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2 years ago

7

A rocket is 1 mile above the earth in 30 seconds and 5 miles above the earth in 2.5 minutes. What is the rockets rate of change

in miles per second?

1 answer:

tamaranim1 [39]2 years ago

6 0

The rockets rate of change in miles per second is: (5 - 1)/(2.5*60 - 30) = 1/30 miler per second or 0.033 the rockets rate of change in miles per minute is: (5 - 1)/(2.5 - 30/60) = 2 miles per minute

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Work out 6/5 of 200 and show working out

katrin [286]

Answer:

240.

Step-by-step explanation:

200 * 6/5

= 1200/5

= 240

5 0

2 years ago

Use the Commutative Property to write an expression equivalent to -5d + 6

Ludmilka [50]

Answer:

6 - 5d is an expression equivalent to -5d + 6 using the commutative Property of Addition.

Step-by-step explanation:

Commutative Property of Addition

We know that we can add two numbers in any order.

For example,

Let 'a' and 'b' be two numbers.

We can add 'a' and 'b' numbers in any order, such as

a + b = b + a

Thus,

a + b = b + a is represented using the commutative Property of Addition.

In our case,

-5d + 6 can be written or represented using the commutative Property of Addition, such as

-5d + 6 = 6 - 5d

It is clear that -5d + 6 can be written in any order such as 6 - 5d.

In other words, 6 - 5d is an expression equivalent to -5d + 6 using the commutative Property of Addition.

Therefore, 6 - 5d is an expression equivalent to -5d + 6 using the commutative Property of Addition.

7 0

2 years ago

Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

$(x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}$

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago

Mike is reserving a room in frances, which uses euros. The room charge is 75 euros. If the conversion rate was 1 euro equals $1.

rusak2 [61]

To convert the euros into dollars simply multiply 75x1.29.

8 0

2 years ago

Is (-3,4) a solution of the inequality y> - 2x – 3?

jeyben [28]

Answer:

(-3, 4) is a solution

Step-by-step explanation:

The point (-3, 4) is inside the shaded area of the graph, so is a solution.

You can check in the inequality

y > -2x -3

4 > -2(-3) -3 . . . . substitute for x and y

4 > 3 . . . . . . . true; the given point is a solution

8 0

3 years ago