If a skier is going down a mountain with an angle of depression at 60 degrees from the top of the mountain which is at 10000 ft from ground level. If they want to beat the person who is in first place who went down the slope in exactly 3 minutes, how fast (in terms of nearest miles per hour) must they go (at least) to beat the person in first place?
Please answer with written explanation asap!

The solution of the given differential equation by using variable separable is [tex]y=\frac{x^2c}{2}-2[/tex]

An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a particular moment is determined by the function's derivatives. It is mostly employed in disciplines like biology, engineering, and physics. The study of solutions that satisfy the equations and the characteristics of the solutions is the main goal of the differential equation.

The rules to solve differential equations using variables separable,

1) [tex]\frac{dy}{dx}=f(x)/f(y)[/tex]

2) separate terms with the same variable

f(y)dy=f(x)dx

3) Take integration on both sides

4) solve integration by using a suitable method

5) Then get the Solution of the differential equation.

The given differential equation is-

[tex]\frac{dy}{dx}=\frac{2y+4}{x}\\\\\frac{dy}{2y+4}=\frac{dx}{x}\\\\\int\frac{dy}{2y+4}=\int\frac{dx}{x}\\\\\frac{log(2y+4)}{2}=logx+logc\\log(2y+4)=2logxc\\2y+4=x^2c\\2y=x^2c-4\\y=\frac{x^2c}{2}-2[/tex]

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Answer:

AAS

Step-by-step explanation:

They share the same side, and the 2 angles are the same as well and match

Perimeter of the figure is 56 units.

Area of figure is 100sq. units²

Cost to sold the yard is $299

For edging, total cost is $82.8

Perimeter and area are two important measurements used in geometry to describe the size and shape of two-dimensional figures.

Perimeter is the measurement of the distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

Area is the measurement of the space inside a two-dimensional shape. It is the amount of surface that the shape covers. For example, the area of a rectangle can be calculated by multiplying the length of the rectangle by its width.

Perimeter of the figure=sum of all sides of the figure

=10+4+2+12+6+6+2+4+6+4=56 units.

Area of figure=10×4+6×6+4×6

=40+36+24

=100sq. units²

Cost to sold the yard=area× cost per square foot

=100×2.99

=$299

Given: edging  costs $8.87 per 6 foot piece

For edging, total cost =total perimeter/no.of foot piece×$8.87

=(56/6)×8.87

=496.72/6

=$82.78≈$82.8

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Answer:

The divisors of 20 are 1, 2, 4, 5, 10, and 20. A 6-sided dice has the numbers 1 to 6 on its faces. The probability of rolling a number that is a divisor of 20 is the number of favorable outcomes divided by the number of possible outcomes. There are four favorable outcomes (1, 2, 4, and 5) and six possible outcomes (1 to 6). Therefore, the probability is 4/6 or 2/3 or about 0.67.

The Volume of the pyramid.

Volume = 288.67 m³

As the volume of the pyramid is the amount of space enclosed inside the pyramid, the formula to find the volume of a square pyramid is given as;

Volume = (1/3) × base area × height.

Where: Base area (B) = s²

Where; s = length of the square pyramid side

And, Height (h) = perpendicular height to the base.

Substituting the given values in the formula we get;

Volume = (1/3) × s² × h

Given, s = 8.5m and h = 12m

Therefore, Volume = (1/3) × 8.5² × 12

= (1/3) × 72.25 × 12

= 288.67 m³

Thus, the volume of the given square pyramid is 288.67 m³, to the nearest hundredth of a cubic meter.

The volume of any pyramid is a measure of the total amount of space enclosed within the pyramid. If you have a pyramid of a specific shape and size, you can calculate its volume by using an appropriate formula. In this case, we have been given the length of the square pyramid side (s) and the perpendicular height (h) of the pyramid to the base. We can use the formula to calculate the volume of the pyramid.

The formula is Volume = (1/3) × base area × height.

For a square pyramid, the base area is the area of the square that forms the base. Since all four sides of the square are of equal length, the area is given as the square of the length of one of the sides. Thus, Base area (B) = s².

