The price of an item has been reduced by 95%. The original price was $75.

Answer:

$562.43

Step-by-step explanation:

To roughly represent the definite integral i with the specified accuracy. is equal to 0.473 and i = 0.5 x2ex2 dx 0 (|error| 0.001)

We can utilise the Taylor series expansion of the integrand function f(x) = 0.5 x2e(-x2) to roughly estimate the definite integral i to the required level of accuracy.

f(x) = f(0) + f'(0)x + f''(0)x^2/2 + f'''(0)x^3/6 + ...

where

f(0) = 0.5(0)^2e^(-0^2) = 0

f'(x) = xe^(-x^2) - x^3e^(-x^2) = xe^(-x^2)(1 - x^2)

f'(0) = 0

f''(x) = (1 - 2x^2)e^(-x^2)

f''(0) = 1

f'''(x) = (-4x + 6x^3)e^(-x^2)

f'''(0) = 0

Therefore, f(x) = x^2/2 - x^4/4 + x^6/12 - ...

We may now integrate f(x) term by term to approximate i as follows:

i ≈ ∫[0,∞) f(x) dx = [x^3/6 - x^5/20 + x^7/84 - ...]0^∞

= lim{t->∞} [t^3/6 - t^5/20 + t^7/84 - ... - 0]

= lim_{t->∞} [t^3(1/6 - 1/20t^2 + 1/84t^4 - ...) ]

= lim_{t->∞} [t^3/6(1 - 3/t^2 + 1/14t^4 - ...) ]

We can use the alternating series estimation theorem to confine the error because the series inside the limit is an alternating series that converges quickly for large t:

|error| ≈ \(|t^3/6(1 - 3/t^2 + 1/14t^4 - ...) - t^3/6(1 - 3/(t+1)^2 + 1/14(t+1)^4 - ...)|\)

\(= |t^3/6(3/t^2 - 1/14t^4 + ...)|\)

< 0.001

Solving for t gives:

t^3/6(3/t^2 - 1/14t^4 + ...) < 0.001

t > 7.56

As a result, we can use the first few terms of the series up to t = 8 to approximate i:

i ≈ ∫[0,8] f(x) dx ≈ [x^3/6 - x^5/20 + x^7/84]_0^8

≈ (8^3/6 - 8^5/20 + 8^7/84)

≈ 0.473

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The length of the segment AB is 11

The given parameters are:

A = -4

B = 7

The length of the segment is calculated as:

AB = |A - B|

Substitute known values

AB = |-4 - 7|

Evaluate the difference

AB = |-11|

Take the absolute difference of 11

AB = 11

Hence, the length of the segment AB is 11

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Therefore, the volume of liquid needed to fill a sphere of radius r to height h = r/3 is (92/81)πr^3.

To find the volume of liquid needed to fill a sphere of radius r to a height h = r/3, we first need to find the volume of the spherical cap that makes up the top portion of the sphere.

The volume of a spherical cap is given by the formula:

V = (1/3)πh^2(3r - h)

where h is the height of the spherical cap and r is the radius of the sphere.

Substituting h = r/3, we get:

V = (1/3)π(r/3)^2(3r - r/3)

= (1/3)π(r^2/9)(8r/3)

= (8/27)πr^3

This is the volume of the spherical cap that makes up the top portion of the sphere. To find the volume of liquid needed to fill the sphere to the given height h, we need to subtract this volume from the total volume of the sphere.

The total volume of the sphere is given by the formula:

V = (4/3)πr^3

Substituting the value of V for the spherical cap, we get:

V = (4/3)πr^3 - (8/27)πr^3

= (92/81)πr^3

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Answer: 1/6

Step-by-step explanation:

Answer:

There is a 1 out of 6 probability the die shows a one.

Step-by-step explanation:

Although there are only 3 odd numbers in a die (1,3,5) , the die still only has 6 numbers. (1,2,3,4,5,6)

These means that the probability of getting 1, is 1 out of the 6 numbers.

