which is a factored form of 216p^3 + 125q^3?

Final answer:

To find dy/dx by implicit differentiation of the equation xy=35, differentiate both sides with respect to x. Use the product rule to obtain x * (dy/dx) + y = 0 and solve for dy/dx, giving dy/dx = -y / x. Evaluate this at a specific point by substituting the x and y values from that point into the derived formula.

Explanation:

To find dy/dx by implicit differentiation of the equation xy = 35, we differentiate both sides of the equation with respect to x. Since y is a function of x, when we differentiate y we must apply the chain rule, resulting in the derivative y with respect to x, or dy/dx.

Starting with the original equation:

xy = 35

We apply differentiation to both sides with respect to x:

Using the product rule for the left side: d/dx (xy) = d/dx (35)

This gives us x * (dy/dx) + y * (1) = 0 because the derivative of a constant, like 35, is 0.

We then solve for dy/dx: dy/dx = -y / x.

To evaluate the derivative at a given point, you substitute the x and y coordinates of that point into the derivative equation. For example, if we are given a point (5,7), we substitute into the dy/dx equation to find the derivative at that point:

dy/dx = -y / x = -(7) / (5)

Therefore, dy/dx at the point (5,7) is -7/5 or -1.4.

The corresponding reference angle to 17π/7 radians is π/7.

The corresponding reference angle to 17π/7 radians is found by determining the smallest positive angle such that when added to 17π/7 radians, the resulting angle lies between 0 and 2π radians.

To find the reference angle, we can subtract 2π radians repeatedly until we obtain an angle between 0 and 2π radians.

In this case, we have:

17π/7 - 2π = π/7

Therefore, the corresponding reference angle to 17π/7 is π/7 radians.

Answer:

Step-by-step explanation:

First, add 9 to each side

Then subtract 2x from each side

Divide each side by 3

Sorry my answer may be a bit late

The equation of a line parallel to y=23x+1 that passes through the point (-5, -2) is y = 23x + 113.

The subject of this question is geometry, specifically, the formulation of a linear equation. You're asked to write an equation of a line that passes through point (-5,-2) and is parallel to the line defined by the equation y=23x+1.

Parallel lines have the same slope, so since the given line has a slope of 23, our line will also have a slope of 23. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Here, 'm' is already known as 23. So, our equation currently is y = 23x + b.

We can determine 'b' using the given point (-5,-2). Substituting these coordinates into our equation gives -2 = 23*(-5) + b. Solving for 'b' renders b = -2 - (23*-5) = 113.

Therefore, the equation of the line that passes through (-5, -2) and is parallel to y=23x+1 is y = 23x + 113.

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Final answer:

To solve for final velocity (Vf) in acceleration calculations, identify the initial velocity (Vo), acceleration (a), and time (t), then use the formula Vf = Vo + at to find Vf. Substitute the known values into the formula to calculate the final velocity.

Explanation:

To solve for final velocity (Vf) in the formula for acceleration, follow these steps:

Identify the initial velocity, Vo, and any other known variables such as acceleration (a) and time (t).

Determine which equation to use, using the relationship that acceleration is the change in velocity over time (Δv/Δt). The formula to calculate final velocity is v = Vo + at.

Substitute the known values into the equation to solve for Vf. For example, with an initial velocity (Vo) of 30.0 km/h (which converts to 8.333 m/s), an unknown final velocity (Vf), and a time (Δt) of 8.00 seconds, the change in velocity (Δv) would be Vf - Vo.

To find Vf, rearrange the equation: Vf = Vo + (a Δt). Insert the known values into the equation and calculate the result.

As an example, if the initial velocity Vo is 0 and the acceleration is 0.40 m/s² over a time of 100 seconds, then the final velocity Vf is calculated as:

Vf = Vo + at = 0 + (0.40 m/s²) (100 s) = 40 m/s.

This procedure will yield the final velocity of an object assuming constant acceleration over the given time period.

Answer: Hello there!

