11
and 15 please
- 11-16 Find dy/dx and d’y/dx?. For which values of t is the curve concave upward? 11. X = x2 + 1, y = 12 + + 12. X= t - 12t, y = t2 – 1 = 13. X=2 sint, y = 3 cos t, 0 < t < 21 14. X = cos 21, y F
Answers
11. The value of \(d^2y/dx^2\) is constant and equal to 2, indicating that the curve is concave upward for all values of t.
12.The curve is concave upward for values of t in the interval -1 < t < 1.
13. To determine when the curve is concave upward, we need to find the values of t for which \(d^2y/dx^2\) > 0. Since -3/2 * \(sec^2\)(t) is negative for all values of t, the curve is never concave upward.
14. The derivative dy/dx is sin(t) / (2sin(2t)), and the second derivative \(d^2y/dx^2\)is (2cos(t)sin(2t) - 4sin(t)cos(2t)) / (4\(sin^2(\)2t)).
11. Find dy/dx and\(d^2y/dx^2\)for the curve defined by the equations x = \(x^2 + 1\)and y = 12 + t. Also, determine the values of t for which the curve is concave upward.
To find dy/dx, we differentiate y with respect to x:
dy/dx = dy/dt / dx/dt
Given y = 12 + t, the derivative dy/dt is simply 1. For x = \(x^2 + 1,\) we differentiate both sides with respect to x:
1 = 2x * dx/dt
Simplifying, we have dx/dt = 1 / (2x)
Now, we can calculate dy/dx:
dy/dx = dy/dt / dx/dt = 1 / (1 / (2x)) = 2x
To find \(d^2y/dx^2\), we differentiate dy/dx with respect to x:
\(d^2y/dx^2\) = d(2x)/dx = 2
12.To find the derivatives dy/dx and d²y/dx², we differentiate the given equations with respect to t and then apply the chain rule.
Given: x = t³ - 12t, y = t² - 1
To find dy/dx, we differentiate y with respect to t and divide it by dx/dt:
dy/dx = (dy/dt) / (dx/dt)
Differentiating x and y with respect to t:
dx/dt = 3t² - 12
dy/dt = 2t
Substituting these values into the equation for dy/dx:
dy/dx = (2t) / (3t² - 12)
To find d²y/dx², we differentiate dy/dx with respect to t and divide it by dx/dt:
d²y/dx² = (d/dt(dy/dx)) / (dx/dt)
Differentiating dy/dx with respect to t:
d(dy/dx)/dt = (2(3t² - 12) - 2t(6t)) / (3t² - 12)²
Simplifying the expression, we have:
d²y/dx² = (12 - 12t²) / (3t² - 12)²
To determine the values of t for which the curve is concave upward, we need to find the values of t that make d²y/dx² positive. In other words, we are looking for the values of t that make the numerator of d²y/dx², 12 - 12t², greater than 0.
Solving the inequality 12 - 12t² > 0, we find t² < 1. This implies -1 < t < 1.
13. Find dy/dx and \(d^2y/dx^2\) for the curve defined by x = 2sin(t) and y = 3cos(t), where 0 < t < 2π. Also, determine the values of t for which the curve is concave upward.
To find dy/dx, we differentiate y with respect to x:
dy/dx = dy/dt / dx/dt
Given y = 3cos(t), the derivative dy/dt is -3sin(t). For x = 2sin(t), we differentiate both sides with respect to t:
dx/dt = 2cos(t)
Now, we can calculate dy/dx:
dy/dx = dy/dt / dx/dt = (-3sin(t)) / (2cos(t)) = -3/2 * tan(t)
To find \(d^2y/dx^2\), we differentiate dy/dx with respect to t:
\(d^2y/dx^2\) = d/dt (-3/2 * tan(t))
Differentiating -3/2 * tan(t), we have:
\(d^2y/dx^2\) = -3/2 * \(sec^2\)(t)
14. For the equation x = cos(2t) and y = cos(t), we are asked to find the derivatives.
To find dy/dx, we differentiate y with respect to x:
dy/dx = dy/dt / dx/dt
Given y = cos(t), the derivative dy/dt is -sin(t). For x = cos(2t), we differentiate both sides with respect to t:
dx/dt = -2sin(2t)
Now, we can calculate dy/dx:
dy/dx = dy/dt / dx/dt = (-sin(t)) / (-2sin(2t)) = sin(t) / (2sin(2t))
To find d^2y
/dx^2, we differentiate dy/dx with respect to t:
\(d^2y/dx^2\) = d/dt (sin(t) / (2sin(2t)))
Differentiating sin(t) / (2sin(2t)), we have:
\(d^2y/dx^2\) = (2cos(t)sin(2t) - sin(t)(4cos(2t))) / (4\(sin^2\)(2t))
Simplifying the expression, we have:
\(d^2y/dx^2\) = (2cos(t)sin(2t) - 4sin(t)cos(2t)) / (4\(sin^2\)(2t))
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Related Questions
If (2x + 4) - (x + 3) = 15, then x =
Answers
Answer:
x=14
Step-by-step explanation:
im 68inches tall so how much is that into feet?
