let R be the region bounded by the functions f(x)=-x^2 and g(x)=-9 as shown in the diagram below. find the exact area of the region R. write your answer in the simplest form. zoom in photo

Answer:

Step-by-step explanation:

The nth term of an arithmetic sequence:  aₙ = a₁ + d(n - 1)

{d = common difference}

a₁ = 5

a₄ = 5 + d(4 - 1)

-4 = 5 + 3d

-4 - 5 = 3d

3d = -9

 d = -3

Therefore;

                  aₙ = 5 + (-3)(n - 1)

                   aₙ = -3n + 8

Check:  a₁₀ = 5 + (-3)(10 - 1) = 5 - 27 = - 22

The nth term of the sequence is Tn = 8 - 3n

The given parameters are:

a = 5, first term

T4 = -4 --- the 4th term

T10 = -22 --- the 10th term

The nth term of an arithmetic sequence is:

Tn = a + (n - 1) * d

So, we  have:

T4 = a + (4 - 1) * d

Substitute known values

-4 = 5 +(4 -1) * d

This gives

-4 = 5 + 3d

Subtract 5 from both sides

3d = -9

Divide by 3

d = -3

Recall that:

Tn = a + (n - 1) * d

So, we have:

Tn = 5 + (n - 1) * -3

Expand

Tn = 5 + 3 - 3n

Solve

Tn = 8 - 3n

Hence, the nth term of the sequence is Tn = 8 - 3n

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Answer:

(a + 4)(b + 1)

Step-by-step explanation:

ab + 4 + a + 4b

Rearrange the expression to find the GCF.

ab + a + 4b + 4

Now find the GCF.

a (b + 1) + 4 (b + 1)

Divide the whole thing by b+1

(a + 4)(b + 1)

Answer:

d=2_f - 9h_f

Step-by-step explanation:

es la segunda opción

Answer:

it represents a variable

Step-by-step explanation:

The number 8 is the coefficient of the variable k.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.

Given that the expression is 8k + 5. In the given expression the number 8 is the coefficient of the given expression.

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The hair color of the players on a tennis team would be considered nominal data. Therefore, the most appropriate answer is option (c): Nominal data.

In data classification, there are four main levels of measurement: nominal, ordinal, interval, and ratio. Nominal data is the lowest level of measurement and represents categories or labels that cannot be ranked or ordered. Hair color falls into this category as it represents different categories or labels such as blonde, brunette, red, etc. Nominal data does not have any inherent numerical value or order.

On the other hand, ordinal data represents categories that can be ordered or ranked but do not have a consistent interval between them. Interval and ratio data involve numerical values with a consistent interval and a true zero point, with ratio data having a meaningful zero point.

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Answer:

p < 2

Step-by-step explanation:

hope this is right and have a good day

The following functions 1. f(x) = x+ex 3 2. f(x) = X - C03 X € = 0.0001 2 3. f(x) = x - x + sinx-1 2  By using Newton-Raphson method √29 is 4.5826.

Solve f(x) = x + e^x = 0:

Unfortunately, this equation cannot be solved analytically. We can use numerical methods such as the Newton-Raphson method to find an approximate solution. However, in this case, we will move on to the next function.

Solve f(x) = x^3 - 0.0001 = 0:

To solve this equation, we can rearrange it as follows:

x^3 = 0.0001

Taking the cube root of both sides, we get:

x = ∛0.0001

Using a calculator, we find that ∛0.0001 ≈ 0.04641588834.

Therefore, the solution to the equation f(x) = x^3 - 0.0001 = 0 is approximately x ≈ 0.0464.

Solve f(x) = x - x^2 + sin(x) - 1 = 0:

This equation also cannot be solved analytically. We can use numerical methods such as the Newton-Raphson method or graphing methods to find an approximate solution. Let's use the Newton-Raphson method.

Applying the Newton-Raphson method, we start with an initial guess, let's say x0 = 1:

Iteratively, we update x using the formula:

x_n+1 = x_n - f(x_n) / f'(x_n)

The derivative of f(x) is:

f'(x) = 1 - 2x + cos(x)

Using the initial guess:

x1 = x0 - f(x0) / f'(x0)

= 1 - (1 - 1^2 + sin(1) - 1) / (1 - 2(1) + cos(1))

≈ 1.2227

We repeat the process with x1 as the new guess:

x2 = x1 - f(x1) / f'(x1)

≈ 1.2196

Continuing this iterative process, we find:

x3 ≈ 1.2196

x4 ≈ 1.2196

The solution to the equation f(x) = x - x^2 + sin(x) - 1 = 0 is approximately x ≈ 1.2196.

Now, let's move on to finding √29 using the Newton-Raphson method.

To find √29 using the Newton-Raphson method, we need to solve the equation f(x) = x^2 - 29 = 0.

Using the Newton-Raphson method, we start with an initial guess, let's say x0 = 5:

Iteratively, we update x using the formula:

x_n+1 = x_n - f(x_n) / f'(x_n)

The derivative of f(x) is:

f'(x) = 2x

Using the initial guess:

x1 = x0 - f(x0) / f'(x0)

= 5 - (5^2 - 29) / (2 * 5)

= 5 - (25 - 29) / 10

= 5 - 4 / 10

= 5 - 0.4

= 4.6

We repeat the process with x1 as the new guess:

x2 = x1 - f(x1) / f'(x1)

= 4.6 - (4.6^2 - 29) / (2 * 4.6)

≈ 4.5826

Continuing this iterative process, we find:

x3 ≈ 4.5826

x4 ≈ 4.5826

The solution to the equation f(x) = x^2 - 29 = 0, which gives √29, is approximately x ≈ 4.5826.

