Reasoning Practice
w
w
w
w
20
3
W
Х
Х
24
w
Х
Х
Y у
25
w
Х
Y у
Z
30
The sum of each row is given. Find w, x, y and z.

Evaluating the integral, the value of the integral ∫[1/(4x² + 49)]dx is c. π/84

An integral is the anti derivative of a function

Given the integral \(\int\limits^{\frac{7\sqrt{2} }{2} }_{\frac{7}{2\sqrt{2}} } {\frac{1}{4x^{2} + 49} } \, dx\), to evaluate it, we proceed as follows

\(\int\limits^{\frac{7\sqrt{2} }{2} }_{\frac{7}{2\sqrt{2}} } {\frac{1}{4x^{2} + 49} } \, dx = \int\limits^{\frac{7\sqrt{2} }{2} }_{\frac{7}{2\sqrt{2}} } {\frac{1}{4(x^{2} + \frac{49}{4} )} } \, dx = \int\limits^{\frac{7\sqrt{2} }{2} }_{\frac{7}{2\sqrt{2}} } {\frac{1}{4(x^{2} + (\frac{7}{2})^{2} )} } \, dx\)

We know that ∫(1/(x² + a²)dx = 1/a[tan⁻¹(x/a)]

So, we have that

\(\int\limits^{\frac{7\sqrt{2} }{2} }_{\frac{7}{2\sqrt{2}} } {\frac{1}{4(x^{2} + (\frac{7}{2})^{2} )} } \, dx\)= 1/4 × 1/7/2[tan⁻¹(x/(7/2))]

= 1/4 × 2/7[tan⁻¹(x/(7/2))]

= 1/2 × 1/7[tan⁻¹(2x/7)]

= 1/14[tan⁻¹(2x/7)]

Now evaluating the integral from x = 7/2√3 to 7√3/2, we have that

\(\int\limits^{\frac{7\sqrt{2} }{2} }_{\frac{7}{2\sqrt{2}} } {\frac{1}{4(x^{2} + (\frac{7}{2})^{2} )} } \, dx\)= 1/14[tan⁻¹(2x/7)] -

= 1/14[tan⁻¹(2(7√3/2)/7)] -  1/14[tan⁻¹(2(7/2√3)/7)]

= 1/14[tan⁻¹(√3)] -  1/14[tan⁻¹(1/√3)]

= 1/14 × π/3 -  1/14 × π/6]

= 1/14(π/3 - π/6)

= 1/14[(2π - π)/6]

= 1/14 × π/6

= π/84

So, the value of the integral is c. π/84

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Answer:

\(\textsf{C.} \quad \dfrac{\pi}{84}\)

Step-by-step explanation:

Given definite integral:

\(\displaystyle \int^{\frac{7 \sqrt{3}}{2}}_{\frac{7}{2\sqrt{3}}}\dfrac{1}{4x^2+49}\; \text{d}x\)

Factor out 4 from the denominator of the integral.

\(\displaystyle \int^{\frac{7 \sqrt{3}}{2}}_{\frac{7}{2\sqrt{3}}}\dfrac{1}{4\left(x^2+\dfrac{49}{4}\right)}\; \text{d}x\)

Now we can take 1/4 outside the integral.

\(\dfrac{1}{4}\displaystyle \int^{\frac{7 \sqrt{3}}{2}}_{\frac{7}{2\sqrt{3}}}\dfrac{1}{x^2+\dfrac{49}{4}}\; \text{d}x\)

\(\boxed{\begin{minipage}{6cm}\underline{\sf Inverse\;trigonometric\;integral}\\\\$\displaystyle \int\dfrac{1}{a^2+x^2}\; \text{d}x=\dfrac{1}{a} \arctan \left(\dfrac{x}{a}\right)+\text{(C)}$\\\end{minipage}}\)

Use the inverse trigonometric integral to integrate the integral.