I understand the notation 5 1/3 is equivalent to 5 + 1/3 = 5.333...

our equation is 5 +1/3 +(-3 +9/18)

first we could simplify the 9/18 as 1/2 (dividing both numerator and denominator by 9)

then the equation is:

=5+ 1/3 - (3 +1/2)

=5 + 1/3 - 3 - 1/2

=5 -3 + (1/3 - 1/2)

the common factor betwe 3 and 2 is 6, then:

=2 + (2/6 - 3/6) = 2 -1/6

this can be written as:

= 2 - 1/6 = 1 + 1 -1/6 = 1 + ( 1-1/6) = 1 + 5/6

or = 1 5/6 using the original notation.

Answer:

Option 4 - domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

Step-by-step explanation:

Given :  [tex]h(x)=(0.5)^x-9[/tex]

To find : What are the domain, range, and asymptote of h(x) ?

Solution :  

Domain of the function is where the function is defined

The given function  [tex]h(x)=(0.5)^x-9[/tex] is an exponential function

So, the domain of the function is,

[tex]D=(-\infty,\infty) , x|x\in \mathbb{R}[/tex]

i.e, The set of all real numbers.

Range is the set of value that corresponds to the domain.

Let  [tex]y=(0.5)^x-9[/tex]

If [tex]x\rightarrow \infty , y\rightarrow -9[/tex]

If [tex]x\rightarrow -\infty , y\rightarrow \infty[/tex]

So, The range of the function is

[tex]R=(-9,\infty) , y|y>-9[/tex]

The asymptote of the function,

Exponential functions have a horizontal asymptote.

The equation of the horizontal asymptote is  when

[tex]x\rightarrow \infty[/tex]

[tex]y=(0.5)^\infty-9[/tex]

[tex]y=-9[/tex]

Therefore, Option 4 is correct.

Domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

Answer with explanation:

⇒Domain:

f(x)= -x² -2 x +15

   = - (x²+2 x -15)

Splitting the middle term

 = - (x²+5 x - 3 x -15)

= -[ x × (x+5) -3× (x+5)]

= -(x-3)(x+5)

y=f(x)=(3 -x)(x+5)

Domain of the function is defined as set of all values of x, for which y is defined.

f(x) is defined as all real values of x.So, Domain = R.

⇒Range:

[tex]y=-x^2-2 x +15\\\\y=-(x^2+2 x-15)\\\\ y=-[(x+1)^2-1-15]\\\\y= -(x+1)^2+16\\\\ 16 -y=(x+1)^2\\\\x+1=\pm\sqrt{16-y}\\\\x=\pm\sqrt{16-y}-1[/tex]

Range of the function is defined as set of all values of y, for which x is defined.

⇒16 -y ≥ 0

⇒y ≤ 16

Option B

The domain is all real numbers. The range is {y|y ≤ 16}.

24 is 30% of 80

Image provided.

The farmer owns 8 10/45 acres of land.

To find out how many acres of land the farmer owns, we need to multiply the number of sections by the size of each section. The size of each section is 2 1/5 acres.

The number of sections is 4 4/9. Using multiplication, we can calculate the total number of acres:

(2 1/5) x (4 4/9) = 10/5 x 40/9 = 400/45 = 8 10/45

Therefore, the farmer owns 8 10/45 acres of land.

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Final answer:

The integer 27 can be written as the product of the perfect square 9 and the integer 3, expressed as 9 x 3.

Explanation:

To write the integer 27 as a product of two integers such that one of the factors is a perfect square, we can break down 27 into its prime factors. The prime factorization of 27 is 3 x 3 x 3, which can be written as 9 x 3 because 9 is a perfect square (3 x 3).

Therefore, the integer 27 can be written as the product of the perfect square 9 and the integer 3, which is 9 x 3.

The car will need approximately 8.76 more gallons of gas to complete the remaining 440 miles of the 650-mile trip, assuming it continues to get the same mileage rate of 26.25 miles per gallon.

