Sammy the snail travels 20 mm for 1 seconds at the same speed what is the snails speed

To find the derivative of the function y=(x^2+4)/(x^2-4)^5, we need to use the chain rule and the quotient rule.
First, we can simplify the function by factoring the numerator and denominator:
y = [(x^2+4)/(x^2-4)]^5
y = [(x^2-4+8)/(x^2-4)]^5
y = [(x^2-4)/(x^2-4) + 8/(x^2-4)]^5
y = [1 + 8/(x^2-4)]^5

Now, we can use the chain rule:
Let u = x^2-4
y = [1 + 8/u]^5
y' = 5[1 + 8/u]^4 * (8/u^2) * u'
y' = 40(x^2-4)^-2(1+8/(x^2-4))^4(x)

Therefore, the derivative of the function y=(x^2+4)/(x^2-4)^5 is:
y' = 40(x^2-4)^-2(1+8/(x^2-4))^4(x)

Step 1: Identify the outer function and the inner function.
Outer function: f(u) = u^5
Inner function: u = x^2 + 4/(x^2 - 4)

Step 2: Find the derivatives of the outer function and the inner function.
f'(u) = 5u^4 (derivative of the outer function)
du/dx = 2x - 4(x^2 - 4)^(-1)(2x) (derivative of the inner function)

Step 3: Apply the chain rule.
dy/dx = f'(u) * du/dx
dy/dx = 5u^4 * (2x - 4(x^2 - 4)^(-1)(2x))
dy/dx = 5(x^2 + 4/(x^2 - 4))^4 * (2x - 4(x^2 - 4)^(-1)(2x))

So, the derivative of the function y = (x^2 + 4/(x^2 - 4))^5 is:

dy/dx = 5(x^2 + 4/(x^2 - 4))^4 * (2x - 4(x^2 - 4)^(-1)(2x))

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Answer:

n is greater than - 6.

Step-by-step explanation:

4+n>-2

subtract 4 on both sides

4-4+n>-2-4

n>-6

n is greater than - 6

Answer:

-1 over 2

Step-by-step explanation:

give brainliest lol

Answer:

\(\frac{\sqrt{21} }{6}\)

Step-by-step explanation:

Using the half angle identity

cos(\(\frac{1}{2}\) x ) = ± \(\sqrt{\frac{1+cosx}{2} }\)

Given cosx = \(\frac{1}{6}\) , then

cos(\(\frac{1}{2}\) x )

= ± \(\sqrt{\frac{1+\frac{1}{6} }{2} }\)

= ± \(\sqrt{\frac{\frac{7}{6} }{2} }\)

= ± \(\sqrt{\frac{7}{12} }\)

= ± \(\frac{\sqrt{7} }{\sqrt{12} }\) × \(\frac{\sqrt{12} }{\sqrt{12} }\)  ( rationalising the denominator )

= ± \(\frac{\sqrt{84} }{12}\)

= ± \(\frac{2\sqrt{21} }{12}\)

= \(\frac{\sqrt{21} }{6}\) ← positive value

Answer:

8,7

Step-by-step explanation:

i hope this helps!

Answer:

the answer is 5

Step-by-step explanation:

The least common factor of 10 and 25 is: 1. The HIGHEST common factor is 5, and the least common MULTIPLE is 50.

hope it helps

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Since there wer two penalties, each of five yard, the total change in yards due to the penalties is:

there was a change of 10 yards due to the penalties

Answer:

RS= 17

Step-by-step explanation:

l hope l can help You

Answer:

60

Step-by-step explanation:

60 plus 60 plus 60 is 180

has to add up to 180

Answer:

55

Step-by-step explanation:

D : G : M

5  : 5 :  1

5-1=4

4u-> 20

1u-> 5

11u-> 55

Answer:

Truee

Step-by-step explanation:

The house was in the shape of an octagon, with eight separate bedrooms on each side.

The house described in the statement has an octagonal shape. An octagon is a polygon with eight sides, characterized by its eight equal angles. In this case, each side of the house corresponds to one of these angles, resulting in eight separate bedrooms on each side of the octagonal structure.

The choice of an octagon as the shape of the house can have various implications. Octagonal buildings are often admired for their unique architectural design and aesthetic appeal. The shape provides symmetry and balance, allowing for an interesting and visually pleasing structure. Additionally, an octagonal layout can offer practical advantages in terms of space utilization and room distribution. In the case of the house described, each side of the octagon accommodates a separate bedroom, providing privacy and ample living space for its occupants. The symmetrical arrangement of the bedrooms around the central area of the house could create a harmonious and well-organized living environment. Overall, the octagonal shape of the house with eight separate bedrooms on each side offers both architectural and functional benefits.

