Lunar Projectile Motion
A rock thrown vertically upward from the surface of the moonat a velocity of 24 m/s reaches a height of s = 24t -0.8t2 meters in t seconds
a) find the rock's velocity and acceleration at time t.(the acceleration of gravity due to the moon)
b) how long does it take the rock to reach its highestpoint?
c) how high does the rock go?
d) how long does it take the rock to reach half itsmaximum height?
e) how long is the rock aloft

The inequality to model the situation will be 24b ≤ 250

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Based on the information, the inequality to model the situation will be 24b ≤ 250. The number of baseball will be:

24b ≤ 250

b ≤ 250 / 24

b ≤ 10

The number of baseball will be 10 or less.

Learn more about inequalities on:

brainly.com/question/24372553

#SPJ1

Step-by-step explanation:

Since, Point E is the midpoint of DF

Therefore,

DE = EF

10x = 4x + 12

10x - 4x = 12

6x = 12

x = 12/6

x = 2

EF = 4x + 12 = 4*2+12 = 8 * 12 = 20

EF = 20

AB = BC

6x + 2 = 9x - 10

10 + 2 = 9x - 6x

12 = 3x

12/3 = x

x = 4

BC = 9x - 10 = 9*4 - 10 = 36 - 10 = 26

Answer: \(3^{\circ}C\)

Step-by-step explanation:

Given

The temperature on Monday was \(-5^{\circ}C\)

By Tuesday, it becomes \(-2^{\circ}C\)

Change in temperature is the difference between the two temperatures.

\(\Rightarrow \Delta T=-2-(-5)\\\Rightarrow \Delta T=-2+5\\\Rightarrow \Delta T=3^{\circ}C\)

Therefore, the change in temperature is \(3^{\circ}C\).

Answer:

D. im answering for the purpose of the first person getting brainliest

Step-by-step explanation:

Step-by-step explanation:

V epual to L x W x H

9.6cm x 0.8cm

9.6

x 0.8

46

Answer:

12 cm

Step-by-step explanation:

\(v_{eraser} = area \: of \: base \times height \\ \\ \therefore \: area \: of \: base = \frac{v_{eraser}}{height} \\ \\ = \frac{9.6}{0.8} \\ \\ = 12 \: cm\)

Answer:

6=b

Switch sides

b=6

Answer:

a=10 and b=6

Step-by-step explanation:

it is in picture

Please mark me as brainliest

Answer:

Square

4,4,4

Step-by-step explanation:

Note the derivative rule

\(\\ \boxed{\star\bf \dfrac{d}{dx}(x^n)=nx^{n-1}}\)

Let's see

\(\\ \rm\Rrightarrow \dfrac{d}{dx}(2^{x+1}-2^{x-1})\)

\(\\ \rm\Rrightarrow \dfrac{d}{dx}2^{x+1}-\dfrac{d}{dx}2^{x-1}\)

\(\\ \rm\Rrightarrow (x+1)2^{x+1-1}-(x-1)2^{x-1-1}\)

\(\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^{x-2}\)

\(\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x/2^2\)

\(\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x2^{-2}\)

\(\\ \rm\Rrightarrow 2^x(x+1-(x-1)2^{-2})\)

\(\\ \rm\Rrightarrow 2^x(x+1-x/4-1/4)\)

There are number of factors of 36 are 9 and number of array Courtney can make with the photo is 9.

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

In math, an array refers to a set of numbers or objects that will follow a specific pattern.

the arrays can Courtney make with the 36 photos are,

1 by 36,

36 by 1,

2 by 18,

18by 2,

3 by 12,

12 by 3,

4 by 9,

9 by 4,

6 by 6.

the factors of 36 are,

1, 2, 3, 4, 6, 9, 12, 18, 36

∴ 9 ( factors ) = 9 ( arrays )

Therefore, there are number of factors of 36 are 9 and number of array Courtney can make with the photo is 9.