To calculate the additional amount of gas needed to complete the 650-mile trip, given that the car used eight gallons to travel the first 210 miles, we need to find the car's mileage rate and then determine how much more gas is required for the remaining distance.

Step-by-Step Explanation

Therefore, the car will need approximately 8.76 more gallons of gas to complete the rest of the trip at the same rate.

To calculate the additional gas needed for the remainder of a 650-mile trip after using 8 gallons for the first 210 miles, first determine the gas mileage and then calculate the gas required for the remaining 440 miles. The car will need approximately 16.76 more gallons of gas to complete the trip.

To determine how much more gas you will need to complete your 650-mile trip, after having used 8 gallons for the first 210 miles, you need to calculate your car's gas mileage and then use that information to find the amount of gas needed for the remaining distance.

First, let's compute your car's mileage:

Now, let's subtract the miles you have already traveled from the total trip length to find the remaining miles:

Finally, we calculate the amount of gas needed for the remaining distance:

Therefore, you will need approximately 16.76 more gallons of gas to complete your trip, assuming the gas mileage remains consistent.

Answer:

Total money Zinnia and Ruby earned for delivering pizzas is 58x + 13 + 58y .    

Step-by-step explanation:

As given

Zinnia and Ruby earn $58 per week for delivering pizzas.

Zinnia worked for x weeks and earned an additional total bonus of $13.

Ruby worked for y weeks.

Thus

Money Zinnia earns = Money earns per week × Number of weeks + Additional total bonus .

Put all the values in the above

Money Zinnia earns = 58 × x + 13

Money Zinnia earns = 58x + 13

Thus

Money  Ruby earns = Money earns per week × Number of weeks

Put all the values in the above

Money  Ruby earns = 58 × y

Money Ruby earns = = 58y

Thus

Total Zinnia and Ruby earned for delivering pizzas = Money Zinnia earns  + Money Ruby earns

Total Zinnia and Ruby earned for delivering pizzas = 58x + 13  + 58y

Therefore the total money Zinnia and Ruby earned for delivering pizzas is 58x + 13 + 58y .                          

Convert the line equation to 'y = mx + c' form. We calculate the orthogonal distance from the point to a generic point on the line using the formula 'd = |Ax1 + By1 + C| / sqrt(A^2 + B^2)'. Solve the line equation for 'y' using the computed 'd'. This yields the point closest to (-3,1) on the line.

The subject of the question involves the algebra of straight lines, specifically finding points on lines. The given line in the question is '6x + y = 9'. We want to find the point along this line that is closest to a given point (-3,1).

First, rewrite the equation in slope-intercept form: y = -6x + 9. Now recall the formula for the shortest distance from a point to a line, d = |Ax1 + By1 + C| / sqrt(A^2 + B^2), where 'A', 'B' and 'C' are the coefficients in the equation of the line, and '(x1, y1)' is the point.

In this case, A = -6, B = 1, C = -9, and the point is (-3,1). If we plug these into the formula, we can solve for 'd'. Then we solve the given equation for 'y' using the resulting 'd' value and we get the point which is closest to (-3,1) on the line '6x + y = 9'.

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Answer:

pb and 5

Step-by-step explanation:

The rate at which the radius of the balloon is changing can be found by differentiating the volume formula for a sphere. Substituting the given values into the formula, we can calculate the rate of change at specific radii.

To find the rate at which the radius of the balloon is changing, we can use the relationship between the volume and the radius of a sphere. The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius. Taking the derivative of both sides with respect to time, we get dV/dt = 4πr²(dr/dt). We are given that dV/dt = 900 cm³/min and we need to find dr/dt when r = 40 cm and r = 90 cm.

(a) Plug in the values into the formula: 900 = 4π(40)²(dr/dt). Solve for dr/dt: dr/dt = 900/(4π(40)²) ≈ 0.178 cm/min.

(b) Repeat the same steps for r = 90 cm: 900 = 4π(90)²(dr/dt). Solve for dr/dt: dr/dt = 900/(4π(90)²) ≈ 0.020 cm/min.

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