Find the first derivative of x²/³ + y²/³ = 12

The ellipses centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1) is mathematically given as

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

Generally, the equation for three points is mathematically given as

a+2b+4c=1.....1  for the variable (1, 2)

4a+4b+4c=1.....2  for the variable (2, 2)

9a+3b+c=1.....3  for the variable (3, 1)

Step 1

Here we solve equations 1 and 2 simultaneously to find the value of b

Therefore

equ 2-equ1

3a+2b=0

b=-1.5a....4

Step 2

We solve equations 1 and 3 simultaneously to find the value of c

Where

9*equ1-equ3 gives

-15b-35c=-8

c=8-15b

subbing equ 4 we have

c=8+22.5a ....5

Step 3

Put values of b and c in equation 2, and we have

4a-6a+32+90a=1

a=-31/88

a=-0.3523

The value of b will be

b=-1.5*a

b=0.5284

The value of b will be

c=8-22.5*a

c=15.9268

Step 4

In conclusion, the equation is given as

By substituting the values of a b and c into the general formula we have

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

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Answer:

yes

Step-by-step explanation:

No, the lengths 3, 4, and 9 cannot form the sides of a triangle.

The triangle inequality is a fundamental geometric principle that states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

We have sides as 3, 4 and 9.

For a triangle to be valid, the sum of the lengths of any two sides must be greater than the length of the third side.

In this case, let's check if this condition is satisfied:

3 + 4 = 7

7 is less than 9

Therefore, these lengths do not satisfy the triangle inequality theorem, and a triangle cannot be formed with side lengths 3, 4, and 9.

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Answer: I don't quite understand your question. Supplementary angles are angles that equal 180 degrees. You can find missing supplementary angles by adding the two that are given, and then subtracting them by 180.

Max will pay $4,335 in interest over the course of the five-year loan for the $17,000 car he is purchasing with a 5.1% interest rate.

To calculate the interest Max will pay, we need to use the formula: Interest = Principal × Rate × Time. In this case, the principal is $17,000, the rate is 5.1% (or 0.051 as a decimal), and the time is five years. Plugging these values into the formula, we get:

Interest = $17,000 × 0.051 × 5 = $4,335.

Therefore, Max will pay $4,335 in interest over the course of the five-year loan. This additional amount represents the cost of borrowing the money for the car. It is important to consider the interest when budgeting for the total cost of the purchase.

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Answer:

Step-by-step explanation:

Opposite angles in a cyclic quadrilateral are supplementary, so angle C measures 180-105=75 degrees.

The area of the pond after rounding to the nearest hundredth is 39 feet²

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

To find the area of a semicircle, we need to first find the radius of the pond.

Let's assume the diameter of the pond is 10 feet.

Since a semicircle is half of a circle, the radius of the pond is half the diameter, which is 5 feet.

Now we can use the formula for the area of a semicircle, which is:

A = (1/2)πr²

where A is the area and r is the radius.

Plugging in the values, we get:

A = (1/2) × 3.14 × 5²

A = 39.25

Rounding to the nearest whole number, the area of the pond is approximately 39 square feet.

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Answer:

B, 12.48 is the answer

Step-by-step explanation:

Just took the test

Answer:

its b just took the quiz on edge 2020

Step-by-step explanation:

Answer:

The ratio of green apples to red apples is .

Step-by-step explanation:

Given,

Number of red apples = 21

Number of green apples = 18

We have to find out the ratio of green apples to red apples.

Solution,

For finding the ratio we have to divide the number of green apples to the number of red apples.

So, we can frame the above sentence as;

Ratio = number of green apples/number of red apples

Now substituting the values, we get;

Ratio= 18/21 = 6/7

Hence The ratio of green apples to red apples is . 6/7

Attached is a two-way frequency table, to help Hugo organize the results.

A two-way frequency table is a table used to organize and display the relationship between two categorical variables. It is constructed by counting the number of occurrences of each combination of categories and presenting the results in a table format.

1. Identify the categorical variables and list their possible categories.

cat, no cat, dog, no dog

2. Count the number of observations for each combination of categories.

cat = 17

no dog = 20

no cat no dog = 7

3. Organize the counts in a table with the categories of one variable as rows and the categories of the other variable as columns.

          | dog | no dog | total

cat      |        |              |   17  |

no cat |        |     7       |        |

total    |        |     20    |   41  |

4. Fill in the table with the counts of the observed combinations of categories.

cat but no dog = 20 - 7 = 13

both cat and dog = 17 -13 = 4

total no cat = 41 - 17 = 24

total dog = 41 - 20 = 21

dog but no cat = 24 - 7 = 17

          | dog | no dog | total

cat      |   4   |      13     |   17  |

no cat |   17  |     7       |   24  |

total    |   21  |     20    |   41  |

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Answer:

See attached

Step-by-step explanation:

Table filled in, see picture

So you get Q'(-3, 6) from Q(-1, 4) by applying the rule (x + (-4), y + 2).

