Abigail was skateboarding home when the wheel axle of her skateboard broke. She had already traveled two thirds of the way home and had to walk the rest of the way. Walking the rest of the way home took her twice as long as it took her to ride her skateboard. How many times faster is Abigail on her skateboard than she is walking?

Answer:

Option B is correct

It must be a positive number since it represents a number of hours.

Step-by-step explanation:

As per the statement:

Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level.

Given the equation as:

Using distributive property,

Combine like terms;

Subtract 40 from both sides we have;

Divide both sides by -8 we have;

h = 14 hours

Therefore, the statement is true about Pieter’s solution is, It must be a positive number since it represents a number of hours.

the answer is B It must be a positive number since it represents a number of hours.

Answer:

Two color drawings and seven black and white drawings.

Step-by-step explanation:

If it takes 25 minutes for a color drawing it would take him 50 minuies to do two, leaving him with a remainder of 70 minutes.  In that time he can create 7 black and white drawings.  7+2=9, giving you your answer.

To determine the number of black and white and color drawings, set up a system of equations based on the given information. Solve the system of equations by adding them together. The solution is 3 black and white drawings and 6 color drawings.

To solve this problem, we can set up a system of equations. Let the number of black and white drawings be represented by x and the number of color drawings be represented by y.

The first equation is based on the fact that it takes Akira 10 minutes to make a black and white drawing and 25 minutes for a color drawing. So, the total time spent on black and white drawings is 10x minutes and the total time spent on color drawings is 25y minutes.

The second equation states that on Saturday Akira made a total of 9 drawings in 2 hours, which is equivalent to 120 minutes. So, we have x + y = 9.

Adding the equations 10x + 25y = 120 and x + y = 9, we can solve for x and y. Solving this system of equations gives us x = 3 and y = 6.

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First of all we need the line equation so let's find it first :

y = mx + b

y = 2x + b

_______________________________

The line passes through point ( 8 , 3 ) which means if put 8 instead of x the y must equals to 3 :

2(8) + b = 3

16 + b = 3

b = 3 - 16

b = - 13

______________________________

Now we have the equation of the line :

y=2x-13

To find the y-intercept we just need to out 0(zero)instead of x; Let's do it :

y = 2(0) - 13

y = 0 - 13

y = - 13

Thus the y-intercept=-13

Answer:

the y intercept is -13

Step-by-step explanation:

The required, there is no part of the sphere x² + y² + z² = 16 that lies above the cone z = x² + y², where z > x² + y².

To find the part of the sphere x² + y² + z² = 16 that lies above the cone z = x² + y², where z > x² + y², we can use spherical coordinates. In spherical coordinates, the equations for the sphere and the cone are simpler.

Spherical coordinates are represented as (ρ, θ, φ), where ρ is the radial distance, θ is the azimuthal angle (measured from the positive x-axis in the xy-plane), and φ is the polar angle (measured from the positive z-axis).

For the sphere x² + y² + z² = 16, the spherical representation is:

ρ = 4 (since ρ² = x² + y² + z² = 16)

For the cone z = x² + y², the spherical representation is:

ρ = ρ (since ρ^2 = x² + y²)

Now, to find the part of the sphere that lies above the cone (z > x² + y^2), we need to restrict the values of φ.

When z > x² + y², we have z = ρ cos(φ) > ρ².

Since ρ = 4, we get 4 cos(φ) > 4², which simplifies to cos(φ) > 4.

However, the range of φ in spherical coordinates is 0 ≤ φ ≤ π, which means that the values of φ that satisfy cos(φ) > 4 are not within the valid range.

Therefore, there is no part of the sphere x² + y² + z² = 16 that lies above the cone z = x² + y², where z > x² + y².

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Final answer:

We use the given equations of the sphere and cone and express them in spherical coordinates. The sphere lies on or above the cone when z's value in the sphere equation is greater or equal than z's value in the cone equation. One method is to use spherical coordinates and represent the radius and polar angle in terms of u and v.

Explanation:

The question involves spherical and rectangular coordinates and the relationship between the two. We are given the sphere's equation as x^2 + y^2 + z^2 = 16 and the cone's equation as z = x^2 + y^2. Here's one way to think of the part of the sphere that lies on or above the cone. If we view z=x^2 + y^2 as a function of x and y, the sphere lies above this cone when z's value in the equation of the sphere is greater or equal to the value of z in the cone's equation. To express x, y, and z in terms of u and/or v, you can use a method such as spherical coordinates.

In spherical coordinates, the relationship between spherical and rectangular coordinates can be represented as:

• x = r sin θ cos φ
• y = r sin θ sin φ
• z = r cos θ

Here r, θ, and φ are the radius, polar, and azimuthal angles respectively, which we can let u and v represent. One potential assignment is to let r=u and θ=v, assuming we want only two parameters.

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