Answers
Answer:
5.68 ft
Step-by-step explanation:
12 inches = 1 feet
\(68 \: inches \: *\: \frac{1 feet}{12 \: inches} =\frac{68}{12} \: feet= 5.6777...\\\\68 \: inches \approx 5.68 \: feet\)
Solve for x. -3/5x+1/5>7/20
Answers
Answer:
Step-by-step explanation:
15 + 720 is 1120
Find the number of outcomes in the complement of the given event. out of 301 apartments in a complex, 138 are available for rental.
Answers
The number of outcomes in the complement of the event is 163
How to find the number of outcomes in the complement of the event?The statement is given as:
Out of 301 apartments in a complex, 138 are available for rental.
This means that
Apartments = 301
Rental = 138
The complement is calculated as:
Complement = Apartment - Rental
So, we have
Complement = 301 - 138
Evaluate
Complement = 163
Hence, the number of outcomes in the complement of the event is 163
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pls pls pls pls help me istg ill be your best friend and give you brianliest and all the points i can give and ill love you forvever pls pls pls pls
Answers
a. The chart did not maintain consistent scaling
b. The graph is not the appropriate graph type to display such data
c. The display had inaccurate or distorted visual representations
How do we explain?When the actual data may not support it, changing the scales on the axes might give the appearance of big changes or differences.
The visual effect of data can be exaggerated or minimized, for instance, by adopting a non-linear scale or deleting specific sections of the axis.
So it important to Choose appropriate graph type that best represents the data and the relationship you want to convey.
It also advisable to make use of clear and accurate labeling with descriptive titles and units of measurement.
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Write the equation of the line in slope intercept form that passes through (2, -4)and (-1,2)
Answers
y= -2x-2
Step-by-step explanation:
slope = -2 the slope intercept form is y-2= -2(x+2)
y= -2x-2
2 2.1 Mathematical intro show that there is another form for spherical harmonics: 1 3 3 Y₁ x iy 1/√√2 (²-1) 2πT 2π 1 3 3 z YO 2 2π π r 1 3 x iy Y₁¹ 3 2π - - 12 √ √ 2² (²+²) 2 2π
Answers
Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:
Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)
Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:
Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)
Y1,0 = 1/2 √(3/π)cosθ
Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)
Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ
Y2,0 = 1/4 √(5/π)(3cos²θ-1)
Y0,0 = 1/√(4π)
The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.
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One way to divide decimal numbers is to use an equivalent expression.
Complete the statements below to explain one way to find 8.4 ÷ 2.1.
Answers
Answer:
104Step-by-step explanation:
To determine how much a decimal was multiplied, you need to find how many places the decimal moved.
In this case we can see the decimal moved once. How many times the decimal moved can be represented by the zeros in the number. So 10 = 1
100 = 2 1,000 = 3 and it keeps going.
So since the decimal moved 1 time, the answer to question one is 10
Now question 2.
Both 8.4 ÷ 2.1 and 84 ÷ 21 will give the exact same answer. It is just easier to solve. So solve which one is easier for you. I did 84 ÷ 21.
84 ÷ 21 = 4
We can verify our answer by multiplying the the divisor by the quotient
21 * 4 = 84
So 4 is the answer to question 2
the width of a rectangle is 58 units less than its length. if x is the rectangle's length, then its area is
Answers
If the length of the rectangle is represented by "x," then the width is (x - 58), and the area can be calculated as x² - 58x.
Let's go through the problem step by step to find the area of the rectangle.
Let's assume that the length of the rectangle is represented by the variable "x" (as stated in the question). According to the given information, the width of the rectangle is 58 units less than its length.
If the width is 58 units less than the length, we can represent the width as (x - 58). This means that the length minus 58 gives us the width.
Now, to find the area of the rectangle, we use the formula:
Area = Length × Width
Substituting the values we have:
Area = x × (x - 58)
Expanding the equation:
Area = x² - 58x
So, the area of the rectangle is given by the expression x² - 58x.