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Divide total pieces of candy by total people:

35 / 5 = 7

Each person receives 7 pieces of candy

Answer:

7

Step-by-step explanation:

35 divided by 5 equals 7

Answer: 9,536 = 1,192 x 8

Step-by-step explanation: 1,192

                                            x     8

                                       ——————-

                                          9,536

9536 is the correct answer

Answer:

2r-3(r+7)-8r=10(r-1)

2r-3r-21-8r=10r-10

-9r-10r=-10+21

-19r=11

-19/11=r

Step-by-step explanation:

Answer:

Linera

Step-by-step explanation:

f it has exponents, it is nonlinear. If your equation has no exponents, it is linear.

Answer:

Area = 2.88m^

To calculate the area of the rectangle, we can multiply its length and width. Let's perform the calculation:

Length = (2.4 ± 0.1) m

Width = (1.2 ± 0.2) m

Area = Length × Width

Using the given values, we have:

Area = (2.4 ± 0.1) m × (1.2 ± 0.2) m

To find the area and its uncertainty, we'll apply the rules of error propagation. When multiplying two quantities with uncertainties, we add the relative uncertainties:

Relative uncertainty in length = (0.1 / 2.4) = 0.0417

Relative uncertainty in width = (0.2 / 1.2) = 0.1667

Relative uncertainty in area = Relative uncertainty in length + Relative uncertainty in width

= 0.0417 + 0.1667

= 0.2084

Area = (2.4 × 1.2) m² = 2.88 m²

Answer:

4095

Step-by-step explanation:

Answer:

equation: y = 2.5h + 19 for happy paws

y = 3.75p + 10 for woof watchers

hours: 7.2 or 7 hours and 12 minutes

Step-by-step explanation:

lmk if you want an explanation

Using the distributive property to factorize the equation 3x² + 24x = 0, you get 3x(x + 8) = 0 and the solution of the equation is x = -8

The expression is given as:

3x² + 24x = 0

Factor out 3x

3x(x + 8) = 0

Divide both sides by 3x

x + 8 = 0

Subtract 8 from both sides

x = -8

Hence, the solution of the equation is x = -8

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Answer:

3x(x + 8) = 0 and x = -8

Step-by-step explanation:

It was correct for me

Answer:

Step-by-step explanation:

-3b - 2b + 7 = -15

-5b  = -22

b = 22/5

The value of the functions 2f + 4g is {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)} and the value of 2g/h is (1,2.5)

In particular, a function maps each element of a set (called the domain) to a unique element of another set (called the range). In this context, we'll look at two functions, f and g, and explore how we can perform arithmetic operations with them.

We can think of these pairs as points on a Cartesian plane, where the x-coordinate represents the input and the y-coordinate represents the output.

Now, let's move on to the arithmetic operations with functions. The first operation we're asked to perform is 2f + 4g. To do this, we need to apply the following steps:

Multiply each ordered pair in f by 2, and multiply each ordered pair in g by 4. This means that the inputs stay the same, but the outputs are multiplied by their respective constants.

Simplify the resulting set by removing any duplicate ordered pairs.

Let's work through this process step by step for our given functions:

Multiplying f by 2 gives us: {(-2,4), (0,6), (2,10), (-2,6)}

Multiplying g by 4 gives us: {(-8,4), (0,12), (4,20), (-4,12), (12,0)}

Taking the union of these sets gives us: {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)}

Simplifying this set by removing duplicates gives us: {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)}

So, 2f + 4g is the function represented by the set {(-2,4), (0,6), (2,10), (-2,6), (-8,4), (4,20), (-4,12), (12,0)}.

For the ordered pair (1,5) in g, the corresponding ordered pair in h is (5,4). So, we can compute 2g(1)/h(5) as follows:

2g(1) = 2 * 5 = 10

h(5) = 4

2g(1)/h(5) = 10/4 = 2.5

Therefore, the ordered pair (1,2.5) is in the result set.

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Answer:

89.6 meters per minute

Step-by-step explanation:

The number of points of intersection for the graphs of the equations is infinite.

Point of intersection refers to the point at which two lines intersect on a graph. The graph of the equation refers to the visual demonstration of the equation obtained by plotting all the points of an equation on a graph. If there is only one variable, the graph is on a number line. If there are two variables, the graph is on the coordinate plane. If there are three variables, the graph is in three-dimensional coordinates.

Simplifying the given equations:

i) x/2 + 5y = 6

x + 10y = 12

ii) 3x + 30y = 36

3(x + 10y) = 36

x + 10y = 12

As the equations are equal lines, they will intersect at infinite times.

Note: The question is incomplete. The complete question probably is: How many intersections are there of the graphs of the equations below? x/2 + 5y = 6 3x + 30y = 36 none one two infinitely many

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Type I error (also called a false positive) occurs when a null hypothesis is rejected when it is actually true. The probability of committing a Type I error is denoted by the symbol alpha (α), and is typically set at a certain level (e.g., 0.05 or 0.01) depending on the significance level desired for the hypothesis test.