Same steps for other vertices done and shown in the table.

Hope it is more clear.

Answer:

clearly the answer is what the other guy said.... he big brain

Step-by-step explanation:

The inductance L can be expressed as L = ℜN^2, which is an alternative representation of the inductance equation.

To prove that the primary power E1I1 is equal to the negative secondary power -E2I2 in an ideal transformer, we start by considering the relationship between the primary and secondary emfs and currents.

The primary emfs (E1) is related to the secondary emf (E2) by the turns ratio of the transformer, denoted as a. Therefore, we can write E2 = aE1.

Similarly, the primary current (I1) is related to the secondary current (I2) by the inverse of the turn ratio, which can be written as I2 = (1/a)I1.

Now, let's consider the power in the primary and secondary circuits. The power in the primary circuit is given by P1 = E1I1, and the power in the secondary circuit is given by P2 = E2I2.

Substituting the expressions for E2 and I2, we have P2 = (aE1)(1/a)I1, which simplifies to P2 = E1I1.

Therefore, we can conclude that the primary power E1I1 is equal to the negative secondary power -E2I2.

Regarding the expression of inductance, given as L = NiΦ, where N is the number of turns and Φ is the magnetic flux, we can further simplify it.

We know that the magnetic flux Φ is related to the current I by the inductance L, i.e., Φ = LI. Substituting this into the previous expression, we have L = NLI.

Since L is a scalar quantity, we can express it as L = ℜN^2, where ℜ is a constant that depends on the physical properties of the transformer.

Therefore, the inductance L can be expressed as L = ℜN^2, which is an alternative representation of the inductance equation.

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I hope this helps you

Answer:

A on edge

Step-by-step explanation:

When the density of the substance is 1 g/ml at room temperature, then 1 milliliter is equal to 1 milligram

The answer to this question depends on the substance in question because the density (mass per unit volume) of a substance can vary.

However, if we assume that we are dealing with water at room temperature (approximately 20°C or 68°F), then 1 milliliter (mL) of water is equivalent to 1 gram (g) of water, which is also equivalent to 1000 milligrams (mg) of water. This relationship is due to the fact that water has a density of 1 g/mL at this temperature.

So in general, if the substance in question has a density of 1 g/mL, then 1 mL of the substance would also be equal to 1000 mg of the substance.

However, if the density of the substance is different from 1 g/mL, then the conversion factor between milliliters and milligrams will also be different. In this case, you would need to know the density of the substance and use a conversion factor based on its density to convert between milliliters and milligrams.

Therefore, one milliliter is equal to 1000 milligram when the density is 1 g/ml

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The length of the path described by the parametric equations

 is 3/2units.

We can find the length of the path described by the parametric equations x=cos³t and y=sin³t by using the arc length formula.

The arc length formula for a parametric curve given by:

x=f(t) and y=g(t) is given by:

L = ∫[a,b] √[f'(t)² + g'(t)²] dt

where f'(t) and g'(t) are the derivatives of f(t) and g(t), respectively.

In this case, we have:

x = cos³t, so x' = -3cos²t sin t

y = sin³t, so y' = 3sin²t cos t

Therefore,

f'(t)² + g'(t)² = (-3cos²t sin t)² + (3sin²t cos t)²

= 9(cos⁴t sin²t + sin⁴t cos²t)

= 9(cos²t sin²t)(cos²t + sin²t)

= 9(cos²t sin²t)

Thus, we have:

L = ∫[0,2π] √[f'(t)² + g'(t)²] dt

= ∫[0,2π] √[9(cos²t sin²t)] dt

= 3∫[0,2π] sin t cos t dt

Using the identity sin 2t = 2sin t cos t, we can rewrite the integral as:

L = 3/2 ∫[0,2π] sin 2t dt

Integrating, we get:

L = 3/2 [-1/2 cos 2t] from 0 to 2π

= 3/4 (cos 0 - cos 4π)

= 3/2

Therefore, the length of the path described by the parametric equations x=cos³t and y=sin³t is 3/2 units.