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Answer:

Point-slope form:

[tex]y - 2 = - 4(x + 1)[/tex]

Slope-intercept form:

[tex]y = - 4x - 2[/tex]

Standard form:

[tex]4x + y = - 2[/tex]

Step-by-step explanation:

[tex]y - 2 = - 4(x + 1)[/tex]

[tex]y - 2 = - 4x - 4[/tex]

[tex]y = - 4x - 2[/tex]

[tex]4x + y = - 2[/tex]

Aryabhata, the famous Indian mathematician discovered 0.

Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.

The concept of zero was first developed by ancient Indian mathematicians as early as the 5th or 6th century CE. However, the actual symbol for zero (a small circle) was invented by the Indian astronomer and mathematician Brahmagupta in 628 CE.

Aryabhatta, the famous Indian mathematician discovered 'zero'. Grutsamad discovered the process of writing zeroes after figures.

Hence, Aryabhata, the famous Indian mathematician discovered 0.

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We can be reasonably confident that our estimate of 67% is within 2.5% of the true proportion.

What is percentage?

A percentage is a way to describe a part of a whole. such as the fraction  1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

To determine if a sample size of 1,400 is adequate for estimating a proportion of 67%, we need to calculate the margin of error and compare it to the given tolerance level of 0.025.

We can use the following formula to calculate the margin of error:

E = z x √(p x (1-p)/n)

where:

Plugging in the values, we get:

E = 1.96 x √(0.67 x (1-0.67)/1400) ≈ 0.025

So, the margin of error is approximately 0.025. This means that we can expect the true proportion to be within 0.025 of the estimated proportion with 95% confidence.

Since the calculated margin of error is equal to the desired tolerance level, we can conclude that a sample size of 1,400 is adequate for estimating a proportion of 67% with the given level of confidence and tolerance. Therefore, we can be reasonably confident that our estimate of 67% is within 2.5% of the true proportion.

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To serve 50 people, the minimum square footage needed would be 750 square feet.

Let us analyze the given question and solve the problem given. The problem is asking about the minimum square footage of the multi-story building that is required to open a small restaurant on the lowest floor. The building is already zoned for mixed use.

John wants to open a small, by-reservation-only restaurant on the lowest floor. He needs to calculate the minimum square footage he needs to serve 50 people. Let's calculate the minimum square footage that John needs to open the restaurant. If local code requires 15 square feet per person, then 15 x 50 = 750 square feet are needed for 50 people. In other words, John needs at least 750 square feet of space to serve 50 people at his restaurant.

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Step-by-step explanation:

4.25 inches  *   16 miles / 1 inch  = 68 miles

It will take 5 minutes to print a batch of newspapers if 20 printers are used.

What is proportionality?

Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.

We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:

m = k/n

where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:

m = 100/n

To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:

m = 100/20 = 5

So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.

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Answer:

L=2x-3

Step-by-step explanation:

A =L×W

Given,

A=6x²-9x

W=3x

Substituting into the main equation

6x²-9x=L×(3x)

3x(2x-3)=L×(3x)

divide both sides by 3x

2x-3=L

L=2x-3

The formula for the number of bacteria at time t is given by N = 10,000e^(0.0173t).

The formula for the number of bacteria at time t can be found using the exponential growth formula. The formula for exponential growth is given by;N = N0ertWhere;N is the number of bacteria after t minutes.N0 is the initial number of bacteria.r is the growth rate.t is the time interval.

To find the formula for the number of bacteria at time t, substitute the given values into the exponential growth formula.N0 = 10,000r = ln2/40 = 0.0173 (since the number of bacteria doubles every 40 minutes, the growth rate is equal to the natural log of 2 divided by 40.)t = t minutesN = 10,000e^(0.0173t)

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The value of k that makes the three points lie on the same line is -8.

To determine the value of k such that the given points lie on the same line, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope of the line, and b is the y-intercept.

