Can someone help me find the way to get this answer??

A ball has been thrown into the air its distance from the ground is given by the function s(t)=-16t^2+96t+100

slega [8]

Answer:

For t=3 sec the velocity change from positive to negative

Step-by-step explanation:

we have

$s(t)=-16t^2+96t+100$

This is the equation of a vertical parabola open downward (the leading coefficient is negative)

where

s(t) is the distance in feet

t is the time in seconds

We know that

To find out when the velocity change from positive to negative, we need to determine the turning point of the quadratic equation

The turning point of the quadratic equation is the vertex

so

Convert the quadratic equation into vertex form

$s(t)=-16t^2+96t+100$

Factor -16

$s(t)=-16(t^2-6t)+100$

Complete the square

$s(t)=-16(t^2-6t+9)+100+144$

$s(t)=-16(t^2-6t+9)+244$

Rewrite as perfect squares

$s(t)=-16(t-3)^2+244$

The vertex is the point (3,244)

therefore

For t=3 sec the velocity change from positive to negative

8 0

3 years ago

The amount of soda dispensing machine pours into a can of soda is normally distributedwith a mean of 12 ounces and a standard de

kaheart [24]

Answer:

0.1056

Step-by-step explanation:

Mean(μ) = 12 ounce

Standard deviation (σ) = 0.2 ounce

P(x<11.75) = ???

Let x be the random variable for the amount of soda a machine will dispense.

Using normal distribution

Z = (x - μ) / σ

Z = (11.75 - 12) / 0.2

Z = (-0.25)/0.2

Z = -1.25

From the normal distribution table

1.28 is 0.3944

Φ(z) is the tabular value of z

Φ(z) = 0.3944

Recall that when Z is negative

P(x<a) = 0.5 - Φ(z)

P(x < 11.75) = 0.5 - 0.3944

= 0.1056

7 0

3 years ago

Hello, can any one help me? Please

cricket20 [7]

Answer:

d divided by 1/15 is o.75

Step-by-step explanation:

5 0

2 years ago

Combine the like terms to create an equivalent expression: \large{-k-(-8k)}−k−(−8k)minus, k, minus, (, minus, 8, k, )

PIT_PIT [208]

Answer:

7k

Step-by-step explanation:

The given expression is

$-k-(-8k)$

We need to find the simplified form of the given expression.

Like terms: The terms which have same variables of same degree and known as like terms. For example: 2x and 4x are like terms.

The given expression can be rewritten as

$-k+8k$

On combining like terms we get

$(-1+8)k$

$7k$

Therefore, the equivalent expression of the given expression is 7k.

3 0

3 years ago

If mc010-1.jp g and mc010-2.jp g, which expression could be used to verify that mc010-3.jp g is the inverse of mc010-4. ? mc010-

solmaris [256]

if indeed two functions are inverse of each other, then their composite will render a result of "x", namely, if g(x) is indeed an inverse of f(x), then

$\bf (g\circ f)(x)=x\implies g(~~f(x)~~)=x \\\\\\ \begin{cases} f(x) = 3x\\ g(x)=\cfrac{1}{3}x \end{cases}\qquad \qquad g(~~f(x)~~)=\cfrac{1}{3}[f(x)]\implies g(~~f(x)~~)=\cfrac{1}{3}(3x)$

5 0

3 years ago