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Shtirlitz [24]
3 years ago
14

F(x)=x+3 , G(x)=x^2-2 (F/G)(-1)-G(3)

Mathematics
1 answer:
trapecia [35]3 years ago
7 0

f(x)=x+3;\ g(x)=x^2-2\\\\\left(\dfrac{f}{g}\right)(-1)-g(3)=?\\\\\left(\dfrac{f}{g}\right)(x)=\dfrac{f(x)}{g(x)}\\\\g(3)=3^2-2=9-2=7\\\\f(-1)=-1+3=2\\\\g(-1)=(-1)^2-2=1-2=-1\\\\\left(\dfrac{f}{g}\right)(-1)-g(3)=\dfrac{2}{-1}-7=-2-7=-9

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Solve the equation 5=1/2 v-3 <br><br> v=?
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3 years ago
In an arithmetic​ sequence, the nth term an is given by the formula an=a1+(n−1)d​, where a1 is the first term and d is the commo
Dmitry_Shevchenko [17]

Answer:

a_{10} = \frac{10}{65536}

Step-by-step explanation:

The first step to solving this problem is verifying if this sequence is an arithmetic sequence or a geometric sequence.

This sequence is arithmetic if:

a_{3} - a_{2} = a_{2} - a_{1}

We have that:

a_{3} = 40, a_{2} = 10, a_{3} = \frac{5}{2}

a_{3} - a_{2} = a_{2} - a_{1}

\frac{5}{2} - 10 = 10 - 40

\frac{-15}{2} \neq -30

This is not an arithmetic sequence.

This sequence is geometric if:

\frac{a_{3}}{a_{2}} = \frac{a_{2}}{a_{1}}

\frac{\frac{5}[2}}{10} = \frac{10}{40}

\frac{5}{20} = \frac{1}{4}

\frac{1}{4} = \frac{1}{4}

This is a geometric sequence, in which:

The first term is 40, so a_{1} = 40

The common ratio is \frac{1}{4}, so r = \frac{1}{4}.

We have that:

a_{n} = a_{1}*r^{n-1}

The 10th term is a_{10}. So:

a_{10} = a_{1}*r^{9}

a_{10} = 40*(\frac{1}{4})^{9}

a_{10} = \frac{40}{262144}

Simplifying by 4, we have:

a_{10} = \frac{10}{65536}

3 0
3 years ago
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co
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Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If \sum a_n is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho

If \rho < 1, the series converges absolutely

If \rho > 1, the series diverges

If \rho = 1, the test fails.

Given the series \sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}

To test for convergence or divergence using ratio test, we will use the condition above.

a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}

\frac{a_n_+_1}{a_n} =  \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\

\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\

aₙ₊₁/aₙ =

\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\

note that any constant dividing infinity is equal to zero

|\frac{1+2/\infty+1/\infty^2}{5}|\\\\

\frac{1+0+0}{5}\\ = 1/5

\rho = 1/5

Since The limit of the sequence given is less than 1, hence the series converges.

5 0
3 years ago
Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep,
Lina20 [59]

The shortest distance between the tip of the cone and its rim exits 51.11cm.

<h3>What is the shortest distance between the tip of the cone and its rim?​</h3>

If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.

Cos 38.5 = 40 / x

Solving the value of x, we get

Multiply both sides by x

$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x

$\cos \left(38.5^{\circ}\right) x=40

Divide both sides by $\cos \left(38.5^{\circ}\right)$

$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}

simplifying the above equation, we get

$x=\frac{40}{\cos \left(38.5^{\circ}\right)}

x = 51.11cm

The shortest distance between the tip of the cone and its rim exits 51.11cm.

To learn more about right triangles refer to:

brainly.com/question/12111621

#SPJ9

7 0
1 year ago
Read 2 more answers
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