A snake is slithering toward you at 1.5 m/s. If you start walking when it is 5.0 m away, how fast must you go in order that the snake not overtake you when you have gone 40.0 m?

Final answer:

To show that the differential equation M(x) + N(y)dy/dx=0 is separable, we must demonstrate that M and N can be expressed as functions of x and y respectively, without overlap, leading to an equation of the form f(y)dy/dx + g(x) = 0. Explanation of separable equations through specific cases and integration methods.

Explanation:

Separable equations involve the relationship M(x) + N(y)dy/dx = 0. To show this, you can use specific cases where M and N can be separated into functions of only x or y.

For example, if M/N can be expressed as f(y)/g(x), then the separable equation becomes f(y)(dy/dx) + g(x) = 0.

Integrating M(x, y) with respect to x can lead to finding a function f(x, y) that satisfies the given differential relationship.

Answer:

C just did this

Step-by-step explanation:

Answer:

30 feet, 24 feet, 24 feet

Step-by-step explanation:

A kite is a quadrilateral with two pairs of congruent adjacent sides.

One of the longer sides measures 30 feet. According to the definition, the kite has two sides of length 30 feet. Let x feet be the length of another side.

The perimeter of the kite is

[tex]2\cdot 30+2\cdot x\ feet[/tex]

Since the kite has a perimeter of 108 feet, we have

[tex]2\cdot 30+2\cdot x=108\\ \\60+2x=108\\ \\2x=108-60\\ \\2x=48\\ \\x=24[/tex]

The length of two another sides is 24 feet. The kite has two sides of 30 feet and two sides of 24 feet.

Answer: Hello mate!

The kite has two equal-length long sides and two equal-length shorter sides. We also know that the perimeter is the addition of the four sides, where we have two long sides, L, and two short sides, S.

Then 2S + 2L = 108ft

S + L = 54 ft

if L = 30 feet

S + 30 ft = 54ft

S = 54ft - 30 ft = 24ft

Then the other long side also has 30ft length, and the two shorter sides have 24ft length.

Answer: The number of successful throw made in that season in total is 30

Step-by-step explanation:

On average the player successfully made 5 out of 6 free throws .

Thus if number of free throws is x then number of successful throw will be [tex]\frac{5}{6}\times x[/tex] .

The basketball player attempted 36 free trials in a season .

Here x=36

Therefore No of successful throws [tex]=\frac{5}{6}\times 36=30[/tex]

Thus the number of successful throw made in that season in total is 30

Answer:

235 workers

Step-by-step explanation:

Factory operates on a standard work week shift for 5 days = 8 hours per day

In one week working hours are = 8 × 5 = 40 hours.

Company has an order for 7,500 new cars to be delivered in one week.

One car requires time to be fitted with a new hood ornament that requires to install = 1 hour and 15 minutes ( 1.25 hours )

In 40 hours (one week) cars will install with one worker = [tex]\frac{40}{1.25}[/tex] = 32 cars

To fulfill the order of 7,500 cars, Company needs workers = 7,500 ÷ 32 = 234.375 ≈ 235 workers.

235 workers must be assigned this job to meet the deadline.

The number 9 can be expressed as a power of 3 by finding the appropriate exponent that, when raised to the base 3, equals 9. This exponent is 2, making 9 written as a power of 3 to be 3².

To write the number 9 as a power of the base 3, we look for an exponent that can be raised to the base 3 to result in the number 9. This is achieved by recognizing that 3 squared (3²) equals 9. So, 9 expressed as a power of 3 is 3².

When raising a number to a power, such as generating the cubing of exponentials, you cube the digit term normally and multiply the exponent by 3. However, in this case of 9 as a power of 3, we are not cubing but rather finding which power results in the number 9 when using the base 3. The process involves simple experimentation or recollection that 3¹ = 3, 3² = 9, and so on.

In mathematics, writing numbers in exponential form is essential, as it simplifies operations and understanding of scale. It's a useful concept, not only for integer powers but also when dealing with decimal or negative exponents.

Answer:

the answer is 16

The expression for adding 8 to the sum of 23 and 10 is (23 + 10) + 8. This is due to the commutative property of addition, which states that the order in which you add numbers does not change the result.

The question asks for an expression to calculate adding 8 to the sum of 23 and 10. The first step is to add 23 and 10 together, which equals 33. Then add 8 to that sum. You can represent this process mathematically as (23 + 10) + 8. So if you need to write an expression for adding 8 to the sum of 23 and 10, it would be (23 + 10) + 8. Remember, adding numbers together (a process called addition) is commutative, meaning you can add numbers in any order and still get the same result.

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Answer:

[tex]p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}[/tex]

Step-by-step explanation:

Let premium p for age of a , (p,a)

# An insurance company charges a 35-year old non-smoker an annual premium of $118 for a $100,000 term life insurance policy.

(35,118)

# An insurance company charges a 45-year old non-smoker an annual premium of $218 for a $100,000 term life insurance policy.

(45,218)

# An insurance company charges a 55-year old non-smoker an annual premium of $563 for a $100,000 term life insurance policy.

(55,563)

Let quadratic model be p=Aa²+Ba+C

Substitute the points into equation

[tex]118=35^2A+35B+C[/tex]

[tex]118=1225A+35B+C[/tex] -------------(1)

[tex]218=45^2A+45B+C[/tex]

[tex]218=2025A+45B+C[/tex] -------------(2)

[tex]563=55^2A+55B+C[/tex]

[tex]563=3025A+55B+C[/tex] -------------(3)

Solve system of equation and find out A, B and C using calculator.

[tex]A=\dfrac{49}{40},B=-88,C=\dfrac{13579}{8}[/tex]

Quadratic model:

[tex]p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}[/tex]

To determine how long Mrs. Liu can drive before her car runs out of gas, one needs to analyze the slope of the graph that shows the rate of gasoline consumption, know the total capacity of the tank, and perform a calculation to estimate the remaining driving time assuming constant consumption.

The question asks to determine how long Mrs. Liu can drive her car before the gas tank is empty, based on the graph showing the amount of gas left as she drives at a steady speed for 2 hours. To answer this, we need to find the rate at which the gas is being used and then use it to estimate the time until the tank reaches empty.

To find the rate of gasoline consumption, you would typically look at the slope of the graph, which shows the decrease in gas over time. If the graph shows a linear decrease, the slope will give you the rate (e.g., gallons per hour). Suppose the graph indicates that the tank started full and decreased to half over 2 hours. In that case, the consumption rate is half the tank's capacity divided by 2 hours. If you know the total capacity of the tank, you can calculate the driving time until empty.

However, since the actual graph and numerical data are not provided here, we can only guide you through the process hypothetically. With the actual graph, you would:

Remember, this calculation assumes a constant rate of consumption, which may not be accurate in real-life scenarios due to variations in driving conditions and car performances.

To find out the number of toothpicks required to form 100 adjacent squares, one can use the formula 4 + 3(n - 1), resulting in 301 toothpicks.

To determine how many toothpicks are required to form 100 adjacent squares, we must first understand the pattern established by the initial set of squares. When forming three adjacent squares, 10 toothpicks are used. This is because the first square requires 4 toothpicks, and each subsequent square shares a side with the previous square, thus requiring only 3 additional toothpicks for each new square.

For n adjacent squares, the number of toothpicks required can be calculated with the formula: 4 + 3(n - 1), since the first square uses 4 toothpicks and each additional square uses 3 more toothpicks.

Now, let's apply this to 100 adjacent squares:

Therefore, 301 toothpicks are required to form 100 adjacent squares.

The relationship is that for each square, we need 4 toothpicks (1 new side for each square). So, for 100 adjacent squares, we require 400 toothpicks.

Let's analyze the pattern to determine the relationship between the number of squares and the toothpicks required. Consider the formation of 3 adjacent squares:

For the first square, we need 4 sides (4 toothpicks).

For the second square, we have 3 shared sides with the first square and 1 new side (3 + 1 = 4 toothpicks).

For the third square, we have 3 shared sides with the second square and 1 new side (3 + 1 = 4 toothpicks).

So, for 3 adjacent squares, we need a total of 12 toothpicks (4 + 4 + 4).

Now, let's generalize this pattern. For each additional square beyond the third, we are adding 4 toothpicks (1 new side for each square). Therefore, the toothpicks required to form n adjacent squares can be expressed as 4n.

For 100 adjacent squares:

Toothpicks=4×100=400

Hence, 400 toothpicks are required to form 100 adjacent squares.

The question probable may be:

To form 3 adjacent squares, 10 toothpicks are required. How many toothpicks are required to form 100 adjacent squares?

The number -9 is a rational number as it can be written as a fraction of two integers, specifically -9/1.

The number -9 is a rational number because it can be expressed as a fraction of two integers: -9/1 where -9 is the numerator and 1 is the denominator. By definition, rational numbers include all integers, as each integer can be written as a fraction with a denominator of 1. This is different from irrational numbers, which cannot be written as a simple fraction. An example of an irrational number is the square root of 2, which cannot be precisely expressed as a fraction of two integers.