Factor −1/2−1/2 out of −1/2x+6.

The area of the plane 5x + 4y + z = 20 in the first octant is calculated using a double integral over the xy-plane. The limits are defined by the intersection of x and y with the xy-plane when z=0, and the solution is approximately 66.67 square units.

To solve for the area of the part of the plane that lies in the first octant, we first need to isolate z in our equation. z = 20 - 5x - 4y. The limits for x and y in the first octant are from 0 to positive infinity, but in this case, they will be limited by the plane defined by z = 0 (the xy-plane). x and y will range from 0 to the point where they meet the plane. Therefore, we set z = 0 and solve for both x and y, giving us x = 4 and y = 5.

Now in order to calculate the area, we must interpret this integral on the xyz-plane as a double integral on the xy-plane. Now, we integrate over the region in the xy-plane that x and y range over:

Area = ∫ from 0 to 4 ∫ from 0 to (5 - 1.25x) (20 - 5x - 4y) dy dx

And that is the integral you need to calculate to find the area. Attempting to calculate this integral results in the area ≈ 66.67 square units.

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Answer:

The simplest form of the ratio is: [tex]\dfrac{865}{2678}[/tex]

Step-by-step explanation:

We are given information about the buffalo in  New york in the year 2015 as:

Number of arrests= 8,625

Number of robberies=2678

Number of assaults= 865

Number of murders= 20

The population of Buffalo is 258,959.

he ratio of the number of assaults to the number of robberies in simplest form is given by:

[tex]\dfrac{865}{2678}[/tex]

As the number in the numerator and the denominator do not have a common factor. hence the simplest form of the ratio is:

[tex]\dfrac{865}{2678}[/tex]

To solve the system of linear equations, use the method of substitution by solving for one variable and substituting it into the other equation.

To solve the system of linear equations:

6x + 20y = -62

3x - 9y = -12

We can use the method of substitution:

After finding the value of y, substitute it back into the first equation to solve for x. The solution is: x = -2, y = 4.

Answer: Option (A) is the correct answer.

Explanation:

Kinetic energy is defined as the energy possessed by an object because of it's motion.

Whereas average kinetic energy is the sum of kinetic energy of all the particles of a substance.

Therefore, when water freezes then there will decrease in kinetic energy of particles and thus, particles will gain potential energy.

Hence, we can conclude that when water freezes average kinetic energy of water molecules decreases as the water releases energy to its surroundings.

The average "kinetic-energy" of water molecules decreases as water freezes, because water releases energy to its surroundings, option (a) is correct.

When water freezes, it undergoes a phase transition from a liquid to a solid state. During this process, water molecules lose energy and slow down, causing decrease in their average kinetic energy.

As temperature decreases, water molecules arrange themselves into a more structured pattern due to the formation of hydrogen bonds.

In order for water to freeze, it needs to release energy to its surroundings, in form of heat. This release of energy is necessary to facilitate transformation from a higher-energy liquid state to lower-energy solid state. As a result, average kinetic energy of water molecules decreases as water freezes.

Therefore, the correct option is (a).

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Answer:

[tex]a_n=5a_{n-1}[/tex]

Step-by-step explanation:

Given fifth term of a geometric sequence is 781.25.

[tex]a_5= 781.25[/tex].

Also, each previous term is 1/5 of the value of the current term.

Therefore, common ratio would be 5.

But we just need to find the recursive formula .

Recursive formula of a geometric sequence is given by

[tex]a_n=ra_{n-1}[/tex]

Plugging value of r in above formula, we get

[tex]a_n=5a_{n-1}[/tex]

Answer: c

Step-by-step explanation:

buddy beneath me is blabbin to much

Final answer:

To answer the question, we need to convert the mass from pounds to kilograms, use the ideal gas law equation to calculate the pressure in atmospheres, and then convert atmospheres to psig.

Explanation:

In this question, we are given that 100 pounds of CO2 is contained in a 10.0-ft3 tank and the safety limit of the tank is 1600 psig. To convert pounds to kilograms, we can use the conversion factor of 1 pound = 0.4536 kilograms. So, 100 pounds of CO2 is equal to 45.36 kilograms. Now, we can use the ideal gas law equation PV = nRT to find the pressure in bar. Rearranging the equation, we have P = (nRT) / V. Plugging in the values given, n = mass / molar mass, R = 0.0821 atm L / mol K, T = 273 + degrees Celsius, and V = 10.0 ft3 converted to liters, we can calculate the pressure in atmospheres. Finally, we can convert atmospheres to psig by multiplying by 14.7.

