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3 years ago

Find the average value of f(x) = 1/x over the interval [e, 2e].

1 answer:

8 0

$\bf \displaystyle \cfrac{1}{2e-e}\int_{e}^{2e}~\cfrac{1}{x}\cdot dx\implies \left. \cfrac{1}{e}\cdot ln(x) \right]_{e}^{2e}\implies \left[ \cfrac{ln(2e)}{e} \right]-\left[ \cfrac{ln(e)}{e}\right]
\\\\\\
\left[ \cfrac{ln(2)+ln(e)}{2e} \right]-\left[ \cfrac{1}{e} \right]\implies \cfrac{ln(2)}{e}+\cfrac{ln(e)}{e}-\cfrac{1}{e}\implies \cfrac{ln(2)}{e}+\cfrac{1}{e}-\cfrac{1}{e}
\\\\\\
\cfrac{ln(2)}{e}$

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What is the estimate of 206,834 and 194,268

Lena [83]

Answer:I can help you round 206834 and 194268 to its nearest thousands place. 207000 would be the estimate for the first number and 194000 would be the estimate for the second number.

7 0

3 years ago

Two forces with magnitudes of 100 and 50 pounds act on an object at angles of 50° and 160°, respectively. Find the direction and

shusha [124]

Forces in direction x:
fx1 = 100 * cos (50) = 64.28
fx2 = 50 * cos (160) = - 46.99
The resultant is:
fx = fx1 + fx2 = 17.29

Forces in direction y:
fy1 = 100 * sine (50) = 76.60
fy2 = 50 * sine (160) = 17.10
The resultant is:
fy = fy1 + fy2 = 93.70
The magnitude of the resulting force is:
f = root (fx ^ 2 + fy ^ 2)
f = root ((17.29) ^ 2 + (93.70) ^ 2)
f = 95.28
The angle is:
theta = atan (fy / fx)
theta = atan (93.70 / 17.29)
theta = 79.55 degrees
Answer:
The direction and magnitude of the resultant force are:
f = 95.28 pounds at theta = 79.55 degrees

6 0

3 years ago

Divide the rational expressions and express in simplest form. When typing your answer for the numerator and denominator be sure

Veseljchak [2.6K]

Dividing by a fraction is equivalent to multiply by its reciprocal, then:

$\begin{gathered} \frac{3y^2-7y-6}{2y^2-3y-9}\div\frac{y^2+y-2}{2y^2+y-3^{}}= \\ =\frac{3y^2-7y-6}{2y^2-3y-9}\cdot\frac{2y^2+y-3}{y^2+y-2}= \\ =\frac{(3y^2-7y-6)(2y^2+y-3)}{(2y^2-3y-9)(y^2+y-2)} \end{gathered}$

Now, we need to express the quadratic polynomials using their roots, as follows:

$ay^2+by+c=a(y-y_1)(y-y_2)$

where y1 and y2 are the roots.

Applying the quadratic formula to the first polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{7\pm\sqrt[]{(-7)^2-4\cdot3\cdot(-6)}}{2\cdot3} \\ y_{1,2}=\frac{7\pm\sqrt[]{121}}{6} \\ y_1=\frac{7+11}{6}=3 \\ y_2=\frac{7-11}{6}=-\frac{2}{3} \end{gathered}$

Applying the quadratic formula to the second polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{-1\pm\sqrt[]{1^2-4\cdot2\cdot(-3)}}{2\cdot2} \\ y_{1,2}=\frac{-1\pm\sqrt[]{25}}{4} \\ y_1=\frac{-1+5}{4}=1 \\ y_2=\frac{-1-5}{4}=-\frac{3}{2} \end{gathered}$

Applying the quadratic formula to the third polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{3\pm\sqrt[]{(-3)^2-4\cdot2\cdot(-9)}}{2\cdot2} \\ y_{1,2}=\frac{3\pm\sqrt[]{81}}{4} \\ y_1=\frac{3+9}{4}=3 \\ y_2=\frac{3-9}{4}=-\frac{3}{2} \end{gathered}$

Applying the quadratic formula to the fourth polynomial:

$\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{-1\pm\sqrt[]{1^2-4\cdot1\cdot(-2)}}{2\cdot1} \\ y_{1,2}=\frac{-1\pm\sqrt[]{9}}{2} \\ y_1=\frac{-1+3}{2}=1 \\ y_2=\frac{-1-3}{2}=-2 \end{gathered}$

Substituting into the rational expression and simplifying:

$\begin{gathered} \frac{3(y-3)(y+\frac{2}{3})2(y-1)(y+\frac{3}{2})}{2(y-3)(y+\frac{3}{2})(y-1)(y+2)}= \\ =\frac{3(y+\frac{2}{3})}{2(y+2)}= \\ =\frac{3y+2}{2y+4} \end{gathered}$

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1 year ago

Semisuma lungimii bazelor este formula de calcul pentru: *

fredd [130]

Answer:

Can I Know Which Language Is This??

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3 years ago

Big Louie's Pizza House sells a 12" square pan pizza for $3.95 and a 24" square pan pizza for $14.95. Which pizza is a better de

Alex_Xolod [135]

Answer:

The pizza that is a better deal is 12" square pan pizza for $3.95.

Step-by-step explanation:

This is because if you get 2 of the 12" square pan pizzas it will be 24" and you will only have to pay $7.90. but if you bought the 24" square pan pizza you would have to pay $14.95 which isnt a fair price.

4 0

2 years ago