Answer:
t = 2.5 s
Step-by-step explanation:
Suppose you have a water-balloon launcher. The balloon is 3 ft high when it leaves the launcher. Its equation is :
[tex]16t^2 + 38.8t + 3 =0[/tex]
The above equation is a quadratic equation. The general equation is :
[tex]ax^2+bx+c=0[/tex]
Here, a = 16, b = 38.8 and c = 3
The solution of quadratic equation is given by :
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\\\\t=\dfrac{-38.8\pm \sqrt{(38.8)^2-4\times (-16)\times 3} }{2\times (-16)}\\\\t=\dfrac{-38.8+\sqrt{(38.8)^{2}-4\times-16\times3}}{-2\times16}, \dfrac{-38.8-\sqrt{(38.8)^{2}-4\times-16\times3}}{-2\times16}\\\\t=-0.075\ s,2.5\ s[/tex]
So, at t = 2.5 s the balloon is in air.
The water balloon is in the air for approximately 2.51 seconds. We discard the negative solution as time cannot be negative.
To determine the number of seconds t that the balloon is in the air, we need to solve the quadratic equation 0 = -16t² + 38.8t + 3. This can be solved using the quadratic formula:
⇒ t = (-b ± √(b² - 4ac)) ÷ 2a,
where a = -16, b = 38.8, and c = 3.
Calculate the discriminant:⇒ Δ = b² - 4ac
⇒ (38.8)² - 4(-16)(3) = 1505.44 + 192
= 1697.44.
Find the square root of the discriminant:⇒ √1697.44 ≈ 41.21.
Apply the quadratic formula:⇒ t = ( -38.8 ± 41.21 ) ÷ -32.
Thus, we have two solutions:⇒ t₁ = ( -38.8 + 41.21 ) ÷ -32
≈ -0.076 (discarded because time cannot be negative).
⇒ t₂ = ( -38.8 - 41.21 ) ÷ -32
≈ 2.51 seconds.
The balloon is in the air for approximately 2.51 seconds.
Complete question:
Suppose you have a water-balloon launcher. The balloon is 3 ft high when it leaves the launcher. Use the equation 0 = -16t² + 38.8t + 3 to find the number of seconds t that the balloon is in the air.
Write the number 0.72 with 72 repeating as a fraction or a mixed number
Answer:
If repeating 72/99 always create the non repeating and subtract 1 from the denom. now reduce ... subtract the equations with the same digits after the decimal point 72.727272= 100x ... Which numbers from 1 to 10 could be the denominator? THANK YOU! ... Write the fraction in simplest form and equivalent decimal. asked by ...
25 answers
Step-by-step explanation:
Answer:
Step-by-step explanation:
x = 0.7272....
Two digits are repeating. so, multiply both sides by 100
100x = 72.7272.......
x = 0.7272........ {Subrtact}
99x = 72
[tex]x=\frac{72}{99}\\\\x=\frac{8}{11}[/tex]
Ray uses 8 pieces of wood for each box he makes. Ray writes an equation to describe how many boxes, y, he can make with x pieces of wood. Which equation did Ray write?
Considering Ray uses 8 pieces of wood per box, the equation representing how many boxes, y, Ray can make with x pieces of wood is y = x/8. This concept originates from the field of algebra, part of middle school mathematics.
Explanation:The subject of this question is mathematics as it discusses an equation that needs to be solved, a key component in algebra. The grade level of the student asking this question sits around middle school, as learning to solve these kinds of algebraic problems are typically introduced at this stage.
If Ray uses 8 pieces of wood for each box he makes, we can say that the number of boxes, y, that Ray can make given x pieces of wood is represented by the equation y = x/8. This equation basically says that the number of boxes Ray can make (y) equals the total number of pieces of wood he has (x) divided by the number of pieces each box requires (8). So if Ray has say, 80 pieces of wood, he could make 10 boxes because 80 divided by 8 is 10.
.
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answer quick for brainliest
Answer:
Step-by-step explanation:
y = mx + c
Here, m is the slope & c is the y-intercept
y = -3x - 1
Slope = -3
y intercept = -1
Find two numbers that multiply to 20 and add to 9.
Answer:
The answer is 5 and 4
Step-by-step explanation:
The reason this is the answer is 5*4 is 20 and 5+4 is 9
Your friend tells you that if you let him keep 50 of your Pokemon cards for a month, he will give you 1 card extra when he returns your cards. What is the annual rate of interest he is willing to pay for the borrowed cards? Note: Even though he only keeps your cards for a month, we can still calculate an annual interest rate
Answer:
the answer depends on which type of interest we use:
simple interest rate = 24%compound interest rate = 26.82%Step-by-step explanation:
the interest rate paid for holding the cards one month 1/50 or 2%.
to convert 2% monthly interest rate to a simple annual rate:
monthly rate x 12 months = 2% x 12 = 24%
now to convert 2% monthly interest rate to an annual rate (using compound interest):
= (1 + r)ⁿ - 1= (1 + 0.02)¹² - 1 = 1.2682 - 1 = 0.2682 or 26.82%in compound interest, earned interest earns even more interest by itself besides the interest earned by the principal.
