Answer:
A) 2.45 seconds
B)[tex]\begin{center}\begin{tabular}{ c c}\bold{Average Velocity} & \bold{Velocity at strike of water} \\ 39.18 & 78.4 \\ \end{tabular}\end{center}[/tex]
Step-by-step explanation:
Distance [tex]s[/tex] (in feet) from the top of cliff after [tex]t[/tex] seconds when a rock is dropped off the edge of a cliff is given as:
[tex]s(t)=16t^2[/tex]
Distance from the top of cliff to water = 96 ft
To find:
A) When will the rock strike the water
i.e. The time taken by the rock to travel the distance of 96 ft.
B) Table of Average Velocity and approximate velocity at which the rock strikes the water ?
Solution:
A) Given that distance traveled = 96 ft
To find the value of [tex]t[/tex]
Putting the value of [tex]s[/tex] in formula: [tex]s(t)=16t^2[/tex] to find [tex]t[/tex]:
[tex]96 = 16t^2\\\Rightarrow t^2=6\\\Rightarrow \bold{t = 2.45\ sec}[/tex]
B) The velocity at which the rock hits the water:
We need to differentiate [tex]s(t)[/tex] w.r.to [tex]t[/tex] in order to find the velocity at any instant.
[tex]s'(t) =\dfrac{d}{dt}s(t) = \dfrac{d}{dt}(16t^2)\\\Rightarrow v = 2\times 16t^{(2-1)}\\\Rightarrow v = 32t[/tex]
The time taken to reach the water is 2.45 seconds.
Putting [tex]t[/tex] = 2.45 seconds to find the velocity:
[tex]v = 32\times 2.45 = 78.4\ ft/sec[/tex]
Average velocity is given as total distance traveled and total time taken.
[tex]\text{Average Velocity = }\dfrac{\text{Total Distance traveled}}{\text{Total Time Taken}}[/tex]
[tex]\text{Average Velocity = }\dfrac{96}{2.45}\\\text{Average Velocity = 39.18\ ft/s}[/tex]
[tex]\begin{center}\begin{tabular}{ c c}\bold{Average Velocity} & \bold{Velocity at strike of water} \\ 39.18 & 78.4 \\ \end{tabular}\end{center}[/tex]
Point Fis on line segment EG . Given FG = 4 and EF = 9 determine the length EG
Answer:
EG is 13.
Step-by-step explanation:
So we have a line segment EG.
Point F is somewhere on EG.
And we are given that FG is 4 and EF is 9.
Therefore, the length of EG will be the combined lengths of FG and EF. In other words:
[tex]EG=EF+FG[/tex]
Substitute 9 for EF and 4 for FG. Thus: "
[tex]EG=9+4[/tex]
Add:
[tex]EG=13[/tex]
So, the length is EG is 13.
And we're done!
simply 12 to the power of 16 over 12 to the power of 4
Answer:
12^12
Step-by-step explanation:
If the exponent bases are the same you can subtract the exponents. Numerator minus denominator. (16-4=12)
A cyclist rides his bike at a rate of 15 miles per hour. What is this rate in miles per minute? How many miles will the cyclist travel in 10 minutes?
Answer:
This is 0.25 miles per minute
The cyclist would travel 2.5 miles in 10 minutes
Step-by-step explanation:
The equation to convert miles per hour to miles per minute is to divide by 60, the number of minutes in an hour.
Michael drove 0.5 miles. How many inches did he travel?
Answer:
31680 inches
Step-by-step explanation:
To find miles to inches, multiply by 63360 to get the answer.
0.5 x 63360 = 31680
So, he traveled 31680 inches.
The picture shows the Alamillo bridge in Seville, Spain. In the picture m<1=58 and m<2=24. Find the measure of the supplement of <1= and of <2. Someone please help!
Answer:
Supplement of <1 = 122°
Supplement of <2 = 156°
Step-by-step explanation:
Two pairs of angles are said to be supplementary, if their measures in degrees add up to give us 180°. A supplement of am angle is simply 180° - the measure of that angle.
Given that meadure of angle 1 = 58°, the supplement of angle 1 = 180° - 58° = 122°
Also, if the measure of angle 2 = 24°, the supplement of angle 2 = 180° - 24° = 156°.
Thus:
Supplement of <1 = 122°
Supplement of <2 = 156°
Carla is making bracelets she wants to put 10 charms on each bracelet charms are sold in packets of 12 what is the least number of packages she can buy to make bracelets with no charms left over
Answer:
Carla can buy 5 packets of charms.
Step-by-step explanation:
5 packets of charms would be able to make 6 bracelets.
*please give me brainliest, i only need three more*
can someone help me please
[tex]\large{\bf Step-by-step~explanation:}[/tex]
To simplify this expression, we combine all the like terms. We cannot solve for x because there is no equal sign and/or no value for x.
Equation: (10x² - 10x - 6) + (x + 6)
[tex]\bf Step~1:[/tex]
-10x and x are like terms. Remember: there is an invisible 1 behind the variable x. We add these like normal numbers.
[tex]\bf -10x+1x=-9x[/tex]
[tex]\bf Step~2:[/tex]
-6 and 6 are also like terms. Again, we add them as written.
[tex]\bf -6+6=0[/tex]
Since our answer is 0, we do not have to write it in our simplified expression.
[tex]\bf Step~3:[/tex]
Now, let's add the terms together. Since 10x² doesn't have any like terms, we just let it be. We take our previous number, -9x, and we add it to 10x².
[tex]\bf 10x^2+-9x[/tex]
[tex]\large\boxed{\bf Our~final~answer:10x^2-9x}[/tex]
Point B lies on AC between A and C. If AB = 8 and AC = 10, find BC.
A. 2
B. 8
C. 10
D. 18
Answer:
BC = 2
Step-by-step explanation:
If B lies on AC it makes the line segments AB and BC.
AC=10
AB+BC=AC
AB+BC=10
8+BC=10
BC=2
The value of BC is 2 which is the correct answer that would be an option (A).
What is a Line Segment?A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.
The figure given below shows a line segment AC , where the length of line segment AC refers to the distance between its endpoints, A and C.
Point B lies on AC between A and C.
A______________B______________C
Given that B lies on AC it makes the line segments AB and BC.
AB = 8 and AC = 10
⇒ AB + BC = AC
⇒ AB + BC = 10
⇒ 8 + BC = 10
⇒ BC = 2
Therefore, the value of BC is 2 which is the correct answer that would be an option (A).
Learn more about the line segment here:
brainly.com/question/25727583
#SPJ5
Solve the equation.
-4+x= 12
Answer:
x = 16
Step-by-step explanation:
Get x alone on one side.
-4 + x = 12
(-4 + x) + 4 = 12 + 4
x = 16
Karims wage was increased from £210 to £225 per week.What was the percentage increase,to one decimal place? please help iam stuck
Answer: 7.1
Step-by-step explanation: 210/255 • x/100. This equals to 7.142857142857142.
Find the interquartile range for the data. {50, 46, 56, 55, 54, 51, 45, 50, 47}
Answer:
51
Step-by-step explanation:
I think the answer is 51 because you have to find the number between the first three to the middle
Answer:8
Step-by-step explanation:
For the diagrams, find the following measures.
X=
DCB=
ABC=
Dave is helping his grandmother make trail mix. His grandmother asks him to add 1/5 cup of fruit for 1/3 every cup of nuts.
To satisfy his grandmother’s request, Dave must mix
cups of fruit for a single cup of nuts.
Answer:
3/5 cup of fruit for every 1 cup of nuts
p=s1t-s2t. Which equation sauce for tea........................
Answer:
f444444444444444444444444Step-by-step explanation:
f
is the quotient of two rational numbers always a rational number explain
Plz help me answer this
Answer:
sure
Step-by-step explanation:
Find the distance between (-4,5) and (4,0) round to the nearest hundredth
Answer:
Solution: 9.43
Step-by-step explanation:
Remember that we can determine the distance between any two points using the distance formula, d = √(x₂ - x₁)² + (y₂ - y₁)². Let's substitute known values to determine the distance:
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2},}\\ \\\\\mathrm{d}= \sqrt{(4 - (-4))^2 + (0 - 5)^2} = \sqrt{(4 + 4)^2 + (- 5)^2} \\= \sqrt{(8)^2 + 25} = \sqrt{64 + 25} = \sqrt{89}[/tex]
Hence the distance between the points (-4,5) and (4,0) is exactly √89. The question asks us to round off to the nearest hundredth, so your solution will be approximated off to two digits → 9.43.
PLEASE HELP! WILL GIVE BRAINLIEST!
Answer:
(18+21+17+x)÷4=20
x=24 students
Step-by-step explanation:
(18+21+17+x)÷4=20
(56+x)÷4=20
56+x=20*4
56+x=80
x=80-56
x=24
The manager of a factory collected data in order to analyze the relationship
between the number of hours of training a worker receives and
the worker's error rate. The line of best fit for the collected data is y = 0.1 -0.005x, where x is the number of hours of training a worker
receives and y is the error rate.
What approximate error rate should the manager expect for a worker who receives 6 hours of training?
O A. 0.01
OB. 0.07
OC. 0.13
OD. 0.17
Answer:
B. 0.07
Step-by-step explanation:
You can use the "Desmos Graphing Calculator". It helps a lot.
