An airplane on auto pilot took 5 hours to travel 3,475 kilometers. What is the unit rate for kilometers per hour?

Sally launches a rocket off of a platform. The height of the rocket, in meters, can be modeled by the function, h(x) = -5(x - 3)

Lorico [155]

Answer:

Time = 3secs

Max height = 56m

Step-by-step explanation:

Given the height reached by the rocket modeled by the equation;

h(x) = -5(x - 3)² + 56 where;

x is in seconds

The rocket velocity at its maximum height is zero.

Hence dh/dx = 0

dh/dx = 2(-5)(x-3)

dh/dx = -10(x-3)

Since dh/dx = 0

0 = -10(x-3)

0 = -10x + 30

10x = 30

x = 3secs

Hence it takes 3 secs to reach the maximum height.

Get the maximum height reached by the rocket. Substitute x = 3 into the equation given;

Recall that:

h(x) = -5(x - 3)² + 56

If x = 3

h(3) = -5(3 - 3)² + 56

h(3) = 0 + 56

h(3) = 56

Hence the maximum height that the rocket reaches is 56m

4 0

3 years ago

A bag contains yellow marbles and red marbles, 19 in total. The number of yellow marbles is 5 less than 3 times the number of re

Bad White [126]

Answer of this question =8

3 0

3 years ago

Determine the equation for the parabola graphed below

Elza [17]

Answer:

$y=(x-2)^2-1$

Step-by-step explanation:

The given function:

Since the function is open upwards means is of $y=x^2$

And we can see one unit down and 2 units shifted on right in parent function.

Therefore, the function is of $y=(x-2)^2-1$

Graph takes parabola shape by quadratic function.

4 0

3 years ago

Find the sum. Express your answer in simplest form. 9a^2-5/b^2+2 + -2a^2+4/b^2+2

KonstantinChe [14]

Answer:

Step-by-step explanation:

$\frac{9a^{2}-5}{b^{2}+2}+\frac{-2a^{2}+4}{b^{2}+2}=\frac{9a^{2}-5-2a^{2}+4}{b^{2}+2}\\\\=\frac{9a^{2}-2a^{2}-5+2}{b^{2}+2}\\\\=\frac{7a^{2}-3}{b^{2}+2}$

5 0

3 years ago

Correctly complete this sequence: 88511, 16351, ?, 10251

IgorC [24]

Answer:

73155 will be the 3rd number in the sequence: 88511, 16351, ?, 10251.

So, the complete sequence will be: 88511, 16351, 73155, 10251.

Step-by-step explanation:

As 88511 is the first number.

The number 88511 has a certain pattern that could help us finding the next number.

So, let us consider 88511 and determine the pattern to find the next number and so on to complete the sequence.

Adding the first 2 digits in the number 88511 i.e. 8 + 8 = 16

Subtracting the 3rd digit from the 2nd digit i.e. 8 - 5 = 3

Multiplying the 3rd digit and 4th digit i.e. 5 × 1 = 5

Dividing the 4th digit by the 5th digit i.e. 1 ÷ 1 = 1

Hence, using these steps would get us the number 16351.

So, the next number would obtained using same steps:

Adding the first 2 digits in the number 16351 i.e. 1 + 6 = 7

Subtracting the 3rd digit from the 2nd digit i.e. 6 - 3 = 3

Multiplying the 3rd digit and 4th digit i.e. 3 × 5 = 15

Dividing the 4th digit by the 5th digit i.e. 5 ÷ 1 = 5

Hence, using these steps would get us the number 73155.

So, the next number would obtained using same steps:

Adding the first 2 digits in the number 73155 i.e. 7 + 3 = 10

Subtracting the 3rd digit from the 2nd digit i.e. 3 - 1 = 2

Multiplying the 3rd digit and 4th digit i.e. 1 × 5 = 5

Dividing the 4th digit by the 5th digit i.e. 5 ÷ 5 = 1

Hence, using these steps would get us the final number 10251.

So, from this observation, we determine that 73155 will be the 3rd number in the sequence: 88511,16351,?,10251.

So, the complete sequence will be: 88511, 16351, 73155, 10251.

Keywords: sequence, number

Learn more about sequence from brainly.com/question/13257823

#learnwithBrainly

3 0

3 years ago