First, we can find the slope of the line passing through the two points (0, -2) and (10, -7):

m = (y2 - y1) / (x2 - x1)

m = (-7 - (-2)) / (10 - 0)

m = -5 / 10

m = -1/2

Now, we can use the slope-intercept form with the point (0, -2) to find the value of b:

-2 = (-1/2)(0) + b

b = -2

So the equation of the line passing through the two points (0, -2) and (10, -7) is:

y = (-1/2)x - 2

To check if the point (k, 2) lies on this line, we can substitute k for x and 2 for y in the equation:

2 = (-1/2)k - 2

4 = (-1/2)k

k = -8

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Answer:198.447

Step-by-step explanation:

just search 7 ounces to grams

The depth of water changes at a rate of -13/72π feet per minute when the water is 2 feet high.

To begin, we must use the formula for the volume of a cone, which is given as:

V = 1/3πr2hwhere V represents the volume, π represents the constant pi, r represents the radius, and h represents the height.

Substituting the given values into the formula, we get:

V = 1/3π (6 ft)2(14 ft)V = 1/3π (36 ft2) (14 ft)V = 1/3π (504 ft3)V = 168π ft^3

Now, we must determine the rate at which water is leaking. It is given that the cone leaks water at a rate of 13 cubic feet per minute. This implies that the volume of the water reduces by 13 cubic feet every minute. Therefore, the rate of change of the volume of water is -13 cubic feet per minute. Here, the negative sign indicates a decrease in the volume of water.

Now, we must find how fast the depth of water changes when the water is 2 feet high. Let d represent the depth of water. Then, the volume of water is given as:

V = 1/3πr^2d

We know that when d = 2 ft, V = 1/3π(6 ft)2(2 ft)

V = 8π ft^3

Now, we must determine how fast the volume of water is changing with respect to time when d = 2 ft. We differentiate the expression for V with respect to time to get:

dV/dt = (d/dt)[1/3πr2d]

dV/dt = 1/3πr^2(d/dt)[d]

dV/dt = 1/3πr^2(d/dt)[2]

dV/dt = 2/3πr^2

The rate of change of the volume of water with respect to time is given as -13 cubic feet per minute. Therefore, substituting this into the expression above, we get:

-13 = 2/3π(6 ft)2(d/dt)

When we simplify the above equation, we get:

d/dt = -13/72π

Therefore, when the water is 2 feet high, the depth of the water changes at a rate of -13/72π feet per minute.

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Therefore, the derivative of y = 7x⁴ with respect to x is dy/dx = 28x³.

Differentiation is a mathematical concept that refers to the process of finding the derivative of a function. The derivative of a function is the rate at which the function changes with respect to its independent variable. In other words, it measures how quickly the output of the function is changing as the input value is changing.

The derivative of a function can be used to determine many properties of the function, such as its slope, maximum and minimum values, and whether it is increasing or decreasing. It is an important tool in calculus and is used in many fields, including physics, engineering, economics, and finance.

The process of differentiation involves applying specific rules to a given function to determine its derivative. The most common method of differentiation is using the power rule, which states that the derivative of a function raised to a power is equal to the product of the power and the function raised to the power minus one. Other rules include the product rule, the quotient rule, and the chain rule, which are used to differentiate more complex functions.

by the question.

To differentiate y = 7x⁴, we need to use the power rule of differentiation, which states that if [tex]y = kx^{n}[/tex], where k is a constant and n is a non-negative integer, then the derivative of y with respect to x is dy/dx = [tex]\frac{dy}{dx} = nkx^{(n-1)}[/tex].

Using this rule, we can differentiate y = 7x⁴ as follows:

dy/dx = 47[tex]x^{4-1}[/tex] [applying the power rule]

dy/dx = 28x³

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The probability of spinning purple on the spinner is 1/4 or 25%.

Calculating the variety of ways to select or arrange a collection of items is a key component of the probability theory concepts of permutation and combination. The key distinction between combination and permutation is whether or not order matters. Contrarily, combination refers to the variety of ways to choose a smaller subset of items from a larger collection, where the order of the items is irrelevant. For instance, there are three potential two-letter combinations if you have the letters A, B, and C: AB, AC, and BC.

