help me please im in a rush

Answers

Answer 1

Answer:

a.1

b. 17

Step-by-step explanation:

So the | | around an equation makes it an absolute value which can be defined as the "distance from zero" or in other words, if a value is positive, it stays positive, and if a value is negative, it becomes positive.

|-8 + 9| = |1| = 1

|-8| + 9 = 8 + 9 = 17

Related Questions

Find the area of a regular hexagon with radius 12 in

Answers

The area of the regular hexagon is 216√3

How to find the area of a regular hexagon

From the question, we have the following parameters that can be used in our computation:

Radius = 12 in

The area of a regular hexagon is calculated as

Area = 3√3/2 * r²

substitute the known values in the above equation, so, we have the following representation

Area = 3√3/2 * 12²

Evaluate

Area = 216√3

Hence, the area of the regular hexagon is 216√3

Answers

As n increases, the approximation error decreases. Also, as n doubles, the error is reduced by a factor of 16 times.

Given integral is [tex]$I = \int_{1}^{2} \frac{1}{x^2} dx$[/tex]

Using the formula of Simpson’s Rule as below:

[tex]$$\int_{a}^{b} f(x) dx \approx \frac{b-a}{6} \left[ f(a) + 4f\left(\frac{a+b}{2}\right) + f(b) \right]$$[/tex]

We have,

a = 1 and

b = 2, and

n = 5, 10, 20

Simpson’s Rule approximations using the above formula for

n = 5, 10, 20 are as follows:

[tex]$$\begin{aligned}T_{5} &= \frac{1}{6} \left[ f(1) + 4f\left(\frac{1+2}{2}\right) + f(2) \right] \\&= \frac{1}{6} \left[ 1 + 4 \times \frac{1}{\left(\frac{3}{2}\right)^2} + \frac{1}{4} \right] \\&= 0.78333\end{aligned}$$[/tex]

[tex]$$\begin{aligned}T_{10} &= \frac{1}{30} \left[ f(1) + 4f\left(\frac{1+\frac{3}{4}}{2}\right) + 2f\left(\frac{3}{4}\right) + 4f\left(\frac{3}{4}+\frac{1}{4}\right) + 2f\left(\frac{5}{4}\right) + 4f\left(\frac{5}{4}+\frac{1}{4}\right) + f(2) \right] \\&= \frac{1}{30} \left[ 1 + 4 \times \frac{16}{9} + 2 \times \frac{16}{9} + 4 \times \frac{4}{25} + 2 \times \frac{16}{25} + 4 \times \frac{16}{49} + \frac{1}{4} \right] \\&= 0.78343\end{aligned}$$[/tex]

Using the formula for the error of Simpson’s Rule, given by

[tex]$$Error \approx \frac{(b-a)^5}{180n^4}f^{(4)}(\xi)$$where $\xi$[/tex]

where [tex]$\xi$[/tex] lies in the interval [a,b], and [tex]$f^{(4)}(x)$[/tex] is the fourth derivative of f(x) and is equal to [tex]$\frac{24}{x^5}$[/tex] in this case.

We have, a = 1,

b = 2, and

[tex]$f^{(4)}(x) = \frac{24}{x^5}$[/tex]

Hence, errors for Simpson’s Rule using the above formula for

n = 5, 10, 20 are as follows:

[tex]$$\begin{aligned}E_{5} &\approx \frac{(2-1)^5}{180 \times 5^4} \max_{1 \le x \le 2} \left\vert \frac{24}{x^5} \right\vert \\&\approx 1.83414 \times 10^{-6}\end{aligned}$$[/tex]

[tex]$$\begin{aligned}E_{10} &\approx \frac{(2-1)^5}{180 \times 10^4} \max_{1 \le x \le 2} \left\vert \frac{24}{x^5} \right\vert \\&\approx 4.58535 \times 10^{-8}\end{aligned}$$[/tex]

[tex]$$\begin{aligned}E_{20} &\approx \frac{(2-1)^5}{180 \times 20^4} \max_{1 \le x \le 2} \left\vert \frac{24}{x^5} \right\vert \\&\approx 1.14634 \times 10^{-9}\end{aligned}$$[/tex]

When n is doubled, E is divided by [tex]2^4 = 16[/tex].

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Sujita deposited Rs 4,00,000 in a commercial bank for 2 years at 10% p.a. compounded half yearly. After 1 year the bank changed its policy and decided to give compound interest compounded quarterly at the same rate. The bank charged 5% tax on the interest as per government's rule. What is the percentage difference between the interest of the first and second year after paying tax.

Answers

The percentage difference between the interest of the first and second year, after paying tax, is approximately 100%.