\(\textsf{Let}\;a^2=\dfrac{49}{4} \implies a=\sqrt{\dfrac{49}{4}}=\dfrac{7}{2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{4}\displaystyle \int^{\frac{7 \sqrt{3}}{2}}_{\frac{7}{2\sqrt{3}}}\dfrac{1}{x^2+\dfrac{49}{4}}\; \text{d}x&=\dfrac{1}{4}\left[\dfrac{1}{\frac{7}{2}} \arctan \left(\dfrac{x}{\frac{7}{2}}\right)\right]^{\frac{7 \sqrt{3}}{2}}_{\frac{7}{2\sqrt{3}}}\\\\&=\dfrac{1}{4}\left[\dfrac{2}{7} \arctan \left(\dfrac{2x}{7}\right)\right]^{\frac{7 \sqrt{3}}{2}}_{\frac{7}{2\sqrt{3}}}\end{aligned}\)

Evaluate the integral:

                               \(\begin{aligned}&=\dfrac{1}{4}\left[\dfrac{2}{7}\arctan\left(\dfrac{2\cdot \frac{7 \sqrt{3}}{2}}{7}\right)-\dfrac{2}{7}\arctan\left(\dfrac{2\cdot \frac{7}{2\sqrt{3}}}{7}\right)\right]\\\\&=\dfrac{1}{4}\left[\dfrac{2}{7}\arctan\left(\sqrt{3}\right)-\dfrac{2}{7} \arctan \left(\dfrac{\sqrt{3}}{3}\right)\right]\\\\&=\dfrac{1}{4}\left[\dfrac{2}{7} \cdot \dfrac{\pi}{3}-\dfrac{2}{7} \cdot \dfrac{\pi}{6}\right]\\\\&=\dfrac{1}{4}\left[\dfrac{2\pi}{21}-\dfrac{2\pi}{42}\right]\end{aligned}\)

                               \(\begin{aligned}&=\dfrac{1}{4}\left[\dfrac{\pi}{21}\right]\\\\&=\dfrac{\pi}{84}\end{aligned}\)

\(answer = 66 \: {cm}^{3} \\ solution \\ volume = lwh \\ \: \: \: \: \: \: \: \: \: \: = \: 11 \times 3 \times 2 \\ \: \: \: \: \: \: \: \: \: = 66 \: {cm}^{3} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment\)

Answer:

\(= 66 {cm}^{3} \\ \)

Step-by-step explanation:

\(volume = base \times length \times height \\ = 3cm \times 11cm \times 2cm \\ = 66 {cm}^{3} \)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

7250%

Step-by-step explanation:

To express 72 1/2 as a percentage, you need to convert it to a decimal first and then multiply by 100.

72 1/2 is equivalent to 72.5 as a decimal.

To convert it to a percentage:

72.5 * 100 = 7250

Therefore, 72 1/2 is equal to 7250% when expressed as a percentage.

let me know it is helpful for you or not

Step-by-step explanation:

im sorry but i need more info or a picture or something to actually anwser the question...

Answer:

1

Step-by-step explanation:

5-6 first which is -1 then -1^2 is 1

\(\large\textsf{Hey there!}\)

\(\large\textsf{(5 - 6)}\mathsf{^2}\\\large\textsf{= -1}\mathsf{^2}\\\large\textsf{= -1}\times\large\textsf{-1}\\\large\textsf{= 1}\\\\\large\text{Therefore, your answer is most likley: 1}\)

\(\large\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The required reverse Euclidean algorithm is the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Given that (5*x) mod 91 =32.

To solve the modular equation (5*x) mod 91 =32 using reverse Euclidean algorithm is to find the modular inverse of 5 modulo 91.

Consider  (5*x) mod 91 =32.

5x = 32(mod 91)

Apply the Euclidean algorithm to find GCD of 5 and 91 is

91 = 18 * 5 + 1.

Rewrite it in congruence form,

1 = 91 - 18 *5

On simplifying the equation,

1 = 91 (mod 5)

The modular inverse of 5 modulo 91 is 18.

Multiply equation by 18 on both sides,

90x = 576 (mod91)

To obtain the smallest positive  solution,

91:576 = 6 (mod 91)

Divide both sides by the coefficient of x:

x = 6 * 90^(-1).

Apply the Euclidean algorithm,

91 = 1*90 + 1.

Simplify the equation,

1 + 1 mod (90)

The modular inverse of 90 modulo 91 is 1.