Find the area of the triangle with A = 60°, b = 11 feet, and c= 8 feet. Round to the nearest tenth.
Answer:
38.1 sq. ft
Step-by-step explanation:
angle A = 60 deg.
length a = unknown
b = 11 feet
c = 8 feet
angle B must be larger than angle C
try cos A = 8/11 ? no since cos A = 0.5 so this is not a 30-60-90 triangle
Area of triangle = (1/2)* base * height
height = ...
imagine... 8 is hypotenuse and then adjacent leg = 8*cos 60
then height = 8 * sin 60 = 8 * (root(3)/2) = 4*root(3)
Area of triangle A = (1/2)*11 feet * 4*root(3)
A =22*root(3) sq. ft. = 38.105 sq. ft = 38.1 sq. ft
What is 8 raised to the -2/3 power? I need help
Answer:
The answer will be 0.25 or 1/4
Step-by-step explanation:
8^(-2/3)= 0.25
HOPE THIS HELPS!! PLEASE GIVE BRAINIEST!!
I'll give you BRAINLIEST!!!
Who was the first Math teacher to use Pi?
Answer:
William Jones was the first Math teacher to use pi
Step-by-step explanation:
Answer:
William Jones
Step-by-step explanation:
Find the HCF of 220 and 88.
Answer:
44
Step-by-step explanation:
Nothing that's bigger goes into both numbers
Answer:
44
Step-by-step explanation:
220 and 88 greatest common factor is 44
what is the domain value of 4 f(x)=2x+1
Answer:
D (all real numbers)
Step-by-step explanation:
The domain is the possible input values
The input can be any value of x, so it is all real number
Simplify 2m-5/6m-15
Answer:
Pull out like factors :
6m - 15 = 3 • (2m - 5)
Cancel out (2m - 5) which appears on both sides of the fraction line.
Final result:
1
— = 0.33333
3
Step-by-step explanation:
Answer quick for brainliest
Answer:
x (-11/2,0) y (0, 11)
Step-by-step explanation:
1. When a cannonball is fired, the equation of its pathway can be modeled by h = -1612 + 128t.
a) Find the maximum height of the cannonball.
Answer:
The maximum height of the ball is 256m
Step-by-step explanation:
Given the equation of a pathway modelled as pathway can be modeled by h = -16t² + 128t
At maximum height, the velocity of the ball is zero.
velocity = dh/dt
velocity = -32t + 128
Since v = 0 at maximum height
0 = -32t+128
32t = 128
t = 128/32
t = 4seconds
The maximum height can be gotten by substituting t = 4 into the modelled equation.
h = -16t² + 128t
h = -16(4)²+128(4)
h = -16(16)+512
h = -256+512
h = 256m
The maximum height of the ball is 256m.
Calculation of the maximum height:Since the equation should be [tex]h = -16t^2 + 128t[/tex]
Also we know that at the maximum height, the velocity of the ball should be zero
So,
[tex]velocity = dh/dt[/tex]
velocity = -32t + 128
Now
0 = -32t+128
32t = 128
t = 4seconds
Now
[tex]h = -16t^2 + 128t\\\\h = -16(4)^2+128(4)[/tex]
h = -16(16)+512
h = -256+512
h = 256m
hence, The maximum height of the ball is 256m.
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What is the surface area of the triangular prism? Use a net,
204 cm
216 cm
240 cm
276 cm
Answer:
936cm
Step-by-step explanation:
204+216=420+240=660+276=936
The function g(x) = 10.73 + 8.14(x - 1) represents the charge for parking at the airport for x number of days. Which statement best represents the formula for this charge?
Answer:
This function states that the first hour has a fixed cost of 10.75.Then, every additional hour has an additional cost of $8.14.Step-by-step explanation:
The given function is
[tex]g(x)=10.75+8.14(x-1)[/tex]
The statements that best represent the formula are:
This function states that the first hour has a fixed cost of 10.75.Then, every additional hour has an additional cost of $8.14.You can deduct that from the formula, because [tex]x[/tex] represents hour, so for [tex]x=1[/tex], we have
[tex]g(0)=10.75+8.14(1-1)=10.75[/tex]
Which means 1 hour costs $10.75.
Then, for [tex]x=2[/tex]
[tex]g(2)=10.75+8.14(2-1)=10.75+8.14=18.89[/tex]
Which means an additional hour cost $8.14 additionally.
The function g(x) = 10.73 + 8.14(x - 1) represents the linear charge for airport parking, with a starting fee of $10.73 and an additional daily rate of $8.14.
The function g(x) = 10.73 + 8.14(x - 1) represents the charge for parking at the airport for x number of days. The initial amount, when x=1, is $10.73, which can be interpreted as the base fee for the first day of parking. Each additional day costs $8.14 more than the previous day. This is a typical example of a linear equation, where the constant term represents a starting value and the coefficient of the variable represents the constant rate of change.
