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3 years ago

Solve. log 3 + log x - log(x + 1) = log 2 Please please help

Mathematics

1 answer:

weqwewe [10]3 years ago

8 0

Answer:

x = 2

Step-by-step explanation:

Given the equation as;

log 3 + log x - log(x + 1) = log 2

collect like terms

log x - log(x + 1) = log 2-1og 3

Re-write the equation by applying laws of logarithms in that when you subtract logs you divide the numbers/terms. This will give

log [ x / x+1 ] = log [2/3]

Cancel log on both sides to remain with;

x/ x+1 = 2/3

Apply cross-product

3{x} = 2{x+1}

3x = 2x + 2

3x-2x = 2

x = 2

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A cylinder and a sphere have the same radius and volume. The height of the cylinder is 12 cm. What is the volume of the sphere r

Sedaia [141]

Answer:

3054

Step-by-step explanation:

The formula for cylinder volume is

V1 = π * r^2 *h

while formula for sphere volume is

V2= 4/3 * π * r^3

Since the height of the cylinder is 12, we can substitute h the equation into

V1 = π * r^2 *12

The volume and radius of the cylinder are the same as the sphere, so we can combine both equations to find r.

V1= V2

π * r^2 *12 = 4/3 * π * r^3

12 = 4/3 * r

r= 12*3/4

r=9

After we find the radius, we can find the sphere volume

V2= 4/3 * π * r^3

V2= 4/3 * π * 9^3

V2= 3053.62 = 3054

7 0

3 years ago

Factor the expression completely. x^4-9x^2+14 x 4 −9x 2 +14

Kobotan [32]

Answer: 3x^2(5x^2-6)+14
(WORK SHOWN BELOW)

8 0

2 years ago

Find the coordinates of the points of intersection of the parabola y=x^2+3x-4 and the line y=2x+2

lana [24]

You can set the y values equal to each other and solve the system:

x^2+3x-4=2x+2
x^2+x-6=0
(x+3)(x-2)=0
x=-3,2

So, these are the x values of the intersection. To get the y values, you can just plug them back into either formula:

y=2(-3)+2
y=-4

y2(2)+2
y=6

So the coordinates are (-3,-4) and 2,6).

6 0

3 years ago

A community theater uses the function p (d) = (-4d+40) (d−40) to model the profit (in dollars) expected in a weekend when the ti

fomenos

The theater make the maximum profit at d = $25. Then the maximum profit of the theatre is $ 900.

<h3>What is differentiation?</h3>

The rate of change of a function with respect to the variable is called differentiation. It may be increasing or decreasing.

A community theater uses the function P(d) = (− 4d + 40) (d − 40) to model the profit (in dollars) expected on a weekend when the tickets to a comedy show are priced at d dollars each.

Then the maximum profit of the theatre will be

The function is P(d) = (− 4d + 40) (d − 40)

Differentiate the function with respect to d and put it equal to zero for maximum or minimum profit.

$\begin{aligned} \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= 0\\\\\dfrac{\mathrm{d} }{\mathrm{d} d}(- 4d + 40) (d - 40) &= 0\\\\(-4d+40) -4 (d-40) &= 0\\\\-8d + 200 &= 0\\\\d &= 25 \end{aligned}$

Then the checking for maximum or minimum, again differentiate, we have

$\begin{aligned} \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= \dfrac{\mathrm{d} }{\mathrm{d} d}(- 4d + 40) (d - 40) \\\\\dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= \dfrac{\mathrm{d} }{\mathrm{d} d}(-8d + 200) \\\\\dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= -8\\\\ \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) & < 0\end{aligned}$

The value is less than zero hence maximum value will occur at d = 25.

Then maximum profit will be

P(d) = (− 4×25 + 40) (25 − 40)

P(d) = (− 100 + 40) (−15)

P(d) = (− 60) (− 15)

P(d) = $ 900

More about the differentiation link is given below.

brainly.com/question/24062595

#SPJ1

7 0

2 years ago

What is the cost of the following?

Savatey [412]

$1.\\
6\ cans\\
3\ cans\ cost\ 1\$\\
1\ can\ cost\ \frac{1}{3}\$\\
6*\frac{1}{3}\$=\frac{6}{3}\$=2\$\\\\ \textbf{6\ cans\ cost\ 2\$}\\\\2.\\ 3\ boxes\ of\ cereal\\1\ box\ costs\ 0,99\$\\
3*0,99\$=2,97\$\\\\
\textbf{3\ boxes\ of\ cereal\ cost\ 2,97\$.}\\\\
3.\\
1\ loaf\ of\ bread\ cost\ 0,45\$\\
1*0,45=0,45\$\\\\
\textbf{One\ loaf\ of\ bread\ costs\ 0,45\$}\\\\
4.\\
6\ lbs\\
2\ lbs\ cost\ 0,8\$\\
1\ lbs\ costs\ 0,4\$\\
6*0,4\$=2,4\$\\\\
\textbf{6\ lbs\ of\ aplles\ cost\ 2,4\$}$ $5.\\
1\ box\ of\ jello\\
2\ boxes\ of\ jello\ cost\ 0,54\$\\
1\ box\ costs\ \frac{0,54\$}{2}=0,27\$\\\\
\textbf{1\ box\ of\ jello\ costs\ 0,27\$.}$

5 0

3 years ago