Type II error (also called a false negative) occurs when a null hypothesis is not rejected when it is actually false. The probability of committing a Type II error is denoted by the symbol beta (β). The power of a statistical test is equal to 1 minus the probability of a Type II error (i.e., power = 1 - β).

Therefore, the statement that is true regarding the probability of Type I and Type II errors is that they are complementary to each other. That is, as the probability of a Type I error decreases (by setting a lower significance level), the probability of a Type II error generally increases (i.e., the power of the test decreases). Conversely, as the probability of a Type II error decreases (by increasing the sample size or effect size), the probability of a Type I error generally increases. It is important to strike a balance between controlling these two types of errors, depending on the specific goals and context of the research or hypothesis test.

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Answer:

1) The monthly payment is approximately $292.96

2) The total interest is approximately $2,061.84

Step-by-step explanation:

1) The financing method Nathan Reynolds applied to buy the car is given as follows;

The purchase price of the car = $15,000

The down payment made for the car = $3,000

The

The interest on the loan he took for the balance of the purchase price, R = 8%

The number of years for which he took the loan, n = 4 years = 48 months

We have;

The balance of the purchase price = (The purchase price of the car) - (The down payment made for the car)

∴ The balance of the purchase price = $15,000 - $3,000 = $12,000

The balance of the purchase price = $12,000 = The loan Nathan secured

The monthly payment on a loan is given by the following formula

\(A = P \times \dfrac{r \cdot (1 + r)^n}{(1 + r)^n - 1}\)

Where;

A = The payment amount made  monthly

P = The principal or loan amount = $12,000

r = The interest rate divided by 12 = R/12 = 8/12 = 2/3

n = The number of months the monthly payment will be made = 48 months

By plugging in the variable values, we get;

\(A = 12,000 \times \dfrac{\dfrac{2}{300} \times \left (1 + \dfrac{2}{300} \right ) ^{48}}{ \left (1 + \dfrac{2}{300} \right )^{48} - 1} = 292.955068099 \approx 292.96\)

Therefore, the payment amount made  monthly, A ≈ $292.96

2) The total payment made in the 48 months = A × 48 = 292.955068099 × 48 ≈ 14,061.84

The total payment made in the 48 months ≈ $14,061.84

The total interest = (The total payment made in the 48 months) - (The loan amount)

∴ The total interest = $14,061.84 - $12,000 ≈ $2,061.84

In order to roughly determine the roots of the given equation, the bisection method divides the interval several times.

In order to get close to the equation's roots, the bisection method divides the interval several times.

This strategy is based on the continuous functions intermediate theorem. It works by reducing the gap between the positive and negative intervals as it approaches the desired response.

This method narrows the gap between the variables by averaging the positive and negative intervals. Even though it is a simple process, it proceeds slowly.

The bisection method is also known as the dichotomy method, binary search method, and root-finding method.

Then, according to the intermediate theorem, there is a point x that is a part of (a, b) and has the value f(x) = 0.

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The value of x in the first figure is 10

The value of x in the second figure is 12

In the first figure the value of x is solved using the concept of angels on a straight line which  is 180 degrees

Therefore,

6x - 10 + 4x + 6 + 7x + 14 = 180

collecting like terms

6x + 4x + 7x + 6  + 14 - 10  = 180

17x + 10 = 180

17x = 180 - 10

17x = 170

x = 10

The second figure is solved using alternate interior angles

4x + 10 = 58

solving for x

4x = 58 - 10

4x = 48

x = 12

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Answer:

2(m+8)

Step-by-step explanation:

5(m+2) -3(m-2)

= 5m+10-3m+6

= 2m+16

= 2(m+8)

Answer:

Step-by-step explanation:

\(\begin{aligned}& 5(m+2)-3(m-2) \\\\=& 5 m+5 \times 2-(3 m-6) \\\\=& 5 m+10-3 m+6 \\\\=&(5 m-3 m)+(10+6) \\\\=& 2 m+16\end{aligned}\)

The player's distance from home plate changing at that instant is 37.42 feet per second.

The distance covered by an object in unit time.

First, let's define a few variables.

t = time

x = Distance the player is from third base = 20 feet

dx/dt = Velocity the player is running towards third base = -30 fps

y = Distance between the player and home plate

dy/dt = Rate of change between the player's distance from home plate (This is the answer to our problem)

By Pythagorean theorem

y² = x² + 90²...(*)

Put x = 20

y² = 20² + 90²

y = 92.2 feet

Apply  differentiation to (*)

2ydy/dt = 2xdx/dt + 90²

And let's plug in x, y, and dx/dt to solve for dy/dt.

2(92.2)dy/dt = 2×20×-30 + 90²

dy/dt = 37.42 feet per second

Hence 37.42 feet per second  is the player's distance from home plate changing at that instant

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