To calculate the interest for the first year, compounded half-yearly, we can use the formula for compound interest:

[tex]A = P \times (1 + r/n)^{(n\times t)[/tex]

Where:

A is the total amount including interest,

P is the principal amount (Rs 4,00,000),

r is the annual interest rate (10% or 0.10),

n is the number of times interest is compounded per year (2 for half-yearly),

and t is the number of years (1 for the first year).

Plugging in the values, we find that the total amount after one year is approximately Rs 4,41,000.

Now, for the second year, compounded quarterly, we have:

P = Rs 4,41,000,

r = 0.10,

n = 4 (quarterly),

and t = 1.

Using the same formula, the total amount after the second year is approximately Rs 4,85,610.

To calculate the difference in interest, we subtract the amount after the first year from the amount after the second year: Rs 4,85,610 - Rs 4,41,000 = Rs 44,610.

Now, applying the 5% tax on the interest, the tax amount is 5% of Rs 44,610, which is approximately Rs 2,230.

Therefore, the final interest after paying tax for the first year is Rs 44,610 - Rs 2,230 = Rs 42,380.

The percentage difference between the interest of the first and second year after paying tax can be calculated as follows:

Percentage Difference = (Interest of the Second Year - Interest of the First Year) / Interest of the First Year * 100

= (Rs 42,380 - Rs 0) / Rs 42,380 * 100

≈ 100%

Thus, the percentage difference between the interest of the first and second year, after paying tax, is approximately 100%.

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What is the best way to describe the center of the data represented in this line plot?

Select from the drop-down menus to correctly complete the statement.

The mean/median is 1 inch/1.5 inches/1.8 inches/2 inches

Answers

The best way to describe the center of the data represented in this line plot is; mean = 1.8 inches and median = 1.5 inches

What are line plots?

Line plots, also known as dot plots, are a type of graphical representation used to display data. They are particularly useful for showing the distribution and frequency of values in a dataset.

Line plots consist of a number line where each data point is represented by a dot or symbol placed above the corresponding value on the line.

Considering the given line plot:

Mean = (0 * 3 + 1 * 3 + 2 * 1 + 3 * 1 + 4 * 1 + 6 * 1)/10

Mean = 1.8 inches

Median = (1 + 2)/2

Median = 1.5 inches

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Let f(x)=6sin(x)/(6sin(x)+4cos(x))
Then f′(x)= .
The equation of the tangent line to y=f(x) at a=π/4 can be written in the form y=mx+b where
m= and b= .

Answers

To find f'(x), we can use the quotient rule:

f'(x) = [(6sin(x) + 4cos(x))(6cos(x)) - (6sin(x))(4sin(x))]/(6sin(x) + 4cos(x))^2

Simplifying this expression gives:

f'(x) = (36cos(x)^2 - 24sin(x)^2)/(6sin(x) + 4cos(x))^2

At a=π/4, we have sin(a) = cos(a) = 1/√2, so:

f'(π/4) = (36(1/2) - 24(1/2))/(6(1/√2) + 4(1/√2))^2

f'(π/4) = 3/25

To find the equation of the tangent line at a=π/4, we need both the slope and the y-intercept.

We already know the slope, which is given by f'(π/4) = 3/25. To find the y-intercept, we can plug in a=π/4 into the original function:

f(π/4) = 6sin(π/4)/(6sin(π/4) + 4cos(π/4)) = 6/10 = 3/5

So the equation of the tangent line is y = (3/25)x + 3/5, which can be written in the form y = mx + b with m = 3/25 and b = 3/5.

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find the average value of f over the given rectangle. f(x, y) = 4ey x ey , r = [0, 6] ⨯ [0, 1] fave =

Answers

The average value of f over the rectangle R is 6(e2 - 1).

To find the average value of the function f(x, y) = 4ey x ey over the rectangle R = [0, 6] ⨯ [0, 1], we need to calculate the double integral of f over R and divide it by the area of R:

fave = (1/area(R)) ∬R f(x, y) dA

where dA denotes the area element in the xy-plane.

First, we can simplify the expression for f(x, y) by using the properties of exponentials:

f(x, y) = 4ey x ey = 4e2y x

Now we can evaluate the integral:

f_ave = (1/area(R)) ∬R f(x, y) dA

= (1/(6*1)) ∫[0,6] ∫[0,1] 4e2y x dy dx

= (1/6) ∫[0,6] 4x ∫[0,1] e2y dy dx

= (1/6) ∫[0,6] 4x [e2y/2]0¹ dx

= (1/6) ∫[0,6] 2x (e2 - 1) dx

= (1/3) (e2 - 1) ∫[0,6] x dx

= (1/3) (e2 - 1) [(6²)/2]

= (18/3) (e2 - 1)

= 6(e2 - 1)

