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Identify the surface with the given vector equation. r(s, t) = s sin 4t, s2, s cos 4ta. plane
b. hyperbolic paraboloid
c circular paraboloid
d.circular cylinder
e. elliptic cylinder

Answers

Answer 1
Answer:

Following are the calculation to the given equation:

Given vector equation:  

\to r(s, t)= (s \sin 4t,s^2, s \cos 4t)

The corresponding parametric equations for the given surface is given by,  

x=s \sin 4t\n\n y =s^2\n\n z=s \cos 4t

For any point (x,y,z) we have that,  

x^2+z^2 = (s \sin 4t)^2 +(s \cos 4t)^2

            = s^2 \sin^2 4t +s^2 \cos^2 4t \n\n= s^2 (\sin^2 4t+cos^2 4t) \n\n= s^2 (1) \n\n=s^2\n\n=y \n

So, after eliminating the parameters, we get, x^2 +z^2 = y

Therefore, the answer is "Option c".

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Answer 2
Answer:

Final answer:

The surface represented by the given vector equation r(s, t) = s sin 4t, s2, s cos 4t is a circular cylinder. This can be inferred from the structure of the equation and the characteristics of the represented shapes.

Explanation:

The surface represented by the given vector equation,

r(s, t) = s sin 4t, s2, s cos 4t

, is a type of cylindrical surface due to the structure of the equation. This can be identified by the s terms being tied to sin/cos functions and an independent s^2 term. This shows that the s variable is acting as a 'driver' of the shape, while t coordinates the rotation. Owing to the periodic sin and cos functions in the vector equation, the surface does not lie in a single plane, ruling out the option of a plane. It also does not exhibit features of a paraboloid or hyperbolic paraboloid. Hence, it's shown that the vector equation represents a

circular cylinder

.

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Solve this equation 3x+6=-2-2x

0.00000000005 in scientific notation

Answers

It can be written as 5 x 10^ -11 or 0.5 x 10^ -10

Hope it helps.

The table below shows the linear function f.x: -6,-5,-4,-3,-2
f(x): 22,19,16,13,10
Determine the average rate of change of the given function over an interval [-5, -2].
A. -1/3
b.1/3
c.-3
D.3

Answers

Answer:

The correct choice is C.

Step-by-step explanation:

The average rate of change of the given function over the interval [-5,-2] is the slope of the secant line connecting;

(-5,f(-5))

and

(-2,f(-2))

This implies that the average rate of change over [-5,-2]

=(f(-2)-f(-5))/(-2--5)

From the table; f(-2)=10 and f(-5)=19

We substitute and simplify to obtain;

Average rate of change

=(10-19)/(-2+5)

=(-9)/(3)

=-3

Answer:

C. -3

Step-by-step explanation:

Brandon uses the steps below to solve the equation 15 x + 6 = 14 x + 5 using algebra tiles.Step 1 Add 14 negative x-tiles to both sides.
Step 2 Add 5 negative unit tiles to both sides
Step 3 The solution is x = 1.

Which explains whether Brandon is correct?
Brandon is correct because he has the correct solution in step 3.
Brandon is correct because he forms zero pairs to isolate the variable by using the lowest coefficient each time.
Brandon is not correct because he should have performed step 2 before performing step 1.
Brandon is not correct because he should have added 6 negative unit tiles to isolate the variable in step 2.

Answers

The correct option is Option D: Brandon is not correct because he should add -6 on both sides to isolate the variable in step 2.

What is the linear equation?

The linear equation is an equation where the highest degree of the variable used in the equation is 1.

For example 2x+5=25

Given the equation is 15x +6= 14x+ 5

In order to the linear equation first, try to keep the constant and the variable part to one side by adding or subtracting the constant term.

Then divide the coefficient of the variable (if the coefficient is not equal to 1) on both sides.

Here the given equation is 15x +6= 14x+ 5

Step-1: adding -14x on both sides

⇒15x +6 -14x= 14x+ 5 -14x

⇒x+ 6= 5

Step-2: adding -6 on both side

⇒x+ 6-6 = 5-6

Step-3: solution will be -1

⇒x= -1

Therefore the correct option is Option D: Brandon is not correct because he should add -6 on both sides to isolate the variable in step 2.

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Answer:

Brandon is not correct because he should have added 6 negative unit tiles to isolate the variable in step 2.

Step-by-step explanation:

edge 2020

Factor the expression
X^2-9

Answers

Answer:

(x+3)(x-3)

Step-by-step explanation:

x²-b² = (x+b)(x-b)

x²-9 = x²-3² = (x+3)(x-3)

I need help on a question but im kinda in a rush

Answers

12√3

1) To find out the Lateral Area of this pyramid we need to calculate the area of those three equilateral triangles.

\begin{gathered} Lateral_(Area)=3(s^2\frac{\sqrt[]{3}}{4})=3(16\frac{\sqrt[]{3}}{4}) \n L=3\cdot4\sqrt[]{3} \n L=12\sqrt[]{3} \end{gathered}

2) Hence, the Lateral Area of that pyramid is 12√3 u²

Two trains leave stations 288 miles apart at the same time and travel toward each other. One train travels at 85 miles per hour while the other travels at 95 miles per hour. How long will it take for the two trains to meet?

Answers

Answer:To find out how long it will take for the two trains to meet, you can use the concept of relative speed. When two objects are moving toward each other, their relative speed is the sum of their individual speeds.

In this case, one train is traveling at 85 miles per hour, and the other is traveling at 95 miles per hour. So, their relative speed is:

Relative Speed = 85 mph + 95 mph = 180 mph

Now that you know the relative speed of the two trains, you can use the formula:

Time = Distance / Speed

The distance they need to cover to meet is 288 miles, and their relative speed is 180 mph. Plug these values into the formula:

Time = 288 miles / 180 mph

Time = 1.6 hours

So, it will take 1.6 hours for the two trains to meet. To express this in minutes, you can multiply by 60:

1.6 hours * 60 minutes/hour = 96 minutes

Therefore, it will take 96 minutes for the two trains to meet.

Step-by-step explanation:
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