Find an equation of the sphere that passes through the origin and whose center is (â2,2,3). be sure that your formula is monic.

The angular speed of the wheel is 3960 rad/min and the revolutions per minute is 630 rpm.

The velocity of the truck is 60 mph. We need to convert this speed to inches per minute.

1 mile = 63360 in, 1 hour = 60 minutes

Hence:

60 mph = (60 mile * 63360 in/mi) / (1 hr * 60 min/hr) = 63360 in/min

The diameter = 32 in, hence radius = 32/2 = 16 in

The angular speed = 63360 in/min ÷ 16 in = 3960 rad/min

Revolution per minute = 3960 rad/min ÷ 2π = 630 rpm

Hence the angular speed of the wheel is 3960 rad/min and the revolutions per minute is 630 rpm.

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The wheels make approximately  52.55  revolutions per minute.

To find the angular speed of the wheels in radians per minute, we first need to find the linear speed of a point on the edge of the wheel.

The formula to calculate the linear speed (v) is given by:

[tex]\[ v = r \times \omega \][/tex]

Where:

-  v  is the linear speed,

-  r  is the radius of the wheel, and

- [tex]\( \omega \)[/tex] is the angular speed in radians per second.

Given that the diameter of the wheels is 32 inches, the radius (r ) is half of the diameter, so [tex]\( r = \frac{32}{2} = 16 \)[/tex] inches.

We are given the speed of the truck,  v = 60  mi/h. To convert this to inches per minute, we need to convert miles to inches and hours to minutes:

[tex]\[ 60 \text{ miles/h} = 60 \times 5280 \text{ inches/60 minutes} = 5280 \text{ inches/minute} \][/tex]

Now, we can rearrange the formula to solve for [tex]\( \omega \):[/tex]

[tex]\[ \omega = \frac{v}{r} \][/tex]

Substituting the known values:

[tex]\[ \omega = \frac{5280 \text{ inches/minute}}{16 \text{ inches}} \]\[ \omega = 330 \text{ radians/minute} \][/tex]

So, the angular speed of the wheels is 330 radians per minute.

Now, to find the number of revolutions per minute (rpm), we need to convert the angular speed from radians per minute to revolutions per minute. Since [tex]\( 2\pi \)[/tex] radians is equal to one revolution, we have:

[tex]\[ \text{Revolutions per minute (rpm)} = \frac{\omega}{2\pi} \][/tex]

Substituting the value of [tex]\( \omega \):[/tex]

[tex]\[ \text{rpm} = \frac{330}{2\pi} \]\[ \text{rpm} \approx \frac{330}{6.28} \approx 52.55 \][/tex]

So, the wheels make approximately  52.55  revolutions per minute.

You would need approximately 75.7 liters of lemonade for your event. This is calculated by using the conversion factor of 3.78541 liters per gallon.

To calculate how many liters of lemonade you need for 20 gallons, we first need to know the conversion rate. There are about 3.78541 liters in 1 gallon. Thus, if you need 20 gallons, we can use multiplication to find this.

So, if we multiply 20 (gallons) by 3.78541 (liters per gallon), the result is approximately 75.7 liters. You would therefore need about 75.7 liters of lemonade for your event. This is a simple application of conversion factors, where the given quantity (gallons) is multiplied by a conversion factor (liters per gallon) to obtain the desired quantity (liters).

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The 24-inch pizza is a better deal because it costs slightly less per square inch compared to the 12-inch pizza.

To determine which pizza is a better deal, we need to compare their prices per square inch. First, let's find the area of the 12-inch pizza. The formula to find the area of a square is side length squared, so the area of the 12-inch pizza is 12 x 12 = 144 square inches. Now, we can divide the price of the 12-inch pizza by its area to find the price per square inch: $3.95 / 144 = $0.0274 per square inch.

Next, let's find the area of the 24-inch pizza. The area of the 24-inch pizza is 24 x 24 = 576 square inches. Now, we can divide the price of the 24-inch pizza by its area to find the price per square inch: $14.95 / 576 = $0.0259 per square inch.

Comparing the prices per square inch, we can see that the 24-inch pizza is a better deal, as it costs slightly less per square inch compared to the 12-inch pizza.

Answer:

She need to put on 6 underpants

Step-by-step explanation:

She has learned from experience that she stays warm about 20 minutes for every undershirt she wears.

Time warmed by 1 undershirt = 20 minutes.

Total time she wants to stay out = 120 minutes

Number of underpants required [tex]=\frac{120}{20}=6\texttt{ underpants}[/tex]

So she need to put on 6 underpants

Final answer:

To find the indifference curve passing through 32 apples and 8 bananas, we can set up a system of equations and solve for the relationship between apples and bananas. The indifference curve will also pass through the point where Charlie consumes 4 apples and 2 bananas.

Explanation:

An indifference curve represents a set of choices that have the same level of utility. In this case, Charlie's utility function is u(xa, xb)=xaxb. To find the indifference curve passing through 32 apples and 8 bananas, we can set up a system of equations. If we plug in these points into the utility function, we get 32a*8b=4a*xb. Solving for b, we find that b=1/2a. This means that for every amount of apples, Charlie wants to consume half as many bananas to maintain the same level of utility. Therefore, the indifference curve passing through 32 apples and 8 bananas will also pass through the point where he consumes 4 apples and 2 bananas.

do order of operations:

60 / 5*(7-5)=

 do parenthesis first: 7-5=2

60 / 5*2 =

 now do division: 60/5 =12

12*2 =

now multiply: 12 *2 = 24

answer is 24

divide 279 by 3

279 / 3 = 93

93-2 = 91

first number = 91

N +2 = 91 +2 = 93

N+4 = 91 +4 = 95

91 + 93 +95 =279

The implicit equation for the plane passing through the point (5,0,5) that is perpendicular to the line l(t)=⟨3,−1−5t,−1−2t⟩ is 3x - 5y - 2z = 20.

To find the equation of the plane passing through the point (5,0,5) and perpendicular to the line l(t)=⟨3,−1−5t,−1−2t⟩, we need to find the normal vector of the plane. The normal vector is the direction vector of the line, which is (3, -5, -2). Using the formula for the equation of a plane in standard form, which is ax + by + cz = d, and substituting the coordinates of the point and the normal vector, we get 3x - 5y - 2z = 20

as the implicit equation for the plane.

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Number of ways it can happen is 5832.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

We have eighteen-sided die is rolled three times.

When the die is first rolled, there are 18 possibilities of outcomes.

Again when the die is rolled, again there are 18 possibilities.

In the third rolling also, there are 18 possibilities.

Each die has 18 possibilities of numbers for a number for the other die.

Total number of sets = 18 × 18 × 18

                                   = 5832

Hence the total number of ways that the numbers can be formed is 5832.

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A traditional barbershop quartet has 8 legs since it consists of four people. Female quartets exist alongside male quartets, with popular female groups like The Sweet Adelines International and The Chordettes. The scenario of a quartet having 16 legs is hypothetical and humorous, similar to a comedic tale from 'Only Fools and Horses' regarding a constantly replaced broom.

The question "When does a barbershop quartet have 16 legs?" seems to contain a riddle rather than a direct inquiry into the makeup of a barbershop quartet. Traditionally, a barbershop quartet comprises four individuals, each with two legs, totaling eight legs. This would shift to 16 legs if the quartet consisted of eight people. However, if we're speaking about the traditional four-person quartet, they would only have 16 legs if each member had four legs, which is not characteristic of human anatomy.

It is important to clarify that despite the common misconception that barbershop quartets are exclusively male, there are female quartets as well, such as those associated with The Sweet Adelines International or popular groups like The Chordettes. Neither of these situations normally results in 16 legs unless for comedic or hypothetical scenarios, akin to the tale shared in the comedy "Only Fools and Horses" where Trigger's broom maintains the same identity despite numerous replacements of its parts.

Examples in Pop Culture and Misconceptions

A blend of humor and play on the concept of identity similar to the aforestated barbershop quartet conundrum is seen in the television sitcom "Only Fools and Horses," where a character humorously remarks on the extensive replacement of broom parts, posing a philosophical question of identity and perception.

The solution to the given inequality problem is;

q < 56

We are given the equation;

q + 12 - 2(q - 22) > 0

Step 1; Using distributive property, distribute 6 to the numbers inside the bracket to get;

q + 12 - 2q + 44 > 0

Step 2; Combining similar terms on the left side and simplifying gives us;

56 - q > 0

Step 3; Using addition property of equality, add q to both sides;

56 - q + q > 0 + q

q < 56

Thus, the final solution is q < 56

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