Answer:
B
Step-by-step explanation:
The list below shows the amount of money Hannah earned mowing lawns for the past five weeks.
$40, $15, $20, $40, $35
Which measure shows that the amount of money she earned varied?
Answer:
the answer is mean
Step-by-step explanation:
10 less than a number is equal to 12
Answer:
The number is 22
Step-by-step explanation:
Let x be the number
Plug x in: x - 10 = 12Add 10 to each side, so it now looks like this: x = 22Answer:
22
Step-by-step explanation:
Let the number be x:
x - 10 = 12
x = 12 + 10
x = 22
The answer is 22
3 over 3 - square root 5
Answer:
-1.236.
Step-by-step explanation:
3/3 = 1.
√5 = 2.236.
1.000 - 2.236 = -1.236.
the answer is negative because the smaller number is subtracting the larger number..........u just subtract the normal way,( the larger number take away the smaller number), but u should insert a negative sign to the answer.
Please Help! Thank u!
16=4
49=7
289=17
Step-by-step explanation:
Using inductive reasoning, what number is the most reasonable conjecture for the next number in the pattern 27,23,19,15,
Answer:
11
Step-by-step explanation:
Each number in the sequence decreases by 4, so the next reasonable number would be 11 (15-4=11)
Tracy bought 5 trays of plants for $105.
Each tray contained 12 plants.
Each plant cost the same amount.
Plants can be purchased individually.
How much more money will Tracy need to spend for 15 additional plants?
Answer:
8.75
Step-by-step explanation:
Answer:
$1150
Step-by-step explanation:
If 5stray cost $105
X=$105 ×15 =$1575
f(x) = -3x + 4; Find f(2), f(0), and f(-4). (Select all that apply.) f(2)= 10 f(2) = -2 f(0) =4 f(0) = 0 f(-4) = 16 f(-4) = -8
Answer:
(f)2=-2, (f)0=4 and (f)-4=6
Step-by-step explanation:
f(2)= -3(2)+4
-6+4=
-2
f(0)=-3(0)+4
=4
f(-4)=-3(-4)+4
-6+4
=
-2
I hope this helps.
A rock has a density of 4.56 g/mL. If it weighs 235 g, what is its volume?
Answer:
51.54mL
Step-by-step explanation:
Density can be defined as the mass per unit volume of a particular object , substance or compound.
Density tell us how heavy or dense that object, substance or compound is.
Mathematically, the formula for Density = Mass(grams)/Volume(ml or cm³)
In the above question, a rock has the following criteria:
Density = 4.56 g/mL.
Mass = 235 g
Volume is unknown.
Imputing this values into the formula for Density, we have:
4.56g/mL = 235g/ Volume
Cross Multiply
4.56g/mL × Volume = 235g
Volume = 235g/4.56g/mL
Volume = 51.535087719mL
Approximately, the volume of the rock to 2 decimal places = 51.54mL
How much is 571,863 rounded to the nearest thousand?
Answer:
572000
Step-by-step explanation:
571863 is rounded of to 572000
Because 8 in 571863 is greater than 5
And thus 1 in 571863 changes to 2 with the rest on the right being zero.
Leanne works at a restaurant. For dinner, there is a choice of 3 main dishes and 2 sides.
Main Dish: Burger(B), Chicken (C), Pasta (P)
Sides: Apple (A), Fries (6)
Leanne lists all possible ways a person could order their dinner. She lists these combinations:
BA, BF, CA, CF, PA, PF, AB, FB, AC, FC, AP, FP.
Is Leanne correct? Use the drop-down menus to explain your reasoning.
Click the arrows to choose an answer from each menu.
For each main dish, there are Choose... different sides a person can choose. So, there are
a total of Choose... possible ways a person could choose their dinner. Leanne is
Choose...
Answer:
I feel like its that but im rlly not sure.
Step-by-step explanation:
Leanne's list is incorrect and there are 3 different sides a person can choose. So, there are a total of 6 possible ways a person could choose their dinner.
How to determine the number of combinations?The given parameters are:
Main Dish: B, C and P
Sides: A and F
Using the above parameters, the combination of dishes are:
BA, BF, CA, CF, PA and PF
Hence, we can conclude that Leanne list is incorrect
Also, we have:
Dish = 3
Sides = 2
So, the number of dinner to choose is:
Dinner = 3 * 2 = 6
Hence, a person could choose their dinner in 6 ways
Read more about combination at:
https://brainly.com/question/11732255
#SPJ2
M=2*2*3*5*5 and N=2*2*2*3*3*7 find the largest number that divides exactly M and N please
Answer:
6
Step-by-step explanation:
Given the prime factors of both numbers
Then the greatest common factor GCF is the product of the common factors
Both 2 and 3 are common factors, thus
2 × 3 = 6 is the GCF