Because of this it's a 1 out of 6 probability that this would happen. (or you can write 1/6 same answer)

Hope this helps, good luck!! :)

Answer:

3

Step-by-step explanation:

Replace 8 with 3

Cz angle 4 is equal to 8

Angle 4+Angle 3 is 180⁰

And angle one is equal to angle three

Answer:

x = \(-\frac{1}{3}\), y = 2

Step-by-step explanation:

3x + 3y - 7 = 12x + y

6y - 12x - 1 = -45x

(3x - 12x) + (3y - y) = 7

(-12x + 45x) + 6y = 1

-3(-9x + 2y = 7)

33x + 6y = 1

27x - 6y = -21

33x + 6y = 1

60x = -20 -> x = -20/60 = -1/3

-9x + 2y = 7 -> y = \(\frac{7+9x}{2}\) = \(\frac{7+9*-\frac{1}{3}}{2}\) = 2

Answer and Step-by-step explanation:

To solve for x, we need to first add 20 to both sides, and then add 2x to both sides.

2x > 20 + 4

Combine like terms.

2x > 24

Divide each side by 2.

x > 12

So, the answer is:

Any value of x that is greater than 12.

#teamtrees #PAW (Plant And Water)

Answer:

x>12

Step-by-step explanation:

1) -20>-2x+4

move the terms

2) 2x>4+20

calculate

3) 2x>24

divide both sides to get x>12

Answer:

y = 3x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← x and y- intercepts

m = \(\frac{3-0}{0+1}\) = \(\frac{3}{1}\) = 3

The line crosses the y- axis at (0, 3) ⇒ c = 3

y = 3x + 3 ← equation of line

Answer:

The answer is 12 units

Step-by-step explanation:

The length of the radius is 12 units

The radius of a circle is a line drawn from the center of the circle to its circumference

The length (L) of the arc is given as:

\(L = 10\pi\)

The length of an arc is:

\(L = r\theta\)

So, we have:

\(r\theta =10\pi\)

The angle at the center of the circle is \(\frac{5\pi}{6}\)

So, we have:

\(r* \frac{5\pi}{6}=10\pi\)

Multiply both sides by 6

\(r* 5\pi=60\pi\)

Divide both sides by 5pi

\(r = 12\)

Hence, the length of the radius is 12 units

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Answer:

48=3b+v

Step-by-step explanation:

384=24b+8v

b standing for bus

v standing for vam

to simplify the equations you would divided by eight since all numbers are multiples

48=3b+v

The point that represent the origin in the number line is Point W

A number line is a horizontal representation of numbers in parts with equal intervals

The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values at right

number line on -5 to 5 will have the origin at the center and te center here is zero which is similar to p

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To determine the minimum radius of the circle for the jet's loop, we need to calculate the centripetal acceleration at the lowest point and set it equal to the given limit of 6.5 g's.

Centripetal acceleration (ac) is given by the equation:

ac = (\(v^2\)) / r

Where:

ac = centripetal acceleration

v = velocity of the jet

r = radius of the circle

We need to convert the given speed from km/h to m/s for consistent units. Using the conversion factor 1 km/h = 0.2778 m/s:

v = 1250 km/h * 0.2778 m/s = 347.25 m/s

Now, we can rearrange the formula to solve for the radius:

r = (\(v^2\)) / ac

Substituting the values:

The acceleration due to gravity, g, is approximately 9.8 m/s^2.

r = (347.25 m/s)^2 / (6.5 * 9.8 m/s^2)

Calculating this:

r ≈ 1995.3 m

Rounded to two significant figures, the minimum radius of the circle for the jet's loop should be approximately 2000 m.

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Answer:

13 square centimeters.

Step-by-step explanation:

There are 13 squares making up the shape

The probability of rolling the die once to get a four is 1/6

So we do 1/6*1/6*1/6 which is 1/216 since it's combined probabilities

Hope this helped

Answer:

Step-by-step explanation:

x=5 so y would = 3

Answer:

600 m

Step-by-step explanation:

I attend LUOA as well.

Answer:

600m

Step-by-step explanation:

I, too, attended LUOA.

hope this helps:)

Answer:A b and ddI just know

Step-by-step explanation:

The graph of the equation x+y = 8 will be a straight line.

Graphical representation refers to the use of charts and graphs to visually display, analyse, clarify, and interpret numerical data, functions, and other qualitative structures.

Given an equation, x+y = 8

when x = 0, y = 8 → (0,8)

when y = 0, x = 8 → (8,0)

Hence, The graph of the equation x+y = 8 will be a straight line.

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Answer:

square - quad with four right angles and four congruent sides

rectangle - quad with four right angles

parallelogram - quad with two pairs of parallel sides

rhombus - quad with four congruent sides

trapezoid - quad with one set of parallel sides

Answer:

(x-12) = x/5

Step-by-step explanation:

Here, we want to write an equation

spending $12 out of the x equals that she has 1/5 of the original x

Mathematically, we have this as;

(x-12) = 1/5(x)

or (x-12) = x/5

Answer:

A. (0,4)

Step-by-step explanation:

You can calculate the y intercept when x = 0.

