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!
A ship is 130 m away from the centre of a barrier that measures /
180 m from end to end. What is the minimum angle that the
boat must be turned to avoid hitting the barrier?
Answer:
Step-by-step explanation:
50 meters away
What is the slope of the following line?
Answer:
1/2
Step-by-step explanation:
Can someone help me with this. Will Mark brainliest.
Answer: True!
Step-by-step explanation: Rhombuses are like squares with an 4 equivalent sides!
hope this helped have a nice day ! :)
Plz help question is in pic!
will mark brainliest
After spending 2/3 of his money. Charles has 12 pesos left. How much did he have at first??
The total amount of money charles must have had at the beginning is 36 pesos.
What are fractional linear equations and how one can solve it?
Linear equations which are in the form of fractions are referred as fractional linear equations.
an equation containing the unknown in the denominator of one or more terms (as a/x + b/(x + 1) = c)
It is frequently simplest to eliminate the fraction in the first step when dealing with fractions incorporated into linear equations. Typically, this entails locating the fraction's LCD and multiplying each term in the entire equation.
Solution:
Given:
Money left with charles = 12 pesos
Money spent = 2/3 of the total amount.
Find:
Total Money he had at first = ?
Step-1:
Let x denote the total amount of money he had at the beginning.
After spending 2/3 of his money he is left with 1/3 of part of his money.
Step-2:
So the equation can be written as:
1x/3 = 12
x = 36
Hence the total money he had at the beginning was 36 pesos.
Learn more about "Fractional linear equations" here-
brainly.com/question/14323743
#SPJ2
What is the correct answer for each box
Answer:
1) A ; 2) D ; 3)B ; 4)C
Step-by-step explanation:
we can solve every option and see what trinomal result
A (2x-3)(x-3) = 2x^2 -6x-3x +9 = 2x^2-9x+9
B (2x+3)(x-3) = 2x^2 -6x+3x-9 = 2x^2-3x+9
C (2x-3)(x+3) = 2x^2+6x-3x-9 = 2x^2+3x-9
D (2x+3)(x+3) = 2x^2+6x+3x+9 = 2x^2+9x+9
Write an equation for the line, in point slope form given the following information
Slope = 1/4 contains the point (8,-3)
Answer:
y+3=1/4(x-8)
simplified -> y+3=1/4x-2
Step-by-step explanation:
y-y1=m(x-x1)
y-(-3)=1/4(x-8)
y+3=1/4(x-8)
If you want it to be further simplified
y+3=1/4x-2
three times than five times a number
Answer:
15
Step-by-step explanation:
NEED ASAP . 19 MINUTES LEFT GIVNG BRAINLIEST PLZZZZ
Answer:
9
Step-by-step explanation:
so sorry if im too late...
Which of these is an example of due process?
a search without good reason
a prejudiced jury
a cruel punishment
a fair trial
Answer:
A fair trial.
Answer:
Step-by-step explanation: a search without good reason
HELP OMG
I LOST MY AIRPODS AT SCHOOL
Answer:
how should we help?
Step-by-step explanation:
Answer:
dang that sucks..... try and play music at max vol and see if you hear any music coming from anywhere that's probably were the airpods are, if they are in the case then i dont know if u would hear anything. It all depends...
~ i hope this has helped ya out some how, hope ya find your airpods my friend!~
Step-by-step explanation:
53+2444= ??????? HELP I D K THE ANSWER
Answer:
2497
Step-by-step explanation:
Answer:
2497
Step-by-step explanation:
53 + 2444
= 0053 + 2444
= 2497
can somebody help me get both answers pls? ALSO PLEASE PLEASE DONT SEND YOUR LINKS
Answer:
x=30
m<G
3(30)-17
73
m<H
x+13
43
Step-by-step explanation:
Answer:
m∠G = 73°
m∠H = 43°
Step-by-step explanation:
Use the exterior angle theorem. The exterior angle theorem states that the exterior angle's measurement will be the sum of the two opposite interior angles. Set the equation:
(3x - 17) + (x + 13) = 116
First, combine like terms by simplifying:
3x + x - 17 + 13 = 116
4x - 4 = 116
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, add 4 to both sides of the equation:
4x - 4 = 116
4x - 4 (+4) = 116 (+4)
4x = 116 + 4
4x = 120
Next, divide 4 from both sides of the equation:
(4x)/4 = (120)/4
x = 120/4
x = 30
Plug in 30 for x for each angle measurement:
m∠G = 3x - 17
m∠G = 3(30) -17
m∠G = 90 - 17
m∠G = 73°
m∠H = x + 13
m∠H = 30 + 13
m∠H = 43°
Check:
180 - 73 - 43 = 64 (Summation of a triangle's angle).
180 - 64 = 116 (Theorem of line).
Which table represents a linear function?
Answer:
the first one on the top left corner
it it bc on the right side of the table is counting by twos and so therefore on the left should be added 2 with that number
Answer:
Top left.
Step-by-step explanation:
Because it's constant. X increases by 2 and y increases by 3.
help a girl out please
Answer:4
Step-by-step explanation:ts is = ed
This is due in 2 minutes
Find the value of a. Round your answer to the nearest tenth.
Answer:
Polly do you know the formula for law of Cosines?
find it if you don't
Step-by-step explanation:
a = sqrt( b^2 +c^2 - 2bcCos(A) )
a = sqrt( 100 + 62.41 -34.197)
a = sqrt(128.213)
a = 11.323
a = 11.3 ( to the nearest tenth )
Mary and Carlos are each saving for new skateboards. So far, Mary has $9 saved
and earns $6 per hour babysitting. Carlos has $3 saved and can earn $9 per hour
working at his family's restaurant. After how many hours of work will Mary and
Carlos have saved the same amount and how much money will they both have?
Answer:
After 3 hours, both will have saved $21.
Step-by-step explanation:
I need help please i don’t understand
9514 1404 393
Answer:
no
Step-by-step explanation:
The dimensions will be those of a rectangular mirror if the diagonal measure is the hypotenuse of the right triangle with the given side lengths.
The Pythagorean theorem would require for some width w ...
w^2 +24^2 = 30^2
w^2 = 900 -576 = 324
w = √324 = 18
A rectangular mirror with a length of 24 inches and a diagonal of 30 inches will have a width of 18 inches, not 16.
__
The attachment shows that a width of 16 inches is not consistent with a right-angle corner.
_____
Additional comment
If you reduce the given numbers to lowest terms by dividing them by 2, they become 8, 12, 15. That is, the two shortest sides are even and the longest is odd. Any set of integer dimensions for a right triangle must have an even number of odd numbers (0 or 2). These numbers cannot be a Pythagorean triple, so cannot make a right triangle.
The function y=-0.2x^2+1.9x models the path of a kicked soccer ball.The height is y,the distance is x, and the units are meters.How high does the soccer ball go?
Answer:
The highest height the ball achieves is 4.5125 meters.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
Quadratic function [tex]y = -0.2x^2 + 1.9x[/tex], which has [tex]a = -0.2, b = 1.9[/tex].
The maximum height of the ball is [tex]y_{v}[/tex].
Then
[tex]\Delta = b^2-4ac = (1.9)^2 - 4*(-0.2)(0) = 3.61[/tex]
[tex]y_{v} = -\frac{3.61}{4(-0.2)} = 4.5125[/tex]
The highest height the ball achieves is 4.5125 meters.
A farm stand sells apples pies and jars of applesauce. The table shows the number of apples needed to
make a pie and a jar of applesauce. Yesterday, the farm picked 245 Granny Smith apples and 133 Golden
Delicious apples. How many pies and jars of applesauce can the farm make if every apple is used?
Type of apple Granny Smith Golden Delicious
Needed for a pie
9
5
Needed for a jar of applesauce 4
2
The farm can make
pies and jars of applesauce.
The college athletic director recorded the highest noise levels reached during 7 sporting events. The highs were:
88 decibels 88 decibels 88 decibels 87 decibels 84 decibels 97 decibels 95 decibels
What was the mean noise level recorded? Round your answer to the nearest whole number.
Answer:
90
Step-by-step explanation:
Mean:
(88 + 88 + 88 + 87 + 84 + 97 + 95)/7
627/7
89.57
90
Answer and explanation
Answer:
392in
Step-by-step explanation:
find the areas of all the sides of this shape. Of one you might have to split it into two shpaes.
Audria rode her bicycle for 2 hours. She drove a total of 21 miles. At this rate, how many miles will she bike in ½ hour? A 612 6 1 2 B 634 6 3 4 C 534 5 3 4 D 514
Answer:
5 1/4
Step-by-step explanation:
Speed = distance / time
21 / 2 = 10.5
10.5 = distance / 0.5
distance = 10.5 x 0.5 = 5,25 miles or 5 1/4
What’s the length of the triangle round it to the nearest tenth.
write an equation of the line that passes through 3,1 and 0,10
Answer:y = -3x + 10
Step-by-step explanation:
To find an equation of a line that passes through two points, we have to first find the slope between the two equation. We can do this by using the slope formula:
where (x₁, y₁) and (x₂, y₂) are the two points that we are finding the slope between.
Lets make (x₁, y₁) equal to (0, 10) and (x₂, y₂) equal to (3, 1). Now we plug them into the slope formula:
So the slope between the two points is -3.
From here, I would normally take one of the points given to us and plug in the point and slope into the point-slope form of a line and then simplify until we get it in slope-intercept form. But if you look carefully, the y-intercept is given to us as the point (0, 10). So we now know that the y-intercept of the line is 10. We can now take the y-intercept and the slope and plug it into the slope-intercept form of a line to get out equation:
y = mx + b
plug in -3 for m (the slope) and 10 for b (the y-intercept)
y = -3x + 10
So now we have our equation.
I hope you find my answer and explanation helpful. Happy studying. :)
CHOOSING BRAINLIEST ( SCREENSHOT PROVIDED )
Find the missing number to complete the linear equation that gives the rule for this table.
x | y
0 | 0
1 | 25
2 | 50
3 | 75
Answer:
y= 25
i think
Step-by-step explanation:
Two similar cylinders have heights of 3 cm and 6 cm respectively. If the volume of the smaller cylinder is 30 cm3, find the volume of the larger cylinder.Required to answer. Single line text.
Answer:
the ans is
Step-by-step explanation:
V=πr2h=π·32·6≈169.646
CAN SOMEONE PLEASEEE HELP SIMPLIFY THESE TWO EXPONENT PROBLEMS I HAVE NO CLUE HOW
Answer:
20. [tex]-\frac{y^{12} }{9x^{4} }[/tex]
Step-by-step explanation:
21. [tex]3 x^{2} y^{2}[/tex]
pls help meh plssss asap
Answer:
1.) 150
2.) 10
Step-by-step explanation:
If you look at the chart, above the 25 in the seconds row in the gallons row is 150.
This means that the chart tells you there are 150 gallons for every 25 seconds.
The second question asks about 60 gallons. So, if you look at 60 on the gallons row, and look below it on the seconds row, you see 10.
This means the chart tells you there are 60 gallons for every 10 seconds.