
We have,
The police car is at 80 mph and it is 44 yards from the intersection, is increasing at 45 mph, while the other car is 117 yards away from the intersection.
So, Rate of speeding car
= (45- 80)/ (117- 44)
= -35/(-73)
= 35/73
= 0.493
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Every winter, the math club sells cookie dough to raise money. Last year, they sold 1,080 pounds of cookie dough to 360 people. This year, they predict that they will sell cookie dough to between 460 and 500 people. About how many pounds of cookie dough will they need?
A.
2,880
B.
1,440
C.
720
D.
2,160
The number of pounds of cookie dough needed is 1,440. Therefore, option B is the correct answer.
Given that,
Last year, they sold 1,080 pounds of cookie dough to 360 people.
This means that they sold an average of 3 pounds of cookie dough per person.
Number of pounds of cookie dough = 3 pounds/person × Number of people
Here, 3×460=1,380
3×500=1500
To get a more accurate estimate, we can take the average of these two numbers, which is 1,440 pounds of cookie dough.
Therefore, option B is the correct answer.
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Marcus jogged 1 2/5 miles on Saturday and 9/10 miles on Sunday. Rounding the
fractions to the nearest 1/2, approximately how many miles did he jog over the
weekend? Express your answer as an improper fraction.
Marcus jogged [tex]2\frac{1}{2}[/tex] miles over the weekend.
Marcus jogged [tex]1\frac{2}{5}[/tex] miles on Saturday and 9/10 miles on Sunday.
we first need to find a common denominator:
[tex]1\frac{2}{5}[/tex] = 7/5
9/10 = 0.9 miles
Now, we can round each of these to the nearest 1/2:
7/5 is closer to [tex]1\frac{1}{2}[/tex] than 1, so we round to [tex]1\frac{1}{2}[/tex]
0.9 is closer to 1 than 1/2, so we round to 1
Adding these rounded values, we get:
[tex]1\frac{1}{2}[/tex] + 1 =[tex]2\frac{1}{2}[/tex]
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Find the area of the green region in the circle to the nearest tenth
The area of the green region of the circle is 96.4 ft².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the green region of the circle, we use the formula below
Formula:
A = πr²∅/360Where:
A = Area of the green regionr = Radius of the circle∅ = Angle of the sector at the center of the circleFrom the diagram,
Given:
r = 17/2 = 8.5 feet∅ = (180-27°) = 153°π = 3.14Substitute these values into equation 1
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The area of the green region in the circle given is expressed as approximately: a. 96.5 square feet.
How to Find the Area of a Sector in a Circle?The sector of a circle is calculated as:
A = ∅/360 * πr², where r is the radius and ∅ is the reference or central angle of the sector.
Given the following:
Central or reference angle (∅) = 180 - 27 = 153 degrees
Radius (r) = 17/2 = 8.5 feet
Plug in the values:
Area of the green region = 153/360 * π * 8.5²
Area of the green region ≈ 96.5 square feet.
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What are the polar coordinates of the point P shown below?
Select the correct answer below:
(5,5π4)
(4,−5π4)
(5,7π4)
(4,5π4)
(4,7π4)
(5,−5π4)
Answer:(4,5π/4)
Step-by-step explanation:
Note that the point is on the circle whose radius is labeled 4, so r=4. The angle of the point is 5π4, so θ=5π4. Thus, the polar coordinates are (4,5π4).
A biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road. How much more does he need to travel? (distance)
The biker needs to travel 45 km more to complete his journey.
Given that, a biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road, we need to find how much he need to cover more,
Let the total distance of the road be x,
So,
2x/5 - 5 = 3x/8
2x/5 - 3x/8 = 5
Solving for x,
Multiply by 40 to both sides,
16x-15x = 200
x = 200
Therefore, the total distance of the road is 200 km.
Since, he travelled =
200 (2/5) = 80 km + 200 (3/8) = 75 km = 155 km
Therefore, he needs to travel 200-155 = 45 km more.
Hence, the biker needs to travel 45 km more to complete his journey.
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