To summarize, if the length of the rectangle is represented by "x," then the width is (x - 58), and the area can be calculated as x² - 58x.
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At the end of each week,darius records the weight in pounds of doggie treats eaten as a negative rational number. plot the number of pounds eaten each week on the number line. order the numbers from most pounds eaten to fewest pounds eaten.
Answers
In this representation, the numbers are placed from left to right in order of most pounds eaten to fewest pounds eaten.
To plot the number of pounds eaten each week on a number line and order them from most pounds eaten to fewest pounds eaten, we'll consider the negative rational numbers representing the weight in pounds of doggie treats eaten by Darius. Here's an example ordering:
1. -3.5
2. -2.7
3. -2.5
4. -1.8
5. -1.2
6. -0.9
7. -0.5
8. -0.2
To visualize this on a number line, let's place these numbers accordingly:
```
-3.5 -2.7 -2.5
|---------------------|-----------|
-1.8 -1.2 -0.9 -0.5 -0.2
|-----------|-----------|-----------|
```
In this representation, the numbers are placed from left to right in order of most pounds eaten to fewest pounds eaten. Each number is marked with a vertical line segment, and the length of the line segment corresponds to the magnitude of the number. The numbers are positioned such that they are evenly spaced along the number line.
Please note that this is just one possible ordering and arrangement of the numbers on the number line. The exact values and spacing may vary based on the actual data.
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i need help with this asap!!
Answers
Answer:
perimeter you add all sides together:
5x+2 +5x+2 +x +8 +x+8
12x +20
and for Area you multiply:
(x + 8)(5x + 2)
5x^2 + 2x + 40x +16
5x^2 +42x +16
so your answer is the first one or "A"
CAN SOMEONE PLEASE HELP ME W 1-11 PLEASE (7th grade math)
Answers
Answer:
1. 3x
2. 5x+1
4. 16x
5. 10x+6
10. 8x +2y
11. 2x+6y+3
Step-by-step explanation:
Answer:
1- 3x, 2- 5x+1, 4- 16x, 5- 10x+7, 7- 5x+7, 8- 13x+6, 10- 8x+2y, 11- 2x+6y+3
Step-by-step explanation:
A hollow rectangular section has outside dimensions 30cm x 15cm. The material of the section is 2 5cm thick. The effective length is 6m: Calculate the least radius of gyration. (1) (0) Calculate the slenderness ratio. 60mm is
Answers
To calculate the least radius of gyration and the slenderness ratio of a hollow rectangular section with given dimensions and material thickness, we need to follow the formulas and steps involved. The least radius of gyration is a measure of the distribution of material around the centroid of a section, while the slenderness ratio provides information about the stability of the section under axial loading.
1. To calculate the least radius of gyration, we use the formula:
r_min = sqrt((I / A))
where I is the moment of inertia of the section and A is the cross-sectional area. For a hollow rectangular section, the moment of inertia can be calculated using the formula:
I = ((b1 * h1^3) - (b2 * h2^3)) / 12
where b1 and b2 are the outer and inner dimensions of the section, and h1 and h2 are the outer and inner heights of the section. The cross-sectional area A can be calculated as:
A = (b1 * h1) - (b2 * h2)
2. To calculate the slenderness ratio, we divide the effective length of the section by the least radius of gyration:
Slenderness ratio = L / r_min
Given that the effective length is 6m, and considering the dimensions provided in millimeters (30cm x 15cm), we convert 60mm to meters (0.06m).
By substituting the given values into the formulas and performing the calculations, we can find the least radius of gyration and the slenderness ratio for the hollow rectangular section.
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An angle measures 37.6° more than the measure of its complementary angle. What is the measure of each angle?
Answers
Therefore , the solution of the given problem of angles comes out to be the complementary angle measures 26.2 degrees.
What does an angle mean?The largest and smallest walls of a skew are determined by the intersection of the lines connecting its ends. Two pathways might meet at a crossroads. Another result of two entities interacting is an angle. If anything, they resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their ends to form a two-dimensional curve.
Here,
Let's write x degrees for the initial angle's measure.
The first angle is measured to be 37.6 degrees greater than its complimentary angle based on the information provided.
Because complementary angles sum to 90 degrees, we may construct the equation shown below:
=> x = (90 - x) + 37.6
If we simplify, we get:
=> x = 90 - x + 37.6
=> x + x = 90 + 37.6
=> 2x = 127.6
When you divide both sides by 2, you get:
=> x = 127.6 / 2
=> x ≈ 63.8
Therefore, the initial angle is roughly 63.8 degrees in size.
