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4 years ago

Is it possible for a logarithm to equal zero

Mathematics

1 answer:

tatyana61 [14]4 years ago

6 0

Yes it is. log(1) and ln(1) both equal zero. But you cannot take the logarithm of 0.

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Let u and v be the solutions to 3x^2 + 5x + 7 = 0. Find u/v+v/u

Hitman42 [59]

Answer: $\dfrac{-17}{21}$

Step-by-step explanation:

Given: u and v be are the solutions of $3x^2+5x+7=0$

Let $ax^2+bx+c=0$ is the quadratic equation and u and v are the zeroes/solutions then

Sum of zeroes; $u+v = \dfrac{-b}{a}$

Product of zeroes; $uv= \dfrac{c}{a}$

Comparing $3x^2+5x+7=0$ to $ax^2+bx+c=0$

we get a= 3 , b= 5 and c = 7

$u+v = \dfrac{-b}{a} = \dfrac{-5}{3}----(i)$

$uv= \dfrac{c}{a} = \dfrac{7}{3}----(ii)$

Now we have to find

$\dfrac{u}{v} +\dfrac{v}{u} =\dfrac{u^2+v^2}{uv}$ adding and subtracting 2uv in numerator we get

$= \dfrac{u^2+v^2+2uv-2uv}{uv}= \dfrac{(u+v)^2-2uv}{uv}$

Substituting the values from (i) and (ii) we get

$\dfrac{(\dfrac{-5}{3} )^2-2\times \dfrac{7}{3} }{\dfrac{7}{3} } = \dfrac{\dfrac{25}{9} -\dfrac{14}{3} }{\dfrac{7}{3} }= \dfrac{\dfrac{25-42}{9} }{\dfrac{7}{3}} =\dfrac{-17}{9} \times \dfrac{3}{7} = \dfrac{-17}{21}$

Hence, the value of $\dfrac{u}{v} +\dfrac{v}{u}$ is $\dfrac{-17}{21}$

5 0

3 years ago

What is the slope of the line that passes through the points (-2,-5) and

Gemiola [76]

We can use the points (-2, -5) and (18, -5) to solve.

Slope formula: y2-y1/x2-x1

= -5-(-5)/18-(-2)

= 0/20

= 0

Best of Luck!

8 0

3 years ago

You make one pitcher of iced tea and one pitcher of lemonade for a party. Just before the party starts, you catch a little misch

mario62 [17]

Answer:

Each pitcher has the same fraction of the other drink.

Step-by-step explanation:

After 1 cup of tea is added to x cups of lemonade, the mix has the ratio 1:x of tea to lemonade. So, the fraction of mix that is tea is 1/(x+1).

The 1 cup of mix contains 1/(x+1) cups of tea and so x/(x+1) cups of lemonade. When that amount of lemonade is added to the tea, it brings the proportion of lemonade in the tea to (x/(x+1))/x = 1/(x+1), the same proportion as that of tea in the lemonade.

_____

You can consider the degenerate case of one cup of drink in each pitcher. Then when the 1 cup of tea is removed from its pitcher and added to the lemonade, you have a 50-50 mix of tea and lemonade. Removing 1 cup of that mix and putting it back in the tea pitcher makes there be a 50-50 mix in both pitchers.

Increasing the quantity in each pitcher does nothing to change the fact that the mixes end up in the same ratio:

tea:lemonade in Pitcher 1 = lemonade:tea in Pitcher 2

6 0

3 years ago

What type of triangle do i have if the angles are:15, 10,155

xenn [34]

Obtuse, accute, obtuse, acute, A.

6 0

4 years ago

Diameter is 22.5m. Calculate the area (round your answer to 2 decimal places), Use 3.14 for Pi

alexgriva [62]

Answer:

397.61m

Step-by-step explanation:

A = 1

4πd^2 = 1

4 x π x 22.52 = 397.60782

4 0

3 years ago