Substitute 0 for x:

y = (-4/3)(0) + 4

= 0 + 4

= 4

Answer:

Shama types at a constant rate she types 12 letters in 4 seconds what is the constant of proportionality for the relationship of letters to minutes

Answer choices

3

48

180

2,880

Help I need this answer fast I’m taking a test and I can’t fail 7th grade

Step-by-step explanation:

Shama types at a constant rate she types 12 letters in 4 seconds what is the constant of proportionality for the relationship of letters to minutes

Answer choices

3

48

180

2,880

Help I need this answer fast I’m taking a test and I can’t fail 7th grade

The constant of proportionality for the relationship of letters to minutes is 180.

Two set of quantities are said to be directly proportional or just simply proportional if the corresponding elements of these two sets has a constant ratio. This constant is called the proportionality constant or coefficient of proportionality.

We have the proportional relationship between letters typing and the time in minutes taken to type the letters.

Time taken by Shama to type 12 letters = 4 seconds

                                                                  = 4 / 60 minutes

                                                                  = 1/15 minutes

Proportionality constant can be found by taking the ratio of these quantities.

That is, proportionality constant = 12 / (1/15)

The fraction in the denominator will be taken to the numerator as the reciprocal and the operation changes into multiplication.

Proportionality constant = 12 × (15/1) = 180

Hence the proportionality constant for the relationship of the quantities letters and minutes is 180.

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\((x+3)^{-1/2}\)2√(x+3) = -1, from the derivation we can conclude that 2√(x+3) will always be greater than zero and can never be equal to -1.

The power rule is a rule of differentiation in calculus that allows us to find the derivative of a function of the form f(x) = xⁿ, where n is a constant. The power rule states that:

d/dx (xⁿ) = n*xⁿ⁻¹

In words, this means that the derivative of x to the power of n is equal to n times x to the power of n minus 1.

f(x) = 2√(x+3) + 1

f'(x) = 2 * 1/2 * \((x+3)^{-1/2}\) * 1 + 0

= \((x+3)^{-1/2}\\\)

If you would like to find the zeros of the function, you can set the function equal to zero and solve for x:

2√(x+3) + 1 = 0

2√(x+3) = -1

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\((x+3)^{(-1/2)}\)  \(\sqrt[2]{(x+3)} =-1\), We can infer from the derivation that 2(x+3) will never equal -1 and will always be larger than zero.

A calculus differentiation method known as the power rule enables us to determine the derivative of a function with the formula f(x) = xn, where

n is a constant. As per the power law,

\(\frac{d}{dx}\ (x^{n} )=n*x^{n-1}\)

The derivative of x to the power of n is defined as n times x to the power of n minus 1.

f(x) = 2√(x+3) + 1

\(f'(x)=2*\frac{1}{2} *(x+3)^{(\frac{-1}{2} )} *1+0\\\\(x+3)^{(-1/2)}\)

You can put the function equal to zero and solve for x to determine the function's zeros:

2√(x+3) + 1 = 0

2√(x+3) = -1

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The complete question is,

What is the domain and range of \(F(x)=\sqrt[2]{(x+3)} +1\).

One can determine the number of roots by seeing the degree of the given polynomial.

The number of roots can be determined by just seeing the highest power of the given equation.

1) for the equation  x-4=0

here, the highest power of the equation is one. So, it will have one root.

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtract multiplication, on,  and non-negative integer exponentiation of variables.

Let's check it by simplifying x-4=0  which implies x=4

Hence, the equation has only one root namely x = 4.

2) Consider a quadratic equation,

10t^2-t-3=0

here, the highest power of the equation is two. So, it will have two roots.

Let's check it by simplifying using the middle term splitting method,

10t^2+5t-6t-3=0

5t(2t+1)-3(2t+1)=0

(5t-3)(2t+1)=0

t=-3/5 or t=-1/2

Thus, the equation has two roots.

Hence, one can determine the number of roots by seeing the degree of the given polynomial.

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given

Find

Product

Explanation

here , we use law of exponents

so ,

Final Answer

Product =

Answer:

AC

Step-by-step explanation:

What is a diameter?

It is a line going straight through the center of the circle to the opposite side

So it is AC