To learn more about factors visit : brainly.com/question/26923098

#SPJ4

Answer:  

c

Step-by-step explanation:  

Answer:

1/4

Step-by-step explanation:

Hadley paddle 8/3 miles per hour or \(2\frac{2}{3}\) miles per hour.

What is unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given that Hadley paddled a canoe for 2/3 mile in 1/4 hour.

In other word,

After 1/4 hour, he can cover 2/3 mile.

Now applying unitary method,

After 1 hour, he can cover (2/3) ÷ (1/4) mile.

Now convert division sign to multiplication, by taking reciprocal of the second fraction:

= (2/3) × (4/1) mile

Now multiply the denominator with denominator and numerator with numerator:

= (2 × 4)/ (3 × 1) mile

= 8/3 mile

Rewrite the improper fraction into mixed fraction:

= (6/3) + (2/3) miles

= 2 + (2/3) miles

= \(2\frac{2}{3}\) miles

To learn more about speed, click on below link:

https://brainly.com/question/26048961

#SPJ4

Answer:

1.440kg

Step-by-step explanation:

12 × 120=1440g

converting g to kg, divide by 1000 as 1000g = 1kg

Answer is therefore given as 1.440kg

Answer:

vertex is (6, -11)

Step-by-step explanation:

Given equation
f(x) = x² - 12x + 25

is that of an upward-facing parabola(since the coefficient of x² is positive).

The vertex will be at a minimum and its x-coordinate can be found by finding the first derivative of f(x), setting it equal to zero and solving for x

f'(x) = d/dx(x² - 12x + 25)

= 2x - 12

f'(x) = 0 ==> 2x - 12 = 0

2x = 12

x = 6

Substitute x = 6 in f(x) to get

f(6) = 6² - 12(6) + 25

= 36 - 72 + 25

= -11

So the vertex is at (6, -11)

Answer:

90

Step-by-step explanation:

each dot = 45 bc 540 / how many dots there are which is 12 = 45 then there are 2 dots worth of 45 making it 90

math

540/12=45

45 x 2 = 90

Answer: 135 students

Step-by-step explanation:

1. Divide 540 (total number of students) by the number of dots (12)

2. So then 540/12= 45

3. Then see how many dots are more then 5 miles away so that is 3 dots (2dots on 6 miles, and 1 dot on 7 miles)

4. After 45*3= 135

Given:

Answer: 5

Answer:

254.47 m or B

Step-by-step explanation:

First you find the area of the circle and then you subtract it from the area of the square to get your answer.

Hope it helps c:

Answer: Choice A) about 69.53 m^2

==========================================================

Work Shown:

A = area of the square

A = side*side

A = 18*18

A = 324 square meters

---------

B = area of the circle

B = pi*r^2

B = pi*9^2 ..... note that the radius is half the diameter

B = 81pi

B = 254.469004940773

B = 254.4690 square meters

I used the calculator's stored version of pi to compute that approximate value.

---------

C = area of shaded region

C = A - B

C = 324 - 254.4690

C = 69.531

C = 69.53 square meters

So that points us to choice A as the final answer.

---------

Side note: The shaded region is about C/A = (69.531)/(324) = 0.2146 = 21.46% of the square's area. So this is the approximate chances of landing in the shaded area if you randomly threw a dart.

Answer:

No, she was very close though.

Step-by-step explanation:

Add 81, 87, 91, and 141 and you get 400. Then add 100, 100, 100 and 150 and get 450. then you put 400/450 which equals 88.88... But Jada needs a 80% so she was close but not quite there. :P

No, Jada do not 90% of total possible points.

To determine the volume or chance of commodity in terms of 100, use the chance formula. Per cent simply means one in a hundred. With the chance formula, a number between 0 and 1 can be expressed. A number that's expressed as a bit of 100 is what it is. It's substantially used to compare and determine rates and is represented by the symbol.

Given:

Total of Jada's points = 142 + 87 + 81 + 91

                                    = 401

and, Total points maximum = 150+ 100 + 100 + 100

                                              = 450

So, 90% of total points is

= 90% of 450

= 0.9 x 450

= 405

and, For Jada's total points the percent is

= 401/ 450 x 100

= 0.8911111 x 100

= 89.11 %

So, We have the question "Does Jada have 90% of the total possible points before the final test?"

Thus, No Jada do not 90% of total possible points.

Learn more about Percentage here:

https://brainly.com/question/29306119

#SPJ2

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

Answer:

14: 1/5, 0.35, 12/25, 0.5, 4/5

17: -2 4/5,-2.6, -2.3

18: -6.0, -0.72, -5/8, -7/12

19: 1.2, 1 1/3, 1.45, 1 1/2

20: -3.0, -0.35, 0.5, 0.55

Fraction Into Decimal:

14: 1/5=0.2, 12/25=0.48, 4/5=0.8

17: -2 4/5= -2.8

18: -5/8= -0.625, -7/12=-0.583 (3 is repeated)

19: 1 1/2= 1.5, 1 1/3= 1.3 (3 is repeated)

Explanation:

To start with, you need to convert the fractions into decimals in order to compare them easier

Then, for the negatives, it might be confusing but the bigger negative will be smaller since it's further away from 0 on a number line

Also, for #19, obviously, the negatives go first but for 0.5 and 0.55, it's kinda hard to compare but for 0.5, just add a zero at the end to extend the decimal and compare it. It would become 0.50 and 0.55 would then clearly be greater.

Hope this helped! Please give me brainliest if it did! You don't have to if you don't want to but I spend a lot of time on this, haha!

The volume of the pyramid is approximately 5.9 cm³.

To find the volume of a pyramid with a square base, you can use the formula:

Volume = (1/3) * base area * height

First, let's find the area of the square base. The perimeter of the base is given as 5.7 cm, which means each side of the square has a length of 5.7 cm / 4 = 1.425 cm.

The area of a square is given by the formula:

Area = side length * side length

Substituting the side length, we have:

Area = 1.425 cm * 1.425 cm = 2.030625 cm²

Now, we can calculate the volume of the pyramid:

Volume = (1/3) * base area * height

= (1/3) * 2.030625 cm² * 8.6 cm

= 5.91834375 cm³

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is approximately 5.9 cm³.

Learn more about pyramid

brainly.com/question/13057463

#SPJ11

Answer:

n = cdm/ab

Step-by-step explanation:

Solving for n:

a. Jump with a bobbing motion: Shortest jump  b. Jump from deep knee flexion: Intermediate jump

c. Jump with fully extended knees: Longest jump ,In the long jump activity, three different jumping techniques were observed:

a) The bobbing motion involved bending and extending the knees and arms during the jump.

b) Starting from deep knee flexion meant initiating the jump from a position with knees bent and no motion prior to the jump.

c) Starting with fully extended knees involved jumping with the knees straight and no motion before the jump. During the performance, the lengths of each jump were measured. Trial results consistently indicated that the jump with the bobbing motion had the shortest length, while the jump starting from deep knee flexion had an intermediate length. The jump with fully extended knees consistently achieved the longest distance.

The observations reveal that starting the jump with fully extended knees and no knee motion results in the longest jump. The bobbing motion with knee and arm movements leads to the shortest jump. Deep knee flexion position falls between the two in terms of jump length.

To know more about bobbing visit:

https://brainly.com/question/32261353

#SPJ11

Answer:

if it does not overlap then you just find the possibility if one occurs.

Step-by-step explanation:

Answer:

If events A and B are non-overlapping, then to find their probability we just need to add the probability of each even occurring which will given us A or B.

\(6=\textit{oz of solution at x\%}\\\\ ~~~~~~ x\%~of~6\implies \cfrac{x}{100}(6)\implies \cfrac{6x}{100} \\\\\\ 9=\textit{oz of solution at 0\%}\\\\ ~~~~~~ 0\%~of~9\implies \cfrac{0}{100}(9)\implies 0 \\\\\\ \textit{15 oz of solution at 16\%}\\\\ ~~~~~~ 16\%~of~15\implies \cfrac{16}{100}(15)\implies 2.4 \\\\[-0.35em] ~\dotfill\)

\(\begin{array}{lcccl} &\stackrel{oz}{quantity}&\stackrel{\textit{\% of oz that is}}{\textit{acid only}}&\stackrel{\textit{oz of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&6&\frac{x}{100}&\frac{6x}{100}\\ \textit{2nd Sol'n}&9&0&0\\ \cline{2-4}&\\ mixture&15&0.16&2.4 \end{array}~\hfill \begin{cases} 6 + 9 = 15\\\\ \frac{6x}{100}+0=2.4 \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 2nd equation}}{\cfrac{6x}{100}=2.4}\implies \cfrac{3x}{50}=\cfrac{24}{10}\implies 30x=1200 \\\\\\ x=\cfrac{1200}{30}\implies \boxed{x=\stackrel{\%}{40}}\)

Colby would have 100 bacteria (50 x 2), after 4 hours, he would have 200 bacteria (100 x 2). Jaquan would have 100 bacteria (50 x 2), after 6 hours, he would have 200 bacteria (100 x 2).

In Colby's experiment, the number of bacteria doubles every 2 hours. This means that after 2 hours, Colby would have 100 bacteria (50 x 2), after 4 hours, he would have 200 bacteria (100 x 2), and so on. If we want to calculate how many bacteria Colby will have after x days, we need to convert the days to hours by multiplying x by 24 (since there are 24 hours in a day). So, the equation to model Colby's experiment would be:

y = 50(2)^(x*24/2)

In Jaquan's experiment, the number of bacteria doubles every 3 hours. This means that after 3 hours, Jaquan would have 100 bacteria (50 x 2), after 6 hours, he would have 200 bacteria (100 x 2), and so on. Again, if we want to calculate how many bacteria Jaquan will have after x days, we need to convert the days to hours by multiplying x by 24. So, the equation to model Jaquan's experiment would be:

y = 50(2)^(x*24/3)

Both experiments follow exponential growth models, but with different doubling times. By plugging in different values of x, we can see how the number of bacteria changes over time for each experiment. It's important to note that these models assume ideal conditions and may not perfectly reflect the actual results of the experiments.

Learn more about equation brainly.com/question/10413253

#SPJ11

Answer:

a. r = d/t, 145(rate) = 145(distance)/1(time)

b. The second train is travelling faster

The first train has a rate of 145 mph the second has a rate of 150 mph since r = 300 miles/2 hours = 150

Therefore the second train has a rate of 150 mph while the first train has rate of 145 mph

Answer:

2(x+3)=x-4

2x+6=x-4

2x-x=-4-6

x=-10

The probability that in a randomly selected year, the number of lightning strikes is 4, is 0.098.

What is Poisson distribution?

The Poisson distribution refers to a probability distribution expressing the probability of a specific number of events occurring in a fixed interval of time, if these events occur with a known constant mean rate and independent of the occurrence of the last event.

P(E) = Probability of occurrence of E in a fixed interval 'x', with constant mean = \(\frac{e^{-mean}. mean^{x}}{x!}\)

Step-by-step explanation:

Let A be the number of lightning strikes in a year at the top of particular mountain. Here, A follows Poisson distribution with mean = 2.1.

According to the question, x = 4, mean = 2.1

Thus, putting it in the formula for Poisson distribution, we get:

P(A) = \(\frac{e^{-2.1}(2.1)^{4} }{4!}\) = \(\frac{0.122(19.44)}{24}\) = 0.098

=> P(A) = 0.098

Hence, the probability that in a randomly selected year, the number of lightning strikes is 4, is 0.098.

To learn more about the Poisson distribution, refer to the link:

https://brainly.com/question/10196617

#SPJ4