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3 years ago

The product The product of 5 and a number n is at least -25

Mathematics

2 answers:

kogti [31]3 years ago

5 0

the answer is n > -5

Sophie [7]3 years ago

4 0

Answer:

$n > - 5$

Step-by-step explanation:

$5 \times n > - 25 \\ n > - 25 \div 5 \\ n > - 5$

You might be interested in

Which value satisfies the inequality 5x + 7 ≤ 8x - 3 + 2x?

QveST [7]

Answer:

D) 2

Step-by-step explanation:

5x + 7 $\leq$ 8x -3 +2x

5x + 7 $\leq$ 10x - 3

7 + 3 $\leq$ 10x - 5x

10 $\leq$ 5x

2 $\leq$ x

x $\geq$ 2

8 0

3 years ago

A small rocket is fired from a launch pad 10 m above the ground with an initial velocity left angle 250 comma 450 comma 500 righ

jonny [76]

Let $\vec r(t),\vec v(t),\vec a(t)$ denote the rocket's position, velocity, and acceleration vectors at time $t$ .

We're given its initial position

$\vec r(0)=\langle0,0,10\rangle\,\mathrm m$

and velocity

$\vec v(0)=\langle250,450,500\rangle\dfrac{\rm m}{\rm s}$

Immediately after launch, the rocket is subject to gravity, so its acceleration is

$\vec a(t)=\langle0,2.5,-g\rangle\dfrac{\rm m}{\mathrm s^2}$

where $g=9.8\frac{\rm m}{\mathrm s^2}$ .

a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,

$\vec v(t)=\left(\vec v(0)+\displaystyle\int_0^t\vec a(u)\,\mathrm du\right)\dfrac{\rm m}{\rm s}$

$\vec v(t)=\left(\langle250,450,500\rangle+\langle0,2.5u,-gu\rangle\bigg|_0^t\right)\dfrac{\rm m}{\rm s}$

(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

$\boxed{\vec v(t)=\langle250,450+2.5t,500-gt\rangle\dfrac{\rm m}{\rm s}}$

and

$\vec r(t)=\left(\vec r(0)+\displaystyle\int_0^t\vec v(u)\,\mathrm du\right)\,\rm m$

$\vec r(t)=\left(\langle0,0,10\rangle+\left\langle250u,450u+1.25u^2,500u-\dfrac g2u^2\right\rangle\bigg|_0^t\right)\,\rm m$

$\boxed{\vec r(t)=\left\langle250t,450t+1.25t^2,10+500t-\dfrac g2t^2\right\rangle\,\rm m}$

b. The rocket stays in the air for as long as it takes until $z=0$ , where $z$ is the $z$ -component of the position vector.

$10+500t-\dfrac g2t^2=0\implies t\approx102\,\rm s$

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

$\boxed{\|\vec r(102\,\mathrm s)\|\approx64,233\,\rm m}$

c. The rocket reaches its maximum height when its vertical velocity (the $z$ -component) is 0, at which point we have

$-\left(500\dfrac{\rm m}{\rm s}\right)^2=-2g(z_{\rm max}-10\,\mathrm m)$

$\implies\boxed{z_{\rm max}=125,010\,\rm m}$

7 0

3 years ago

How can you solve a rational equation without graphing?

KiRa [710]

Answer:

To figure out the common denominator for these fractions, I'll first need to factor that quadratic in the denominator on the right-hand side of the rational equation. This will also allow me to find the disallowed values for this equation. Factoring gives me:

x2 – 6x + 8 = (x – 4)(x – 2)

The factors of the quadratic on the right-hand side "just so happen" to be duplicates of the other denominators. This often happens in these exercises. (So often, in fact, that if you get completely different factors, you should probably go back and check your work.)

Step-by-step explanation:

4 0

3 years ago

A rectangular swimming pool is 15 meters long, 11 1/2 meters wide, and 1 1/2 meters deep. What is its volume?

-BARSIC- [3]

258 3/4 cubic meters

Explanation:
Use this formula for volume of rectangular prism: length x width x height

In this case it would be:
15 • 11 1/2 • 1 1/2 = 258 3/4

VOLUME= 258 3/4 cubic meters

Com.ment me if u have any questions
If my answer is correct, braibliest please!
-SpaceMarsg, have a nice day :DD

3 0

3 years ago

Estimate 13.23 - 2.570 by first rounding each number to the nearest tenth.

Temka [501]

Answer:

Step-by-step explanation:

13.23 = 10

2.570= 3

10-3=7

6 0

3 years ago

Read 2 more answers