Substitute the modular inverse in the given question gives,

x = 6*1(mod 91)

x= 6 (mod91)

Therefore, the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

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\(\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\log(x)=2\hspace{5em}\log(y)=3\hspace{4em}\log(2)\approx 0.3\hspace{4em}\log(3)\approx 0.48 \\\\[-0.35em] ~\dotfill\\\\ \log\left(\sqrt[3]{x^4\cdot y^2} \right)\implies \log\left(\left( x^4\cdot y^2 \right)^{\frac{1}{3}} \right)\implies \cfrac{1}{3}\log(x^4 y^2) \\\\\\ \cfrac{1}{3}[\log(x^4)~~ + ~~\log(y^2)]\implies \cfrac{1}{3}[4\log(x)~~ + ~~2\log(y)]\implies \cfrac{1}{3}[4(2)~~ + ~~2(3)] \\\\\\ \cfrac{1}{3}[8~~ + ~~6]\implies {\Large \begin{array}{llll} \cfrac{14}{3} \end{array}}\)

Answer:

f(g(x)) = 9x^2 - 3x - 4

Step-by-step explanation:

Assuming it’s

f(x) = x^2 + 3x - 2

and g(x) is linear:

f(g(x)) = (3x - 2)^2 + 3(3x - 2) - 2

= 9x^2 -12x + 4 + 9x - 6 - 2

= 9x^2 - 3x - 4

The 99% confidence interval for population proportion p is 0.117 < P < 0.243 for the true population proportion of people who received flu vaccinations this year when out of 200 people sampled, 36 received flu vaccinations this year.

Given that,

n = 200

x = 36

Point estimate = sample proportion

= x/n = 36/200 = 0.18

1 - p = 1 - 0.18 = 0.82

At a 99% level, the z is,

α = 1 - 0.99 = 0.01

α/2 = 0.005

Zα/2 = 0.005Z = 2.576

The margin of error = E = Zα/2 \(\sqrt{p(1-p)} /n\)

= 2.576\(\sqrt{0.18*0.82} /200\)

E = 0.063

A 99% confidence interval for population proportion p is,

p - E < P < p + E

0.18 - 0.063 < P < 0.18 + 0.063

0.117 < P < 0.243

Therefore, the 99% confidence interval for population proportion p is 0.117 < P < 0.243 for the true population proportion of people who received flu vaccinations this year when out of 200 people sampled, 36 received flu vaccinations this year.

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Answer:

The answer is 5.5

Step-by-step explanation:

Since you can't divide 44 from 8 evenly you have to look at it a new way by using haves. They have many amazing videos on this online that I recommend!

Answer:

1/3 times 1/3

Step-by-step explanation:

the answer is 1/3 * 1/3 because when you divide with fraction you make the 3 or 3/1 turned around which is 1/3, then you multiply 1/3 * 1/3

The equationfor the line is,

From the points, (4,0) and (8,10)

And

The value of A(190) and its interpretation is: B. A(190) = 2980; If the accountant takes 190 hours to prepare the taxes, the cost will be $2,980.

Given function:

A(x) = 130 + 15x

Let x represent the number of hours

Let the flat fee be 130

Let plug in 190 into the function as this will enable to determine the value of A(1900 and it interpretation.

Hence,

A(x) = 130 + 15x

A(x) = 130 + 15(190)

A(x) = 130 + 2,850

A(x) = 2,980

Therefore the value of A(190) and its interpretation is: B. A(190) = 2980; If the accountant takes 190 hours to prepare the taxes, the cost will be $2,980.

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Answer:

(B)  A(190) = 2980; If the accountant takes 190 hours to prepare the taxes, the cost will be $2,980.

Step-by-step explanation:

Got it right on my quiz

2481.7

         ^ is the tenth place.

The 5 would either round it up or down by one-tenth. Since we like big numbers... we'll round it to 7 from 6.

Answer:

2481.7

Step-by-step explanation:

Find the number in the tenth place

6

and look one place to the right for the rounding digit

5

. Round up if this number is greater than or equal to

5

and round down if it is less than

5

Answer:

37

Step-by-step explanation:

The pattern is

2 (+3 =), 5 (+5 = ), 10 (+7) = , 17 (+9) =, 26 (+11) =, 37

So the difference between terms is +3, +5, +7, +9, +11... adding 2 each time, all odd numbers

Answer:

5th term is 26.

Step-by-step explanation:

5-2 =3. 10 - 5 = 5. 17 - 10 = 7.

notice how the differences are 3, 5, 7?

there's a gap of 2 between each difference.

so, let's call our next term in the sequence a.

a - 17 = (7+2).

a - 17 =9.

a = 26.

so, 5th term is 26.