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Consider the function f(x) = 7x + 8x2 over the interval [0, 1]. Divide the interval into n subintervals of equal length. How long is each subinterval? Length is 1/n In order to determine an overestimate for the area under the graph of the function, at what Z-value should you evaluate f(2) to determine the height of the first rectangle? = 1/n Find a formula for the c-value in the kth subinterval which determines the height of the kth rectangle. = k/n Write down a Riemann sum for f(x) over the given interval using the 2-values you calculated above. Riemann sum is k1 Using the formulas n(n+1) k= and 2 K2 n(n + 1)(2n +1) 6 write down the above Riemann sum without using a . k=1 k=1 Riemann sum is Compute the limit of the above sum as n → 00. The limit is

Answers

The limit is ∫₀¹ [7x + 8x²] dx = 77/12

To find the height of the kth rectangle, we need to evaluate the function at the left endpoint of the kth subinterval, which is (k-1)/n. So the formula for the c-value in the kth subinterval is (k-1)/n.

Now we can write down a Riemann sum for f(x) over the given interval using the values we calculated above. The Riemann sum is:

Σ [f((k-1)/n) * (1/n)]

where the sum is taken from k=1 to k=n.

To simplify this expression, we can use the formulas:

Σ k = n(n+1)/2

Σ k² = n(n+1)(2n+1)/6

Using these formulas, we can rewrite the Riemann sum as:

[7/2n + 8/3n²] Σ k² + [7/n] Σ k

where the sum is taken from k=1 to k=n.

Finally, we can compute the limit of this expression as n approaches infinity to find the area under the curve. The limit is:

∫₀¹ [7x + 8x²] dx = 77/12

which is the exact value of the area under the curve.

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One large jar and three small jars together can hold 14 ounces of jam. One large jar minus one small jar can hold 2 ounces of jam. A matrix with 2 rows and 2 columns, where row 1 is 1 and 3 and row 2 is 1 and negative 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is l and row 2 is s, equals a matrix with 2 rows and 1 column, where row 1 is 14 and row 2 is 2. Use matrices to solve the equation and determine how many ounces of jam are in each type of jar. Show or explain all necessary steps.

Answers

Matrix tells that large jar can hold 5 ounces of jam and small jar can hold 3 ounces of jam

The matrix formed is

[tex]\left[\begin{array}{ccc}1&3\\1&-1\end{array}\right] \left[\begin{array}{ccc}l\\s\end{array}\right] = \left[\begin{array}{ccc}14\\2\end{array}\right][/tex]

Here L is a large jar and S is a small jar

Multiplying the matrix we will get two equation

1 × L + 3 × S = 14

1 × L + (-1) × S = 2

First equation is

L + 3S = 14

L = 14 - 3S

Second equation

L - S = 2

Putting the value of L in second equation

14 - 3S - S = 2

-4S = 2 -14

S = 3

L = 5

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consider the message ""do not pass go"" translate the encrypted numbers to letters for the function f(p)=(p 3) mod 26.

Answers

Answer:

Therefore, the decrypted message is "BXXPABYY".

Step-by-step explanation:

To decrypt the message "do not pass go", we first need to convert each letter to a number based on its position in the alphabet. We can use the convention A=0, B=1, C=2, ..., Z=25.

Thus, "D" corresponds to 3, "O" corresponds to 14, "N" corresponds to 13, "O" corresponds to 14, "T" corresponds to 19, "P" corresponds to 15, "A" corresponds to 0, "S" corresponds to 18, and "S" corresponds to 18.

Next, we apply the function f(p) = (p^3) mod 26 to each number to get the encrypted number:

f(3) = (3^3) mod 26 = 27 mod 26 = 1, which corresponds to the letter "B".

f(14) = (14^3) mod 26 = 2197 mod 26 = 23, which corresponds to the letter "X".

f(13) = (13^3) mod 26 = 2197 mod 26 = 23, which corresponds to the letter "X".

f(14) = (14^3) mod 26 = 2197 mod 26 = 23, which corresponds to the letter "X".

f(19) = (19^3) mod 26 = 6859 mod 26 = 15, which corresponds to the letter "P".

f(15) = (15^3) mod 26 = 3375 mod 26 = 1, which corresponds to the letter "B".

f(0) = (0^3) mod 26 = 0, which corresponds to the letter "A".

f(18) = (18^3) mod 26 = 5832 mod 26 = 24, which corresponds to the letter "Y".

o decrypt the message "do not pass go", we first need to convert each letter to a number based on its position in the alphabet. We can use the convention A=0, B=1, C=2, ..., Z=25.

Thus, "D" corresponds to 3, "O" corresponds to 14, "N" corresponds to 13, "O" corresponds to 14, "T" corresponds to 19, "P" corresponds to 15, "A" corresponds to 0, "S" corresponds to 18, and "S" corresponds to 18.

Next, we apply the function f(p) = (p^3) mod 26 to each number to get the encrypted number: