Answer: p(t) = (-16 ft/s^2)*t^2 + (57.4 ft/s)*t
Step-by-step explanation:
We can suppose that the only force acting on the object is the gravitational force, then the acceleration of the object will be equal to the gravitational acceleration.
Then we can write:
a(t) = -32 ft/s^2
Where the negative sign is because this acceleration is downwards.
Now, to get the vertical velocity of the object, we need to integrate over time to get:
v(t) = (-32 ft/s^2)*t + v0
where t represents time in seconds and v0 is the constant of integration, and in this case, is the initial vertical velocity.
In this case, the initial velocity is 57.4 ft/s upwards, then the velocity equation is:
v(t) = (-32 ft/s^2)*t + 57.4 ft/s
To get the position equation we need to integrate over time again, to get:
p(t) = (1/2)*(-32 ft/s^2)*t^2 + (57.4 ft/s)*t + p0
Where p0 is the initial height of the object, as it was launched from the ground, then the initial position is p0 = 0ft.
then the position equation (that is the function that represents the height of the object as a function over time) is:
p(t) = (1/2)*(-32 ft/s^2)*t^2 + (57.4 ft/s)*t
p(t) = (-16 ft/s^2)*t^2 + (57.4 ft/s)*t
what is -4(x+3)=16-4x
Answer:
There is no solution
Step-by-step explanation:
-4(x+3)=16-4x
expand
−4x−12=16−4x
cancel out
−12=16
because −12=16 is false there is no solution.
Hope this helps :)
The graph of the piecewise function f(x) is shown.
What is the range of f(x)? On edg
which expressions are equivalent to k/2?
A) k - 2
b) 2/k
c) 1/2k
D) k divided by 2
E) k+k
Answer:
C
Step-by-step explanation:
think of a random K number (like 3 for example)
1/2(3) = 3/2
this equals k/2 = 3/2
Which equation is true?
Answer:
2nd option is correct answer
Answer:
-56/8 = -7
Step-by-step explanation:
Please help would mean a lot
Answer: What grade work is this? I think I can help...
Step-by-step explanation:
Julie went to Chili's for dinner with some friends. Her meal total was $15.60 and she wants to leave a 20% tip. What will be her total cost for her meal including the tip?
Two friends share 4 oranges equally. how much does each friend get?
Answer:
2
Step-by-step explanation:
4 divided by 2
Answer:
2 oranges
Step-by-step explanation:
because half of 4 oranges is 2
plz follow me
Use the discriminant to determine the nature of the roots of the following equation.
x2 + 2x + 5 = 0
imaginary root
Double root
real and rational root
real and irrational root
Answer:
Step-by-step explanation:
disc.=b²-4ac=2²-4×1×5=4-20=-16<0
it has imaginary roots.
Will give Brain!! To this
Answer: 13.2
Step-by-step explanation:
the ratio between the given measurements (11 and 5) is 2.2 [5 x 2.2 = 11]
so, i just multiplied 6 by 2.2 , which equals 13.2 .
hope this helps! xoxo
Answer:
13.2
Step-by-step explanation:
6x2.2=13.2 The triangles are equal and its size is increased by 2.2
20 inchs of gold chain we used 3/8 how much is left?
Answer:
12.5 inches
Step-by-step explanation:
3/8 of 20 = 3/8 * 20 = 60/8 = 15/2 = 7.5
20 - 7.5 = 12.5
Answer:
12.5 inches
Step-by-step explanation:
20/8=2.5
2.5*3=7.5
20-7.5=12.5
PLEASE THIS IS URGENT!!
(08.02)Which of the following graphs best represents the solution to the pair of equations below?
y = x + 1
y = −x − 1
Answer:
The 2nd one. With the intersection to the left of the y-axis on the x-axis
Step-by-step explanation:
Zoe went shopping for a new pair of pants. The listed price of the pair of pants was
$45, but the price with tax came to $46.35. Find the percent sales tax.
ASAP!
Answer:
3%
Step-by-step explanation:
46.35 - 45 = 1.35 (change)
change/original price X 100
1.35/45 = 0.03
0.03 X 100 = 3
sales tax 3%
A boarding school distributes 5% of its actual profit Rs.97440 among 20 teachers as a bonus. Find the bonus amount that the each teacher get.
Solve 6 - 5x = 7 + 3x
Answer:
hol up
x=-1/8 negative one over eight
Step-by-step explanation:
Olivia is half the age of her brother, Adam. Olivia's sister, Ava, is twice as old as Adam. Adam is 4 years old. How old is each sibling?
Answer:
Step-by-step explanation:
Adam's age = 4 years
Ava's age = 2 * 4 = 8 years
Olivia's age = 4 ÷ 2 = 2 years
Answer:
Step-by-step explanation:
Adam is 4 years old.
Ava's age = 2 * 4 = 8 years old
Olivia's age = 4 ÷ 2 = 2 years old
A farmer bought 36 ducks and 52 pigeons. Approximately how many birds did the farmer buy?
PLEASE HELP: There is a cylinder with 2 hemispheres on each side, the radius is 6 and the height is 11. Find the surface area and volume.
Use 3.14 as pi
Here is a number machine
Sam writes on a white board the positive integers from 1 to 6 inclusive, once each, She then writes p
additional fives and q sevens on the board. The mean of all the numbers on the board is then 5.3.
What is the smallest possible value of q?
Answer: The smallest possible value of q is 9.
Step-by-step explanation:
If we have the set of N numbers:
{x₁, x₂, x₃, ..., xₙ}
The mean of this set is:
M = (x₁ + x₂ + x₃ + ... + xₙ)/N
Now, in this case our set is:
{1, 2, 3, 4, 5, 6, p times 5, q times 7}
Then we have a total of:
6 + q + p numbers.
The mean of this set will be:
Mean = 5.3 = (1 + 2 + 3 + 4 + 5 + 6 + p*5 + q*7)/(6 + p + q)
This is the equation that we will use now.
First, we can simplify this as:
5.3 = (21 + p*5 + q*7)/(6 + p + q)
Now we can pass the denominator in the right to the other side as:
5.3*(6 + p + q) = (21 + p*5 + q*7)
31.8 + p*5.3 + q*5.3 = 21 + p*5 + q*7
Now we want to isolate the variable p in one side of the equation.
p*5.3 - p*5 = 21 - 31.8 + q*7 - q*5.3
p*0.3 = q*1.7 - 10.8
p = (q*1.7 - 10.8)/0.3 = q*(1.7/0.3) - 36
p = q*(1.7/0.3) - 36
p = q*(17/10)*(10/3) - 36
p = q*(17/3) - 36
Now we can see that the denominator is 3, so q should be a multiple of 3.
We want to start with the smallest multiples of 3, but if we use q = 3, then we will have a negative value of p (the same happens if we use 1 = 6)
We do not want that, then we need to use q = 9
p = 9*(17/3) - 36
p = 3*17 - 36
p = 15
Then we have;
9 times the number 7
15 times the number 5 (plus one, because it was already on the first 6 numbers that Sam wrote)
The smallest possible value of q is 9.
Now we want to get the smallest possible value of q.
Remember, p and q need to be positive numbers.
What is the mean of 84 85 85 86 90 92
Answer: The mean is 87
84+ 85 + 85+ 86 +90+ 92 = 522/6 = 87
Step-by-step explanation:
Answer:
87
Step-by-step explanation:
To find the mean of the a set of numbers, we first need to add all the numbers and divide by the number of terms in the set.
84 + 85 + 85 + 86 + 90 + 92 = 522
There are 6 terms so we divide by 6
522/6 = 87
Describe at least two events where a probability is 100% PLEASE HELP BRAINLIST!
Answer:
1) The probability that at least 2 support Green is 1 minus the probability that 0 people or 1 person supports Green
2) The probability that exactly 1 person supports Green
Step-by-step explanation:
Find the volume of a cylinder that has a diameter of 12 cm and a height of 5
cm. Use 3.14 for pi and round to the nearest tenth. *
Answer:
V≈565.5cm³ is the answer
A standard six-sided die is rolled. What is the probability of rolling a number greater than 5 ? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
Answer:
the probability is one in 6
Step-by-step explanation:
there are 6 sides on a basic die and so the only number higher than 5 is 6. you have a 1/6 chance.
elimination method -2x-7y=13 and 3x+6y=15
Answer:
The answer is (61/3), (-23/3)
Step-by-step explanation:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Hoped this helped!
∠A and \angle B∠B are vertical angles. If m\angle A=(6x-11)^{\circ}∠A=(6x−11) ∘ and m\angle B=(5x+4)^{\circ}∠B=(5x+4) ∘ , then find the measure of \angle B∠B.
Answer: [tex]\angle B=79^{\circ}.[/tex]
Step-by-step explanation:
When two lines cross each other , then the opposite angles are known as vertical angles.
Vertical angles are equal.
Here, ∠A and ∠B are vertical angles.
So, ∠A = ∠B
If [tex]\angle A=(6x-11)^{\circ}[/tex] and [tex]\angle B=(5x+4)^{\circ}[/tex]
Then , [tex]6x-11=5x+4[/tex]
Subtract 5x from both sides, we get
[tex]x-11=4[/tex]
Add 11 on both sides, we get
[tex]x=15[/tex]
Now , [tex]\angle B=(5(15)+4)^{\circ}=79^{\circ}[/tex]
Hence, the measure of [tex]\angle B=79^{\circ}.[/tex]
Laws of indices
a) b^4 x b^5
b) x^6 devided by x
c) 5x^2 x 3x^4
d) 21c^8 devided by 7c^7
Answer:
a) b^4×b^5
hope it helps..,
5. Rule: Add 2, add . First term: 12
what are the first twelve numbers
Answer:
if your going up it is 12 14 16 18 20 22 24 26 28 30 32 34 if you go down 12 10 8 6 4 2 0
The distribution of 4 in the following expression (5+s)4
Answer:
( 5 + s ) 4 = 20 + 4 s
Step-by-step explanation:
Distribution property
Let a, b and c are numbers then distribution property is defined by
a( b + c) = a b + a c
(a+ b) c = a c + b c
Given that
( 5 + s ) 4 = 5× 4 + s× 4
= 20 + 4 s
Final answer:-
( 5 + s ) 4 = 20 + 4 s
This is a pond in the shape of a prism. It is completely full of water
Colin uses a pump to empty the pond.
The level goes down by 30 cm in the first 30 minutes.
Work out how many minutes Colin has to wait for
the pond to completely empty.
Kindly check picture to the question below.
Answer:
150 minutes
Step-by-step explanation:
Volume of prism = height * base area
Height of prism = 1m
Base area = area of a trapezium
Area of trapezium = 0.5(a + b) h
a, b = parallel sides, h= height of trapezium
Area of trapezium = 0.5(1.4+0.6)*2
Area = 0.5(2)*2 = 2m²
Hence,
V of prism = area of trapezium * height of prism
Volume = 2m² * 1m = 2m³
Decrease in water level due to pumping
20cm decrease in 30minutes
(20/100)m in 30 minutes
0.2 m decrease in height of water
Hence, height of water in prism after 30 minutes pumping :
height - 0.2 = 1 - 0.2 = 0.8m
Volume after 30 minutes of pumping :
Base area * new height
2m² * 0.8m = 1.6m³
Decrease in volume over 30 minutes :
(Initial volume - volume after pumping)
2m³ - 1.6m³ = 0.4m³
If ;
0.4m³ = 30 minutes
1.6m³ = x
0.4x = 48
x = 48 / 0.4
x = 120
Hence, it takes 120 minutes for the remaining 1.6m³ to be emptied.
Hence, total wait time :
120 minutes + 30 minutes
= 150 minutes
dave uses the associative property of multiplication to write an expression that is equivalent to 8 times 5 times b which expression did he write
Answer:
The associative property of multiplication
8 . ( 5. b ) = ( 8. 5) . b
Step-by-step explanation:
Explanation
The associative property of multiplication
a . ( b. c ) = ( a. b) . c
Given numbers are 8, 5 and b
The associative property of multiplication
8 . ( 5. b ) = ( 8. 5) . b
8 . ( 5. b ) = ( 8. 5) . b = 40 b