Answer:

D. -6

Step-by-step explanation:

frist elimnate the postive numbers because it is impossible if it was a positve number.

Then you have two numbers left, all you have to do is multiply each one by either 3 or -5.

so -10.3 is too big and -6 is just right

x = -6

Answer:

11 remainder 2 sorry if it's wrong...

Step-by-step explanation:

60.00- 25.00= 35.00 35.00 ÷ 3 = 11 r2

Explanation:

If the dug dosage is 600 mg and 5.3% is eliminated per hour, we have:

Because for each hour the drug is eliminated at a rate of 5.3%, so the 94.7% of the previous amount remains.

Answer:

How much of the drug is left after 4 hours?

Total club members: 25

Club members that chose tulips:

(7+9)/25 = 0.64 x 100 = 64%

Divide the number of members that choose tulips by the total number of members.

Same process for the rest:

Squash:

(9+6)/25 = 0.6 x100 = 60%

Beans and Daises:

3/25 = 0.12 x 100 = 12%

Tulips and Squash:

9/25 = 0.36 = 36%

So, the correct option is A

Answer:

\(\frac{p-2l}{2}\)

Step-by-step explanation:

move the 2l to the other side by subtracting 2l on both sides. you get P - 2l = 2w. now divide both sides by 2 to get the answer.

Answer: B

Step-by-step explanation:

Answer:

I would have to say A) 32 + 45 + 39: 3

Step-by-step explanation:

This is because when finding the average of literally anything, you want to add up all the numbers, and then divide the sum of it by the numbers you added up.

for instance: 32 + 45 + 39 = 116. now, we need to divide by 3 because we added 3 numbers up.

116 divided by 3 = x

x is our average cost per books.

hope this helped, gl on your test!! :')

Answer:

I got -x/2+1/2. I'll get back to you in a lil bit.

Y = 1 - 2x

-1

y-1 = - 2x

÷ -2

y-1/-2 = x

f-1(x) = x - 1/-2

Let's make x = 7

7-1/-2 = - 3

Or

y = 1 - 2x

+2x

y + 2x = 1

-y

2x = 1-x

÷2

x. = 1-x/2

f-1(x) = 1 - x/2 is your answer

Let's make x=7

1-7/2 = - 3

Hope this helps!

1. The domain will be {0, 1, 2, 3}. Thus, the correct option is D.

2. The relation is not a function. Thus, the statement is false.

1. In the following relation {(2,1),(0,1),(3,3),(1,10),(2,5)}. Then the domain of the function is given as,

Domain = {0, 1, 2, 3}

Thus, the correct option is D.

2. For a function, the number of values of 'y' should be one for each value of 'x'.

At x = 2, the number of values of the function is two that is 1 and 5. So, the relation is not a function.

Thus, the statement is false.

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The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

In a geometric sequence,

The third term is 100 and the eighth term is 3.125.

Now,

We know that;

The nth term of geometric sequence is,

⇒ \(T_{n} = a r^{n - 1}\)

Hence, The third term is;

⇒ \(T_{3} = a r^{3 - 1} = 100\)

⇒ \(a r^{2} = 100\)   ..(i)

And, The eighth term is,

⇒ \(T_{8} = a r^{8 - 1} = 3.125\)

⇒ \(a r^{7} = 3.125\)   ..(ii)

Divide equation (ii) by (i), we get;

⇒ ar⁷ / ar² = 3.125/100

⇒ r⁷ / r² = 3125 / 100000

⇒ r⁷⁻² = 3125 / 100000

⇒ r⁵ = 3125 / 100000

⇒ r = 5/10

Thus, The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

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Answer:

Top Right: 26

Bottom Right: 16

Top Left: 36

Bottom Left: 20

Center: 26

Step-by-step explanation:

TR: 5 + 3 + 12 + 6 = 26

BR: 2 + 2 + 4 + 5 + 3 = 16

TL: 14 + 10 + 8 + 3 + 1 = 36

BL: 6 + 6 + 2 + 2 + 2 + 2 = 20

Center: 2 + 2 + 8 + 8 + 6 = 26

Answer:

the answer to your question is C: 9.675

The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

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