By deducting the first angle's measurement from 90 degrees, we may determine the complementary angle's measurement:
=> 90 - x = 90 - 63.8 = 26.2
Consequently, the complementary angle measures 26.2 degrees.
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Rhys is arranging a raffle for a
school fair. The tickets cost
50p each.
The main prize of the raffle is
£20. The second prize is £5.
How much profit will Rhys make if he manages
to sell 140 tickets?
Answers
Answer:
140 divided by 0.50＝140 divide by 2＝70
What is the frequency of the sinusoidal graph?
Answers
Answer:
equal to 1
Step-by-step explanation:
I believe this is the answer. Also I see that ur new. Well welcome to Brainly.
Johann is constructing equilateral triangle WXY inscribed in a circle.
He begins by using a compass to draw circle C. He then uses a straightedge to draw a diameter of the circle and labels the endpoints Y and Z.
What is the next step Johann should perform to find points W and X?
0A. Set the compass width equal to CZ, and draw two intersecting arcs centered at Y and Z.
0B. Set the compass width greater than CZ, and draw two intersecting arcs centered at Y and Z.
0C. Set the compass width equal to CZ, and draw two arcs, centered at Y, that intersect circle C.
0D. Set the compass width equal to CZ, and draw two arcs, centered at Z, that intersect circle C.
Answers
The correct next step is C: Set the compass width equal to CZ, and draw two arcs, centered at Y, that intersect circle C.
What is a circumscribed circle?
The circumscribed circle or circumcircle of a polygon in geometry is a circle that passes through each of the polygon's vertices. This circle's circumcenter and circumradius are its center and radius, respectively.
It should be noted that an equilateral triangle simply means a triangle that has all the sides and angles to be equal.
The correct next step for Johann to find points W and X is option C: Set the compass width equal to CZ, and draw two arcs, centered at Y, that intersect circle C.
This is because an equilateral triangle can be inscribed in a circle by drawing two intersecting arcs that intersect the circle at three points. To find these points, the compass should be set to the length of one side of the equilateral triangle, which in this case is CZ, and two arcs should be drawn centered at Y and intersecting circle C. The two points where the arcs intersect the circle will be points W and X of the equilateral triangle inscribed in the circle.
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Which of the equations below could be the equation of this parabola?
Vertex
(0,0)
. 10
10
10
o A. y = 2x²
O B. yw - 2x²
O c, x==137²
O D. 1/4
Answers
Answer:
Option B: \(y = -\frac{1}{2} x^2\)
Step-by-step explanation:
The parabola has its concavity downwards, so we need a function in the model:
\(y = ax^2 + bx + c\)
With a negative value of 'a'
The vertex is (0,0), so we have that:
\(0 = 0a + 0b + c\)
\(c = 0\)
The x-coordinate of the vertex is given by the equation:
\(x\_vertex = -b/2a\)
\(-b/2a = 0\)
\(b = 0\)
So we have a function in the model:
\(y = ax^2\)
With a < 0
The only option with this format is B:
\(y = -\frac{1}{2} x^2\)
I got 11.9 am I right???
Film studios make a commission from every ticket sold. The movie tickets at Carbob Theatres cost $8.50. The studios earn a 40% commission. What amount of the movie ticket do they earn?
Answers
Answer:
I don't think so
Step-by-step explanation:
The studio earns $3.40 on commision because thats 40% of $8.50
The theater earns $5.10 because that would be the rest of the money
This table shows input and output values for a linear function f(x)
What is the difference of outputs for any two inputs that are three values apart.
Express your answer as a decimal.
Answers
The answer is 0.75 because I took the test and that's what the answer was :)
Phillip Witt, president of Witt Input Devices, wishes to create a portfolio of local suppliers for his new line of key- boards. As the suppliers all reside in a location prone to hurri- canes, tornadoes, flooding, and earthquakes, Phillip believes that the probability in any year of a "super-event" that might shut down all suppliers at the same time for at least 2 weeks is 3%. Such a total shutdown would cost the company approximately $400,000. He estimates the "unique-event" risk for any of the suppliers to be 5%. Assuming that the marginal cost of managing an additional supplier is $15,000 per year, how many suppliers should Witt Input Devices use? Assume that up to three nearly identical local suppliers are available.
Answers
To determine the number of suppliers Witt Input Devices should use, we need to consider the probability of a "super-event" and the marginal cost of managing additional suppliers.
With a 3% probability of a total shutdown and an estimated cost of $400,000, along with a 5% "unique-event" risk per supplier, the company should aim to balance the costs and risks to make an informed decision on the number of suppliers.
Phillip Witt wants to create a portfolio of local suppliers for his keyboards. He faces the risk of "super-events" that could shut down all suppliers simultaneously for at least two weeks. The probability of such an event occurring is 3% per year, which would result in an estimated cost of $400,000 for the company.
Additionally, each individual supplier carries a "unique-event" risk of 5%. To mitigate the risks, Witt Input Devices needs to determine the optimal number of suppliers to use. However, it is stated that up to three nearly identical local suppliers are available.
To make a decision, the company needs to balance the costs and risks. Each additional supplier incurs a marginal cost of $15,000 per year. The company should evaluate the trade-off between the cost of managing additional suppliers and the risk reduction achieved by having multiple suppliers.
Considering these factors, Witt Input Devices should analyze the costs and benefits of each additional supplier and select the number of suppliers that provides an optimal balance between risk mitigation and cost management.
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Two families visited an amusement park. the first family bought 3 hot dogs and 5 bottles of waters, which totaled $20. the second family bought 6 hot dogs and 3 bottles of waters, which totaled $33. how much did one hot dog cost?
a. $3
b. $4
c. $5
d. $6
Answers
Answer: $4
Step-by-step explanation:
based on derivative how many times can function cross the x-asix
Answers
Based on the derivative, a function can cross the x-axis a certain number of times depending on the number of times the derivative changes sign.
A derivative is a mathematical tool that measures the rate of change of a function at a specific point. Specifically, it is the slope of the tangent line to the function at that point. The derivative can be used to determine where a function is increasing, decreasing, or reaching a maximum or minimum value.
When a function crosses the x-axis, it means that the y-value of the function is equal to zero. In order for a function to cross the x-axis, it must change sign from positive to negative or vice versa. This happens when the function passes through a maximum or minimum point.
If the derivative of the function is positive at a point, it means that the function is increasing at that point. If the derivative is negative, the function is decreasing. If the derivative is zero, it means that the function is neither increasing nor decreasing, and it could be at a maximum or minimum point.
Therefore, the number of times a function can cross the x-axis depends on the number of times the derivative changes sign. If the derivative changes sign twice, the function can cross the x-axis twice. However, if the derivative changes sign an odd number of times, the function can only cross the x-axis once.
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Last year a baseball team paid $20 per bat and $12 per glove, spending a total of
$1040. The team bought a total of 72 bats and gloves combined. How many bats and
gloves did they buy?
Answers
Answer:
2,664
Step-by-step explanation:
I just multiplied 20 and 17 by 72 and added the products together to get a sum of 2,664 which is the answer.
Evaluate 7y - 3y for y=3
Answers
7 . 3 - 3 . 3
= 21 - 9
= 12
Just substitute you y = 3 into the equation
Answer:
The correct answer is 12.
Step-by-step explanation:
To solve this problem, we must plug in 3 for each occurrence of y in the expression because we are given that y = 3. In this case, we will get the following:
7y - 3y
7(3) - 3(3)
To evaluate, we must simplify this expression. Due to the order of operations, we should compute the multiplication first. 7*3 = 21 and 3*3=9, so we can plug in these values into our expression.
21 - 9
Now, we can perform the subtraction.
21-9=12
Therefore, the correct answer is 12.
Hope this helps!
Ellen is drawing two polygons. One of the polygons has three more angels than the other. What shapes could she be drawing
Answers
Answer:
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How can you apply it triangle congruence to real life situation?
Answers
Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.
The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.
Congruence :
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.
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if you made a stack of nickels 100 inches tall how many would you need
Answers
Answer:
i would guess 2000
Step-by-step explanation:
hope this helps!!
Answer:
1,600 Nickels
Step-by-step explanation:
1 nickel is 1/16 of an inch.
16 nickels for 1 inch
16 x 100 =1,600 nickels
What is the solution to the system of equations?
y=2/3x+3
x = -2
A)-2, -15
B) -2, 5/3
C) -2,-11/6
D)-2,13/3
Answers
Answer:
(-2, 5/3)
Step-by-step explanation:
y=2/3x+3
x = -2
Substitute x = -2 into the first equation
y = 2/3 (-2) +3
y =-4/3+3
y =-4/3+19/3
y = 5/3
(-2, 5/3)
The total change in Mr. Belt's checking account as a result of three cable bills was -
$312.99. Which one of the following describes what happened to his account each
month?
A. A deposit of $104.33
B. A withdrawal of $104.33
C. A credit of $99.99
D. A debit of $99.99
Plz help
Answers
B
Step-by-step explanation:
312.99 divided by 3 equals 104.33 nothing in his account changed except the 312.99