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Answer: Infinite solutions.

Step-by-step explanation:

To graph both these equations, you need to make them slope intercept form (which is y = mx + b):

x + 2y = -2 in slope intercept form is y = -1/2x - 1 (subtract x from both sides then divide both sides by 2).

-3x - 6y = 6 in slope intercept form is y = -1/2x - 1. (add 3x to both sides then divide both sides by -6).

These are the same lines, so there are an infinite number of solutions when you graph.

Hope this helps!

The total distance traveled by the particle over the time interval [1, 5] is 12 units.

To find the total distance traveled, we need to consider both the magnitude and direction of the velocity function. Since the velocity function given is in meters per second (m/sec), the total distance traveled will be measured in meters.

To calculate the total distance, we need to consider the intervals where the velocity function changes its sign. In this case, the velocity function is linear and increasing, starting at t = 1 with a velocity of 3 m/sec. From t = 1 to t = 3, the particle moves in the positive direction, covering a distance of (3t - 9) × (t - 1) = 12 units. From t = 3 to t = 5, the particle moves in the negative direction with the same magnitude, covering a distance of (-1) × (3t - 9) × (t - 3) = 12 unit

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fourty four percent hope this helps !

Answer:

since the product meaning multiplication, it basically means 11 (q) which is 11q.

Answer:

Step-by-step explanation:

x = 10sqrt(2)*cos(60) = 5sqrt(2) = 7.07 approx.

y = 10sqrt(2)*sin(60) = 10sqrt(2)*sqrt(3)/2 = 5sqrt(6)=12.25 approx.

Step-by-step explanation:

3 is a right answer for your question

Answer:

11a^2 + 122a + 11

Step-by-step explanation:

First, multiply a by 11a, which gives you 11a^2. Then you multiply 11 to 11a, which gives you 122a, then last just multiply 11 to 1 and you get 11. Hope this helps.

Answer:

64,100

Step-by-step explanation:

64,100are the values that are perfect square

Mark me as brainlist

we have is as follows to the query that was asked The cannonball strikes the ground after 14 seconds in the air because t = 0 represents the cannonball's initial position quadratic equation \(16t^2 + 224t = 0\)

A quadratic formula in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of the second rank guarantees that the it has at least a single option according to the Central Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one term in it needs to be squared. One of the common formulas for solving quadratic problems is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical factors or variables a, b, and c.

\(16t^2 + 224t = 0\)

By subtracting 16t, we obtain:

16t(t + 14) = 0

T must therefore be either 0 or -14. Since t = 0 corresponds to the cannonball's starting location, we can disregard it. The cannonball consequently strikes the earth at t = -14 seconds. However, since this negative number of t is illogical from a physical standpoint, we can ignore it.

The only viable option is:

initial location t = 0 or position t = -14 (ground)

The cannonball strikes the ground after 14 seconds in the air because t = 0 represents the cannonball's initial position.

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Answer:

(0, 4.5)

Step-by-step explanation:

*The equation can be put into Desmos, to find the point, but the work to prove it is here*

f(x)=c/1+Ae^-Bx

Y=C

C=18      A=3      -B=-0.1

*Replace x with 0 in the equation, so you know 0 is the x value, and it leads you to the y value*

f(0)=18/1+3e^-o.1(0)

= 18/1+3e^0

=18/1+3(1)

=18/1+3

=18/4

=4.5

x=0    y=4.5

Maximum growth rate = (x,y) --> (0, 4.5)

Hope this helps:))!!

Given:

2x + 4y = 14

4x + y = 20

Required:

We need to find the equivalent to the given system.

Explanation:

Consider the equation

Multiply both sides of the equation by -4, it will not affect the equations of the system

Final answer:

The equivalent system of the equation is

There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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Answer:

$1.5b - $32.76 = $292.74

Step-by-step explanation:

Profit = total revenue - total cost

total revenue = price per unit x total unit of bracelet sold

total revenue = $1.50  x b = $1.50b

b = total units of bracelets sold

total cost = $32.76

$1.5b - $32.76 = $292.74

Answer:

0.75

Step-by-step explanation:

The average length is given as the sum of all the lengths given divided by the number of lengths (frequency).

Mathematically:

Average = (Sum of lengths) / frequency

The lengths given are -3, 3, -4, -3, 4, -2, 6, 5. There are 8 lengths there.

The average is therefore:

Average = (-3 + 3 + (-4) + (-3) + 4 + (-2) + 6 + 5) / 8

Average = 0.75