Which of the following is an arithmetic sequence?

An object is launched from a launching pad 208 ft. above the ground at a velocity of 192ft/sec. what is the maximum height reach

Alexeev081 [22]

Answer:

h(x) = -16x² + 192x + 208

784ft

6 sec

13 sec

Step-by-step explanation:

a)

h(x) = -16x² +vx + h $_{o}$

here v represent velocity

$h_{o}$ represent initial height of launch

h(x) = -16x² + 192x + 208

b)

h(x) = -16x² + 192x + 208

here a = -16

b = 192

c = 208

x = -b/2a

= -192/2(-16)

= 6

plug this value in the equation

h(x) = -16(6)² + 192(6) + 208

= 784ft

e)

Plug h(x)=0 in the equation

0 = -16x² + 192x + 208

divide equation by -16

x² - 12x - 13 = 0

Factors

1x * -13x = -13

1x - 13x = -12

Factorised form

x² - 12x - 13 = 0

x² + x - 13x - 13 = 0

x(x+1) -13(x+1) = 0

(x+1)(x-13) = 0

x = -1

x = 13

Since time can not be negative so we will reject x = -1

3 0

4 years ago

Which of the g-values satisfy the following inequality? 7≥12−g

sergejj [24]

Answer:

g=6

Step-by-step explanation:

g=4 and g=5 will be more than 7 but g=6 is less.

4 0

3 years ago

At the beginning of an experiment, the number of bacteria in a colony was counted at time t=O. The number of bacteria in the col

yan [13]

Answer:

1092

Step-by-step explanation:

We have been given that the number of bacteria in the colony t minutes after the initial count modeled by the function $B(t)=9(3)^t$ . We are asked to find the average rate of change in the number of bacteria over the first 6 minutes of the experiment.

We will use average rate of change formula to solve our given problem.

$\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}$

Upon substituting our given values, we will get:

$\text{Average rate of change}=\frac{b(6)-b(0)}{6-0}$

$\text{Average rate of change}=\frac{9(3)^6-9(3)^0}{6}$

$\text{Average rate of change}=\frac{9(729)-9(1)}{6}$

$\text{Average rate of change}=\frac{6561-9}{6}$

$\text{Average rate of change}=\frac{6552}{6}$

$\text{Average rate of change}=1092$

Therefore, the average rate of change in the number of bacteria is 1092 bacteria per minute.

8 0

3 years ago

If the interest rate on a savings account is 0.02%, approximately how much money do you need to keep in this account for 1 year

astraxan [27]

At first glance, this problem might be overwhelming so try approaching it slowly by doing these steps:

Step 1: Start by understanding what the problem is really asking.
You might notice that the problem is just a percentage problem, with a twist! If you still don't see it, the problem is just asking what the base should be given a percentage and the amount.

Step 2: Recall the concepts relevant to the question.
We can identify a single formula that will be important in getting the answer:
$base*percent=amount$

Step 3: Apply the concept to the context of the problem.
You'll see that we already have the percent from the interest rate which is 0.02% and the amount from the below-minimum-balance fee which is $9.99.

There goes the little twist: you have to manipulate the equation to get the base. Dividing both sides of the equation by the percent we'll have:
$base= \frac{amount}{percent}$

Step 4: Evaluate to get the answer to the problem.
We simply substitute the given numbers and evaluate.
$base= \frac{percent}{amount}= \frac{9.99}{0.0002} =49,950$

Answer: You need $49,950 in the account to cover the Below-Minimum-Balance Fee from your interest.

5 0

4 years ago

Read 2 more answers

Which graph represents -5x+3y is equal to or greater than 9

kifflom [539]

Answer:

First, transform the given equation into the slope intercept form.

-5x + 3y >= 9

3y >= 5x + 9

y >= 5/3x + 3

Then graph the line y = 5/3x + 3. Draw a solid line with y intercept 3 and slope of 5/3.

Finally, shade everything that is above the line.

5 0

1 year ago