Find the difference (-13) - (-5)
Answer:
-8
Step-by-step explanation:
When we subtract a negative it is like adding
-13 + 5
The signs are different so we subtract and take the sign of the larger
13 -5
8
The 13 is larger so we take its sign, which is negative
-8
Answer:
-8
Step-by-step explanation:
-13 - (-5)
-13 + 5
-8
The length of a rectangle plus its width is
13 cm. The area is 12 square cm. What are
the length and width of the rectangle?
Answer:
its 1
Step-by-step explanation:
Let's the length of rectangle x cm, then its width is (13-x) cm. since the area is 12 cm^2 we write:
(13-x)Xx=12
we get the width: x=1cm and the length is 13-12=1cm.
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At the end of the day, a bagel place had 4⁄5 of its bagels left over. The 4 employees each took home the same amount of leftover bagels. How much bagels did each employee take home?
Answer: 1/5
Step-by-step explanation:
Hi, to answer this question we simply have to divide the amount of bagel left over (4/5) by the number of employees (4)
Mathematically speaking:
4/5 bagel ÷ 4 employees = 1/5 bagel
In conclusion, each employee received 1/5 of bagel.
Feel free to ask for more if needed or if you did not understand something.
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Kaylee is mixing paint for an art project. She mixes 5 ounces of green paint with every 3 ounces of white paint. She needs 50 ounces of the paint mixture. I need it as a equation
Answer:
Step-by-step explanation:
Let Kaylee used the amount of green paint in the mixture = x ounces
and the amount of white paint = y ounces
Total amount of mixture = 50 ounces
Equation will be x + y = 50 ------(1)
Ratio of green paint to the white paint in the mixture = 5 : 3
⇒ x : y = 5 : 3
⇒ [tex]\frac{x}{y}=\frac{5}{3}[/tex]
⇒ x = [tex]\frac{5}{3}y[/tex] ---------(2)
Therefore, By solving these two equations by substitution method we can get the amount of green and white paint used in the mixture.
Final answer:
Kaylee mixes paint at a ratio of 5 parts green to 3 parts white and needs 50 ounces of the mixture. By setting up a system of equations with G for green paint and W for white paint, we find that Kaylee will use 31.25 ounces of green paint and 18.75 ounces of white paint.
Explanation:
Kaylee is mixing paint for an art project. She mixes 5 ounces of green paint with every 3 ounces of white paint. She needs to create a total of 50 ounces of the paint mixture. To represent this situation as an equation, we first need to determine the ratio of green to white paint and then find out how many parts of each color we need to make up the 50 ounces.
We know that the mixture is made with 5 parts green for every 3 parts white. If we let G represent the total amount of green paint and W represent the total amount of white paint, we can use the ratio to write the equation G/W = 5/3. We also know that G + W = 50 because the total mixture is 50 ounces.
To solve this system of equations, multiply both sides of the first equation by W to get G = (5/3)W. Substitute this value into the second equation to get (5/3)W + W = 50. To find the value of W, you can solve this equation:
Combine like terms: (5/3)W + (3/3)W = (8/3)W = 50Multiply both sides by 3 to get rid of the fraction: 8W = 150Divide both sides by 8: W = 150/8 = 18.75 ounces of white paint.Now, we substitute W back into G = (5/3)W to find the amount of green paint:
G = (5/3) * 18.75 = 31.25 ounces of green paint.So Kaylee will use 31.25 ounces of green paint and 18.75 ounces of white paint to create her 50 ounces of paint mixture.
What two numbers does the square root of 161 lie between
Answer:
12 and 13
Step-by-step explanation:
use a calculator ツ
Answer:
12-13
Step-by-step explanation:
Kayla rolls two fair number cubes each numbered 1 through 6. She needs to roll a sum of 9 or higher to win a game. She rolls the number cubes one at a time. She rolls a 5 with the first number cube. What is the probability that Kayla will win the game?
Evaluate a+3.45+b at
a
a=2.88 and b=6.02
Answer:
Answer:
12.35
Step-by-step explanation:
Plugin value in place of the variables.
Hope this helps! Good luck :-)
i will be giving brainliest {431, 154, 254, 244, 244, 276, 263, 389, 253, 274, 205}
What is the median of the set of data?
Enter your answer in the box.
Answer:
254
Step-by-step explanation:
The median of a set of data is basically the middle number of the data when placed in least to greater order.
example:
1,2,3,4,5,
in this case (the example) the median is 3 becasue it is the middle number of the 5 numbers (thier are two numbers to the left of 3 and 2 numbers to the right of 3)
Going back to the question being asked if you put that data in order you would get a sequence of
154, 205, 244, 244, 253, 254, 263, 274, 276, 389, 431
now try eliminating a number from each end side one by one (alternating) until you have one number left.
For instance remove 154 and 431, then remove 205 and 389 etc
IF DONE CORRECTLY you would have 254 as the remaining number.
Answer:
254
Step-by-step explanation:
First, put the numbers in order.
431, 154, 254, 244, 244, 276, 263, 389, 253, 274, 205
154, 205, 244, 244, 253, 254, 263, 274, 276, 389, 431
The median of a data set is the middle number.
154, 205, 244, 244, 253, 254, 263, 274, 276, 389, 431
Best of Luck!