Using the L'Hospital's Rule, we differentiate the numerator and denominator of the given function separately, substitute these derivatives back into the function, and then attempt to evaluate the limit as x approaches 0.

To find the limit of the given function as x approaches 0, we will use the L'Hospital's Rule since the function gets an indeterminate form 0/0 as x approaches 0. L'Hospital's Rule states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives.

First, we differentiate the numerator and the denominator separately. For the numerator, the derivative of 2x is 2, and the derivative of sin(2x) is 2cos(2x). So the derivative of the numerator is 2 - 2cos(2x).

For the denominator, the derivative of 2x is 2, and the derivative of tan(2x) is 2sec²(2x), since the derivative of tan(x) is sec²(x) and because of the chain rule, we multiply by 2. So, the derivative of the denominator is 2 - 2sec²(2x).

Now, we substitute these derivatives back into the original function and take the limit as x approaches 0: lim  x→0  (2 - 2cos(2x)) / (2 - 2sec²(2x)).

After further simplifying the above expression, you can evaluate the limit.

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The limit is 0.

We need to find the limit:

lim x→0 (2x − sin(2x)) / (2x − tan(2x))

Both the numerator and the denominator approach 0 as x approaches 0, which means it is in the indeterminate form 0/0. This suggests that we can use L'Hôpital's Rule.

According to L'Hôpital's Rule, we can differentiate the numerator and the denominator and then take the limit of the resulting fraction.

First, let's compute the derivative of the numerator:

Next, let's compute the derivative of the denominator:

Now, we apply L'Hôpital's Rule:

lim x→0 (2 - 2cos(2x)) / (2 - 2sec²(2x))

As x approaches 0, cos(2x) approaches 1 and sec²(2x) also approaches 1, so:

lim x→0 (2 - 2(1)) / (2 - 2(1)) = 0 / 0

This fraction again gives an indeterminate form. Applying L'Hôpital's Rule a second time will be helpful. We need to differentiate the numerator and the denominator again:

Second derivative of the numerator: d/dx [2 - 2cos(2x)] = 4sin(2x)

Second derivative of the denominator: d/dx [2 - 2sec²(2x)] = -8sec²(2x)tan(2x)

Applying L'Hôpital's Rule once more, we get:

lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x))

Substitute x = 0:

lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x)) = 0

Therefore, the limit is 0.

Answer:

Speed of car on the way back = 30 mph

Step-by-step explanation:

Speed of car on the way = 45 mph = 45 x 1.6 = 72 kmph = 20 m/s

Time taken to cross bridge on the way = 40 seconds

Length of bridge = Speed of car on the way x Time taken on the way = 20 x 40 = 800 m

Time taken to cross bridge on the way back = 30 seconds

Length of bridge = Speed of car on the way back x Time taken on the way back

800 = Speed of car on the way back x 30

Speed of car on the way back = 26.67 m/s =96 kmph = 30 mph

Speed of car on the way back = 30 mph

Answer: 140 miles per hour

Step-by-step explanation:

The question is asking us to find out how many players are left-handed from a total of 85 players, given that 80% of the players are left-handed. For this, we perform a simple calculation by finding 80% of 85, which equals 68. So, there are 68 left-handed players in the league.

The subject of this question falls under the category of Mathematics, more specifically, it is about percentage calculations. In order to figure out how many left-handed players there are out of the total 85 players, we need to remember that percent means 'per 100'. So, 80% translates to 80 out of 100. Therefore, to find out how many are left-handed, we need to take 80% of 85.

The calculation is as follows:

Left-handed players = 85 * (80/100)

= 85 * 0.80

= 68

So, there are 68 left-handed players in the local little league.

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There are 210 different ways for the fruits can be consumed.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A student have 3 mangos, 2 papayas, and 2 kiwi fruits.

And, The student eats one piece of fruit each day, and only the type of fruit matters.

Now,

Total number of fruits = 3 + 2 + 2

                                  = 7

And, There are 3 mangos, 2 papayas, and 2 kiwi fruits.

So, Number of ways for the fruits can be consumed, is calculated as;

= 7! / 3! 2! 2!

= 7 x 6 x 5 x 4 x 3! / 3! 2! 2

= 7 x 6 x 5 x 4 / 2 x 1 x 2 x 1

= 7 x 6 x 5

= 210

Thus, There are 210 different ways for the fruits can be consumed.

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