Given there are 4 stations, thus he spinner is equally likely to land on any of the four colors.

The probability of spinning purple is 1/4 or 25%.

Hence, the probability of spinning purple on the spinner is 1/4 or 25%.

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Answer:

x = 7 ft

Step-by-step explanation:

[tex]tan 55=\frac{10}{x}\\x=\frac{10}{tan 55}\\x=7.0020\\x=7[/tex]

The answer of the given question is , the predicted average retail price of a car in 2003 is $9860.40.and  the car will be worth $814 in the year 2010.

A regression equation is a mathematical formula that is used to describe the relationship between two or more variables. It is typically used in statistical analysis to model the relationship between a dependent variable and one or more independent variables.In simple linear regression, there is only one independent variable, and the regression equation takes the form of a straight line. In multiple regression, there are two or more independent variables, and the regression equation takes the form of a more complex mathematical function.

Using a calculator, we can input the data points into a regression equation to find the line of best fit. Using the given data, we get the regression equation:

y = -1357.4x + 18003.8

where y represents the retail price of a car and x corresponds to the year, with x = 1 representing 1998.

To predict the average retail price of a car in 2003, we need to substitute x = 6 (since 2003 corresponds to x = 6) into the regression equation:

y = -1357.4(6) + 18003.8

y = -8144.4 + 18003.8

y = 9860.4

So, the predicted average retail price of a car in 2003 is $9860.40.

To determine the year when the car will be worth $814, we need to substitute y = 814 into the regression equation and solve for x:

814 = -1357.4x + 18003.8

Simplifying, we get:

-1357.4x = -17189.8

x = 12.65

Rounding up to the nearest whole number, we get x = 13, which corresponds to the year 2010. Therefore, the car will be worth $814 in the year 2010.

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The expression for the total length of ribbons left is: r - 16 . But we can also write this expression as: 4 x (r - 4) because 4 x (r - 4) = 4r - 16, which is equivalent to r - 16.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The expression that represents the total length of ribbons left is:

4 x (r - 4)

This is because Ava uses 4 inches from each roll of ribbon, and there are 4 rolls of ribbon in total. So the total length of ribbon used is 4 x 4 = 16 inches.

To find the total length of ribbon left, we need to subtract the length of ribbon used from the original length of ribbon, which is r inches.

Therefore, the expression for the total length of ribbons left is: r - 16

But we can also write this expression as: 4 x (r - 4) because 4 x (r - 4) = 4r - 16, which is equivalent to r - 16.

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Answer:

....

Step-by-step explanation:

can you provide an image if the question instead...

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{OD}\\ o=\stackrel{opposite}{11} \end{cases} \\\\\\ (13)^2= (OD)^2 + (11)^2\implies 13^2-11^2=OD^2\implies 48=OD^2 \\\\\\ \sqrt{48}=OD\implies 6.93\approx OD[/tex]

Answer:

C = 11,21 cm

using the formulas :

A (area) = 10 [tex]cm^{2}[/tex]

A = π [tex]r^{2}[/tex]

C = 2 π r

colving for C :

C = 2 *√(π*Α) = 2 *√(π * 10) = 11,20998 cm

Answer:

Step-by-step explanation:

Domain: D=R-{2}

Asymptote vertical: x=2

Asymptote horizontal: y=1

Hey, I tried to graph this function, I hope you understand something here...

Using diagonals from a common vertex of a 14-gon, a total of 11 triangles can be formed.

To see why, we can apply the formula for the number of triangles formed by drawing all the diagonals from a single vertex of a polygon, which is (number of sides - 2). For a 14-gon, the formula gives us:

number of triangles = (14 - 2) = 12

However, we need to subtract one from the total because the vertex where the diagonals are drawn from is not included in any of the triangles. Therefore, the number of triangles formed by drawing diagonals from a common vertex of a 14-gon is:

number of triangles = 12 - 1 = 11

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Answer: 14-2=12

Step-by-step explanation: