Answer:
The equation of the position at time t will be:
[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+15[/tex]
Step-by-step explanation:
We can start by saying that the acceleration here is g = -9.81 m/s². The minus sign is because the gravity acceleration is a vector downward (negative value), and the ball is going upward (positive value).
And we know that acceleration can be written as a second derivative:
[tex]g=\frac{d^{2}y}{dt^{2}}=y''[/tex] (1)
Now, we can take the integral in each side:
[tex]\int gdt=\int y''dt[/tex]
[tex]\int y''dt=\int -9.81dt[/tex] (2)
Solving the integral in each side we have:
[tex]y'(t)=-9.81t+C[/tex] (3)
Where y'(t) is the velocity at t time (v = dy/dt = y' ) and c is a constant value.
Now, the initial conditions are:
initial height y(0) = 15 feet
initial velocity y'(0) = v(0) = 64 feet/s
Using this condition we can find C. Let's evaluate equation (3) at t = 0.
[tex]y'(0)=-9.81(0)+C[/tex]
[tex]C=64\: feet/s[/tex]
So we have:
[tex]y'(t)=-9.81t+64[/tex] (4)
Now, we need to take the integral of equation (4) to get the position function:
[tex]\int y'(t)dt=\int (-9.81t+64)dt[/tex]
Solving this new integral we have:
[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+D[/tex] (5)
Using the same method above, we can find D evaluating (5) at t = 0, we have:
[tex]y(0)=-\frac{1}{2}9.81(0)^{2}+64(0)+D[/tex]
[tex]D=y(0)[/tex]
[tex]D=15\: feet[/tex]
Finally, the equation of the position at time t will be:
[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+15[/tex]
I hope it helps you!
What is the quotient of ¾ divided by ½?
3/2 is the quotient when 3/4 is divided by 1/2
How to divide fractions?When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction and this can be obtained by reversing its numerator and denominator—is and then dividing the fractions. Multiply the two numerators after that. Multiply the two denominators after that, After that we need to simplify the fraction to its lowest form.
what is quotient?When we divide one number by another, the result obtained is also known as quotient.
so in order to find the quotient when both fraction is divied
quotient of the division = [tex]\frac{3}{4}[/tex] ÷[tex]\frac{1}{2}[/tex]
=> (3/4) / (1/2)
=> (3/4) * 2
=> 3/2
so quotient of the division = 3/2 or 1.5
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These are the first 5 terms in a fibonacci sequence. 1, 4, 5, 9, 14. Write down the next 2 terms in the sequence
Answer:
The next two terms in the Fibonacci sequence would be 23 and 37.
Step-by-step explanation:
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. So the next term in the sequence is found by adding the two previous terms, like this:
1 + 4 = 5
4 + 5 = 9
5 + 9 = 14
9 + 14 = 23
14 + 23 = 37
What is the factor of 42?
Answer:
Step-by-step explanation:
42 is an even number so it is divisible by 2
42 divided by 2=21
42 has digits that add up to give 6
If the sum of a number adds up to give 3, 6 or 9 that number is divisible by 3
42 divided by 3=14
Factors of 42 are 21 and 2 and 14 and 3 and 42 and 1
What does AA SSS and SAS mean in geometry?
SSS means side side side, SAS means side angle side and AAA means angle angle angle.
There are some postulates which can be used to prove that the two given triangles are similar. If two triangles are similar then we can find as a result that their respective sides and angles are also equal.
If three sides are given then we will use the SSS postulate
If two sides and one angle is given then we will use the SAS postulate
If three angles are given then we will use the AAA postulate.
Therefore SSS, SAS, and AAA are postulated that are used to prove two triangles are similar.
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What is Y =- 2x on a graph?
The equation Y=-2x is a linear equation, which can be plotted on a graph as a straight line.
The equation can be written in slope-intercept form as y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=-2 and the y-intercept is b=0. Therefore, the equation can be written as y=-2x+0.
The slope of the line is negative, meaning that as x increases, y decreases. The y-intercept is zero, which means that the line passes through the origin (0,0).
For example, if x = 2, then y = -2(2) + 0 = -4. Therefore, the point (2, -4) is on the line. Similarly, if x = 4, then y = -2(4) + 0 = -8, so the point (4, -8) is also on the line.
The graph of the equation y=-2x would thus be a line starting at the origin (0,0) with a negative slope. As x increases, y decreases, and the line never crosses the y-axis.
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How do you determine if two pairs of functions are inverses?
First make the graph of the functions, then if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.
Symmetric
A figure or shape that can be divided into two equal parts by a line is called symmetric figures.
Inverse Functions
The inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.
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What is 3 decreased by the quotient of 9 and a number
How to find multiple missing numbers in a given integer array with duplicates in Java?
The best way to find multiple missing numbers in a given integer array with duplicates in Java is to use a hash set and loop.
First, create a HashSet and add all elements from the array to it. Then, loop from 1 to the maximum element of the array and check if each number is present in the HashSet. If the number is not present, it is a missing number. To explain further, a hash set is an efficient data structure for storing unique elements of a collection, and using a loop to check for missing numbers ensures that all numbers from the array are accounted for.
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(a.a+a.b+a.c) +b.a+b.b+b.c)
Answer:
this it's no a math problem
The sum of the two numbers is 36. The larger number is 10 more than the smaller number. What is the larger number?.
If the sum of two numbers is 36 and the larger number is 10 more than smaller number then the larger number is .
the Sum of two numbers is given to be = 36 ;
also given that " larger number is 10 more than smaller number " ;
let the larger number be = "x" , and
the smaller number be = "y" .
So , according to the question ⇒ x + y = 36 ;
and x = y + 10 , putting x in above eqn.
we get , y + 10 + y = 36
2y + 10 = 36
2y = 36 - 10
2y = 26
y = 26/2 = 13
and x = 13 + 10 = 23 .
Therefore , the larger number is 23 .
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What's the inverse of 2?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
the inverse of a number a is [tex]\frac{1}{a}[/tex]
then
the inverse of 2 is [tex]\frac{1}{2}[/tex]
What is length base and height?
The base is the length of one of the triangle's sides, and the height is the distance from that side to the triangle's opposite corner.
What is triangle?A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. Triangle ABC represents a triangle with three vertices: A, B, and C. Any three non-collinear points constitute a unique triangle and, by extension, a unique plane in Euclidean geometry. Triangles are polygons with three vertices that have three sides. The triangle's angles are constructed by joining the three sides end to end at a point. The triangle's three angles add up to 180 degrees.
Here,
The base of the triangle is the length of one of its sides, and the height is the distance from that side to the triangle's opposite corner.
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A label printer prints 5 pages of labels in 4.5 seconds. How long will it take to print 160 pages of labels?
Answer:
144 seconds
Step-by-step explanation:
4.5 seconds = 5 pages
x second = 160 pages
cross multiply
you get: 5x= 160 ×4.5
which equals 720 divide it by 5 you get 144
Brayden is ordering T-shirts for Student Government to
wear during the next volunteer event. He ordered 32 T-
shirts from Mascot Universe. However, Mascot Universe
reduced the price of each T-shirt by $6 for being a school
partner. The total came to $288. Write and solve an
equation to determine the cost per T-shirt.
What is the value of x in the equation
7
- =
9
2/3
x-7?
How many pattern block trapezoids would create 2 hexagons?
Hiya, just need help with this. Thanks
Answer:
C, D
Step-by-step explanation:
Compare each choice with
x² + 5x - 8 = 0
A.
x² + 7x - 9 = 2x + 1
x² + 5x - 10 = 0
No
B.
x² + 4x - 5 = x - 3
x² + 3x - 2 = 0
No
C.
x² + 10x - 2 = 5x + 6
x² + 5x - 8 = 0
Yes
D.
12x + 4 = 7x + 12 - x²
x² + 5x - 8 = 0
Yes
Answer: C, D
How do you find the height of a triangle when you know the base and area?
We can determine the height of a triangle when we know the base and area of the triangle using the area formula of triangle in base and height, that is
A = 1/2 × b × h
A triangle is a three sided polygon. The height of the triangle is the perpendicular distance of the not-included vertex to the considered base.
The formula to determine area of a triangle of base b and height h is
A = 1/2 × b × h
Therefore to determine the height of a triangle when base and area is given, we substitute the given values in appropriate units in the formula.
h = 2×A/ b
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Which equation is the inverse of y x2?
The inverse of function y = x² is ±√x .
What is the inverse of a function?A function from a set X to a set Y assigns exactly one element of Y to each element of X.An inverse function is one that "undoes" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f⁻¹ .Given equation,
y = x²
We have to find the inverse.
By interchanging x and y variables,
y² = x
Solve this equation for y now. This is the inverse of this function.
Take the square root of both sides.
y = ±√x
Then the inverse of the function given is :
f⁻¹(x) = ±√x
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What is a domain of a function examples?
The domain of the function [tex]f(x)=\frac{1}{x}[/tex] is all real numbers except 0.
What is the Domain of function?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's domain is the collection of values it can take as input.
For example, let us take a function [tex]f(x)=\frac{1}{x}[/tex].
For this function, the domain is all the values x can take.
Here x cannot take 0 because 1/0 is not defined.
So, the domain of the function is all real values except 0 which can also be written as:
Domain= R-{0}
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A rectangular sheet of paper 42 cm x 16 cm is rolled along its length and a cylinder is formed . Find the volume of the cylinder
Since a rectangle is rolled along length then circumference of circle is equal to length of rectangle and breadth equals to height.
=) 2*pi*r = 42cm
=) 2*22/7 * r = 42cm
=) r = 42*7 / 2*22
=) r = 147/22 cm
Since Volume of cylinder = pi* r^2*h
= 22/7 * 147/22 * 147/22 * 16 cm^3
= 2245.09 cm^3.
Water flow from a faucet into a tank at the rate of 0. 15 liter per minute, and water leak out of the tank at the rate of 0. 27 liter per minute. If there are 4. 8 liter of water in the tank, how long will it take to empty the tank?
The rate of flow for emptying the tank would be 0.15 liter/minute.
The rate at which the water level in the tank is changing is given by the equation:
ΔV/Δt = flow rate in - flow rate out
where ΔV is the change in the volume of water in the tank, Δt is the time interval over which the change occurs, and flow rate in and flow rate out are the rates at which water flows into and out of the tank, respectively.
In this case, the flow rate is 0.15 liter per minute, and the flow rate out is 0.27 liter per minute. The volume of water in the tank is 4.8 liters.
To determine how long it will take to empty the tank, we can set the volume of water in the tank to 0 and solve for the time interval:
0 = flow rate in - flow rate out
flow rate out = flow rate in
0.27 liter/minute = 0.15 liter/minute
Since the equation is not balanced, we cannot determine the time interval. In order to determine the time interval, we need to have information about both the flow rate in and the flow rate out. Without this information, it is not possible to determine how long it will take to empty the tank.
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Determine whether or not the equations represent a direct variation. Sort the equations into the appropriate category.
Direct Variation
Not Direct Variation
y=3x
x=-1
y=(2/7)x
-0.5x=y
y=22x+7
y=4
Answer:
Direct Variation
y = 3x
y = (2/7)x
y = -0.5x
NOT Direct Variation:
x = -1
y = 4
y = 22x + 7
Step-by-step explanation:
Direct Variations are in the form
y = kx
This is very similar to:
y = mx + b except the b MUST be zero.
Also, direct variations always go through (0,0) that's why b must be 0.
So easy to pick out:
y = 3x
y = (2/7)x and
y = -0.5x are all in the form y = kx and have a y-intercept of zero.
y = 22x + 7 has that extra +7 tacked on to the end of the equation. It does not go through (0,0). It has a b that is 7. So it starts at (0,7). It is not a direct variation.
The other two, x = -1 and y=4 are both not direct variations. Neither starts at (0,0).
x=anumber is a vertical line and y=anumber is a horizontal line. These are not direct variations.
The liu family buys 20 pounds of chicken at the local market for $50. Which equation can be used to represent the cost, c, of buying x pounds of chicken at the same price per pound?.
Answer:
[tex]c=2.50x[/tex]
Step-by-step explanation:
The cost per pound of chicken is [tex]50/20=\$2.50[/tex].
So, the equation is [tex]c=2.50x[/tex].
P varies inversely with x. If p = 14 when x = 16, find the value of p when x = 21.
The value of p when x = 21 is p = 32/3 .
Given :
we know that ,
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form p * x = k or p = k / x
we know that
For p = 14, x = 16
Find the value of k
k = p * x
substitute the values
k = 14 * 16
= 224
so
The equation is equal to
p = 224 / x
if x = 21
substitute the value of x in the equation
p = 224 / 21
Divide by 7 both numerator and denominator
p = 32 / 3
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For a normal distribution, a negative value of z indicates O the z is to the right of the mean D a mistake has been made in computations, because z is always positive. o the area corresponding to the z is negative. O the z is to the left of the mean.
For a normal distribution, a negative value of z indicates D. the z is to the left of the mean.
What is a normal distribution?A continuous probability distribution known as the "normal distribution" has values that are symmetrically distributed mostly around the mean.
The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical plot of data around its mean value. It is represented graphically by the "bell curve.
Z is the number of standard deviations from the mean given by the formula:
z = ( X - μ ) ÷ ( σ )
where
x is the raw score,
μ is the population mean, and
σ is the population standard deviation
A negative value means that the number of standard deviations of an observation is to the left of the mean.
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Choose one scenario below and translate it into an inequality (do not solve). Be sure to use the equation editor. (4 points)
Scenario 1: You have $500 to spend on a car rental for your birthday weekend trip. The car rental company charges $95 per day to rent the car and charges $0.85 per mile. If you rent the car for three days, what is the maximum amount of miles you can drive to stay under budget?
Scenario 2: Suppose that you start a lawn mowing business. Your start-up costs include the purchase of a self-propelled mower for $475. On average, you spend $1.50 per lawn for oil and gas. You charge $35 per lawn. How many lawns must you mow to make a profit?
FOLLOW-UP (6 Points)
Solve one of the inequalities written by your peers. Be sure to show ALL work using the equation editor. In your follow-up tell us what you think about the situation. Is it a good idea? Would you partake? If not, what would need to be different for you to be interested in the scenario?
The situation can be expressed in inequality as: 95x + 0.85y ≤ 500
On solving the maximum amount of miles that can be driven to stay under budget is 253
What is inequality?
If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.
For example, x > 3 (x should be greater than 3)
According to the given question:
Total amount to spend is restricted to $500
Let the number of days be x and extra miles covered be y
The car rental company charges $95 per day to rent the car and charges $0.85 per mile.
Therefore the situation van be expressed as:
95x + 0.85y ≤ 500
If the car is rent for 3 days then the maximum amount of miles that can be driven to stay under budget are
95(3) + 0.85y ≤ 500
285 + 0.85y ≤ 500
0.85y ≤ 215
y ≤ 253
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This year, Ken paid $1,611 for season tickets to his favorite baseball team, which is 10% cheaper than last year. What was the price of season tickets last year?
Answer:
$1772.10
Step-by-step explanation:
10% = 0.1
Take 1611 times 0.1 = $161.10
So, the 10% cheaper is $161.10
We add both numbers to find the price of last year's season ticket!
1611 + 161.10 = $1772.10
So, the price of last year season's ticket is $1772.10
Let's check to see if it is correct!
$1772.10 - $161.10 = $1611
So, my answer is correct!
Answer:
$1,790
Step-by-step explanation:
x -.1x = 1611 Combine like terms
.9x = 1611 Divide both sides by .9
x = 1790
Check:
1790 - .1(1790) = 1611
1790 - 179 = 1611
1611 = 1611
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
g
=
p
2
−
m
Step-by-step explanation:
How many four-digit personal identification numbers (pin) are possible if the pin cannot begin with a 0 and the pin must be an odd number?.
If the four-digit personal identification number (PIN) cannot start with a 0 and must be an odd number, then 0 four-digit pins are conceivable.
There are 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) that can be used in a four-digit PIN. However, we are told that the PIN cannot begin with a 0, so there are only 9 possible digits that can be used for the first digit.
For the second, third, and fourth digits, any of the 10 digits can be used. Therefore, there are 9 x 10 x 10 x 10 = 9,000 four-digit PINs that can be created using any of the 10 digits.
We are also told that the PIN must be an odd number. This means that the last digit of the PIN must be odd. There are 5 odd digits (1, 3, 5, 7, and 9), so there are 5 possible digits that can be used for the last digit.
For the first three digits, any of the 9 digits that can be used for the first digit can be used. Therefore, there are 9 x 10 x 10 = 900 four-digit PINs that can be created using only odd digits.
However, we have double-counted the PINs that begin with 0. Since these PINs are not allowed, we need to subtract them from the total number of possible PINs. There are 9 x 10 x 10 = 900 four-digit PINs that begin with 0, so we need to subtract these from the total number of possible PINs.
The final number of possible four-digit PINs that cannot begin with 0 and must be odd is 900 - 900 = 0. Therefore, there are 0 four-digit PINs that meet these criteria.
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What are the 3 consecutive odd numbers whose sum will be 45?
The 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .
What are consecutive numbers ?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.
Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.
Let the 3 numbers be x ,x+2 , x+4
The sum of numbers is 45
⟹x+x+2+x+4=45
3x+6=45
3x=39
x=13
Hence , the 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .
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Is the number 16 a square?
Yes, the number 16 is a square.
It is the square of the number 4, since 4 x 4 = 16.
A square root is a factor in mathematics that, when multiplied by itself, equals the initial number. For instance, 3 and -3 are both square roots of 9.
The square of a number's root is the value under the root. For instance, (3 + 2) = 3. Any even number's square unit will only include even numbers.
Each and every nonnegative real number x has a distinct nonnegative square root, known as the primary square root, which is represented by the symbol x, also known as the radical sign or radix. As an illustration, we write 9=3 to denote that 3 is the number 9's fundamental square root. The word (or integer) whose square root is being examined is known as the radicand. The word or number that appears beneath the radical symbol, in this case, 9, is referred to as the radicand. The principal square root can alternatively be expressed in exponent notation for nonnegative x as x1/2.
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