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Answer:

y = 5, y = 7

Step-by-step explanation:

Answer:

the number of users in the last year is 2,100

Step-by-step explanation:

The computation of the number of users in the last year is shown below:

Given that

The users are 2604 that are increased to 24% as compared with the last year

So, the users in the last year is

= 2604 ×100 ÷ 124

= 2,100

Hence, the number of users in the last year is 2,100

Answer:

688

Step-by-step explanation:

ithink

Answer: quadratic model, 0.866

Step-by-step explanation:

Answer: 7pi

Step-by-step explanation: If it completes the circumference distance (14pi) of the circle in 20 seconds, in 10 seconds it will complete half of that. or 7pi. Hope this helped!

:.the distance travelled after 10sec. =7πm

Answer:

in 20 sec distance travelled =2πr=2π×7=14πm

in 10 sec distance travelled=14πm×10/20=7πm

Answer:

x= 8

Step-by-step explanation:

17x + 3 = 139

17x = 136

x = 8

one hundred and twenty approximately

Answer:

2+3=5

Step-by-step explanation:

prime numbers =2 and 3

sum =5 which is odd

Answer: It is a polynomial, and the degree is 4.

Step-by-step explanation:  The degree is basically the biggest number exponent

Step-by-step explanation:

x xndndjjdjdjdowiekeie

Answer:

y+x = -4

Step-by-step explanation:

-4 indicates where the line intercept the y axis

if we put y=0 we can find where line intercepts the x axis.

it results x = -4

the two values are negative

Answer:

-5/4

Step-by-step explanation:

Answer:

x=2.2

y=-3.4

Step-by-step explanation:

subtract the second from the first

-5x=-11

x=2=2

substituting by x in the first equation

so y=-3.4

Answer:

15

Step-by-step explanation:

Prime Numbers Check

15: 5 * 3

30: 2 * 3 * 5

75: 3 * 5 * 5

Both 3 and 5 are prime numbers present in all 3 greater numbers, then you multiply them

3*5 = 15

GCF is 15

Answer:

YUH

Step-by-step explanation:

Answer:

you'll see...

Step-by-step explanation:

Given that the transformed graph is of function f(x) = (x + 2)^4 + 6 and the parent function g(x) = x^4

The transformed graph function g(x) was shifted two (2) units to the left and was translated six (6) units upward.

When the function is shifted to the right, the factor of x will be negative and when it's shifted to the left, the factor of x will be positive.

Therefore, function g(x) = x^4 is shifted 2 units to the left and translated 6 units upward to form f(x) = ( x + 2 )^4 + 6.

Answer:

b: 118

c: 62

Step-by-step explanation:

Angle B is a vertical angle from the given angle, so they are congruent.

Angle C is supplementary (2 angles that add up to 180 degrees) from the given angle, so we can subtract 118 from 180 to give us 62, which is angle c.

Hope this helps! :)

Answer: b=118 c=62

Step-by-step explanation: All angles add up to 360 degrees. We know one angle equals 118. We can also tell that angle b is identical to angle 118 because they are complementary angles. Now we add 118+118 which equals 236. Subtract 360 from 236. That gives us 124. Divide 124 by two since their are two angles. That gives us 62. c=62 and b=118

At time t = 0, the capacitor in the circuit is charged to its maximum charge, qmax, and the circuit has zero current.

At t = 0, the capacitor in the circuit is fully charged, which means it has accumulated its maximum charge, qmax. The capacitor acts as a temporary energy storage device in the circuit. When the capacitor is fully charged, it contains potential energy. The charge on the capacitor creates an electric field, which opposes the flow of current through the circuit.

Since the capacitor is fully charged at t = 0, it resists any change in the current. Therefore, the circuit has zero current flowing through it. As time progresses, the capacitor will start to discharge, releasing the stored energy and allowing the current to flow. The discharge process is governed by the relationship between the voltage across the capacitor, the capacitance of the capacitor, and the resistance in the circuit.

Finally, at t = 0, the capacitor in the circuit is charged to its maximum capacity, qmax, and the circuit has zero current flowing through it.

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To express the function [tex]\(G\)[/tex] in the form [tex]\(f \circ g\)[/tex] , where [tex]\(y = f(g(x))\)[/tex] , we need to find suitable non-identity functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] that can be composed to yield [tex]\(G(x)\)[/tex].

Let's choose [tex]\(g(x) = \frac{1}{x}\)[/tex]  and [tex]\(f(x) = x + 8\)[/tex].

Now, we can express [tex]\(G\)[/tex] as  [tex]\(G(x) = f(g(x))\)[/tex] , which becomes:

[tex]\[G(x) = f(g(x)) = f\left(\frac{1}{x}\right) = \frac{1}{x} + 8\][/tex]

Therefore, the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] that can be composed to yield [tex]\(G(x) = \frac{1}{x} + 8\) are \(f(x) = x + 8\)[/tex] and [tex]\(g(x) = \frac{1}{x}\)[/tex].

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