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2 years ago

What is the smallest integer $n$ such that $5n + 3 > -10$?

Mathematics

1 answer:

Nataliya [291]2 years ago

8 0

Answer:

-2

Step-by-step explanation:

5n+3= -10

5n = -13

n = -13/5

= -2.6

question is integer

so answer is -2

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What’s the answer to this question

Nataly_w [17]

$6 x^{3}$ + 3x + 5
- $2x^{2}$ + 6x + 5
-----------------------------------------
4x - 3 + 0

5 0

3 years ago

A lacrosse player throws a ball into the air from a height of 6 feet with an initial vertical velocity of 64 feet per second. Wh

-Dominant- [34]

Answer:

Step-by-step explanation:

I'm going to use calculus to solve this, because it's the simplest way.

The acceleration due to gravity in feet is the second derivative of the position function. We will start with the acceleration and work backwards with antiderivatives to get to the position function.

a(t) = -32. Going backwards and using the fact that the initial vertical velocity is 64 ft/sec, our velocity function is

v(t) = -32t + 64. Going backwards and using the fact that the initial height of the ball is 6 feet, our position function is

$s(t)=-16t^2+64t+6$

The first part of this question asks us the maximum height of the ball. From Physics, we learn that the maximum height of a projectile is reached when the velocity is 0, which happens to be right where the projectile stops for a nanosecond in the air to turn around and come back down. We set the velocity function equal to 0 and solve for t.

0 = -32t + 64 and

0 = -32(t - 2). By the Zero Product Property, either -32 = 0 or t - 2 = 0. It's obvious that -32 does not equal 0, so t - 2 must equal 0. Solving this for t:

t - 2 = 0 so

t = 2 seconds. Since the maximum height is reached at a time of 2 seconds, we plug 2 seconds into the position function to get its position at 2 seconds (which is also the max height of the ball).

$s(2)=-16(2)^2+64(2)+6$ and

s(2) = -64 + 128 + 6 so

s(2) = 70 feet

Now we want to know when the ball will hit the ground. "When" is a time value, and we know that the height of the ball on the ground is 0, so we sub in a 0 for s(t) and factor the quadratic.

Using the quadratic formula:

$t=\frac{-64+/-\sqrt{4096-4(-16)(6)} }{-32}$ and

$t=\frac{-64+/-\sqrt{4480} }{-32}$ which gives us the 2 solutions

$t=\frac{-64+\sqrt{4480} }{-32}$ and

$t=\frac{-64-\sqrt{4480} }{-32}$

Plugging into your calculator, the first t = -.0916500 and the second t = 4.091

We all know that time cannot ever be negative, so our t value is 4.09.

Again, from Physics, we know that a projectile reaches it max height at halfway through its travels, so it just goes to follow logically that if it halfway through its travels at 2 seconds, then it will hit the ground at 4 seconds. And it does!! How awesome is that?!

4 0

3 years ago

A group of 24 students have recess together. They are making teams to play a game. Each team has to have exactly 5 players, and

solmaris [256]

Answer:

They can make 4 teams.

Step-by-step explanation:

You can see that 24 cannot be divided by 5, but you can subtract 4 from 24 to get 20, which is a multiple of 5. 20 divided by 5 is 4, so they can make 4 teams.

8 0

2 years ago

Help! Please show work. -14-12x=-3(4x-8)

defon

Answer:

no solution

Step-by-step explanion

there is no solution since the x's cancel out

3 0

3 years ago

A study of 35 golfers showed that their average score on a particular course was 92. The sample standard deviation was 5. We wan

svlad2 [7]

Answer:

$t_{\alpha/2} = t_{0.05/2} = t_{0.025} = 2.0322$

Step-by-step explanation:

We have a sample of size n = 35, $\bar{x} = 92$ and $s = 5$ . As we want to construct a 95% confidence interval to estimate the value of the true population mean $\mu$ , we should use the pivotal quantity given by $T = \frac{\bar{X}-\mu}{S/\sqrt{n}}$ which comes from the t distribution with n - 1 = 35 - 1 = 34 degrees of freedom. Besides we should use the t-value $t_{\alpha/2} = t_{0.05/2} = t_{0.025} = 2.0322$ , i.e., regarding the t-distribution with 34 degrees of freedom, we have an area of 0.025 above 2.0322 and below the probability density function. The rationale behind this is that $P(-2.0322\leq T\leq 2.0322) = 0.95$ because of the simmetry of the t distribution.

7 0

2 years ago