Answer:
t = 5.46 secs and t = 2.42 secs
Step-by-step explanation:
The distance of the ball from the ground is given by:
[tex]s(t) = -16t^2 + 126t[/tex]
When the ball is at a distance 211 ft from the ground, that means s(t) = 211 ft. we need to find t:
[tex]211 = -16t^2 + 126t[/tex]
[tex]=> 16t^2 -126t + 211 = 0[/tex]
Using the quadratic formula:
[tex]t = \frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex] and [tex]t = \frac{-b - \sqrt{b^2 - 4ac} }{2a}[/tex]
where a = 16, b = 126 and c = 211
Hence:
[tex]t = \frac{-(-126) + \sqrt{(-126)^2 - 4(16)(211)} }{2(16)}[/tex] and [tex]t = \frac{-(-126) - \sqrt{(-126)^2 - 4(16)(211)} }{2(16)}[/tex]
[tex]t = \frac{126 + \sqrt{15876 - 13504} }{32}[/tex] and [tex]t = \frac{126 - \sqrt{15876 - 13504} }{32}[/tex]
[tex]t = \frac{126 + \sqrt{2372} }{32}[/tex] and [tex]t = \frac{126 - \sqrt{2372} }{32}[/tex]
[tex]t = \frac{126 + 48.703 }{32}[/tex] and [tex]t = \frac{126 - 48.703 }{32}[/tex]
[tex]t = \frac{174.703}{32}[/tex] and [tex]t = \frac{77.297}{32}[/tex]
=> t = 5.46 secs and t = 2.42 secs
This means that the ball will be at 211 feet at two different times, first, after 2.42 seconds and then after 5.46 seconds.
This makes sense because the ball is projected upwards, which means that when going up, it attains 211 feet and also, when coming back down, it also attains 211 feet.
To determine the time when the ball is 211 feet off the ground, set s(t) equal to 211 and solve the resulting quadratic equation (-16t^2 + 126t - 211 = 0) using the quadratic formula. Discard the negative solution as it represents a time before launch.
Explanation:In response to the given question, we need to determine the time when the ball is 211 feet from the ground given the formula s(t)=-16t^2 + 126t. This is a quadratic equation which can be solved for t using the quadratic formula.
First, we need to set the equation equal to 211 to solve for when the ball is this distance off the ground. So, -16t^2 + 126t = 211. Rearrange the equation: -16t^2 + 126t - 211 = 0.
Now, apply the quadratic formula t = [-b ± sqrt(b^2 - 4ac)] / 2a, where a = -16, b = 126, and c = -211. This yields two solutions corresponding to the times at which the ball is 211 feet from the ground. The negative solution represents a moment before the ball is launched, hence we discard it. The positive value is the time at which the ball attains a height of 211 feet.
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please answer, thanks! :)
what is the mode of this data set 14,79,77,11,14,78,77,65,31,56,16
Answer:
There are 2 modes. They are 14 and 77.
Find the value of X in the triangle shown below
X= ? ( in degrees)
Answer:
x=50
Step-by-step explanation:
since all triangles angles add up to 180 and x and the other corner look equal, than minus 80 from 180 and then divide by two (because of the 2 corners.) x=50 degrees
What is the expanded form of this number?
509.307
The expanded form of 509.307 will be [tex]5\times100+ 9\times1 + 3\times0.1 + 0\times0.01 + 7\times0.001[/tex]
What is an expanded form ?It is a way to write a number by adding the value of its digits
The expanded form of 509.307 will be
= [tex]500 \times (10^2) + 0\times10^1 + 9 \times10^0 + 3\times10^{-1} + 0\times10 ^{-2} + 7 \times10 ^{-3}[/tex]
= [tex]5\times100+ 9\times1 + 3\times0.1 + 0\times0.01 + 7\times0.001[/tex]
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Makena made 11 quarts of punch. How many gallons of punch did she make
Answer:
2 3/4 gallons
Step-by-step explanation:
We know that there are 4 quarts in a gallon
11 quarts * 1 gallon/ 4 quarts
11/4 gallons
Changing to a mixed number
2 3/4 gallons
Please write the answer
x cube + x cube = ?
Answer:
[tex] {2x}^{3} [/tex]
Step-by-step explanation:
[tex] {x}^{3} + {x}^{3} = {2x}^{3} [/tex]
Answer:
[tex]2x^{3}[/tex]
Will mark as brainiest
Answer:
I think it is cos J, because side LI = 17 and IM = 8, adjacent/hypotenuse= cosine, therefore cos J = 8/17 = sin L.
Please mark Brainiest, am trying to become Virtuoso
1. What has left tons of “space junk” in orbit around the earth?
robots sent on space missions
years of space exploration
lack of recycling
missiles in outer space
2. Countries around the world have agreed to limit the time their space tools stay in orbit to 25 years. As explained in the passage, what problem does this solution address?
the increasing amount of space junk in orbit around the earth
space agencies exploring space
Chinese efforts to blow up a satellite
objects moving around the planet at very high speed
3. Trash has become a problem in outer space too.
What evidence from the text best supports this statement?
The Chinese tried to blow up one of its satellites with a missile in 2007.
In England, a metal harpoon is being tested that can be fired into space, gripping space trash and pulling it back into the earth’s atmosphere to burn up.
The Germans have been planning a space mission with robots to collect some space trash and bring it back to Earth.
According to BBC News, there are more than 22,000 pieces of junk in space around the earth.
4. Why have countries agreed to build space tools that must fall safely into the earth’s atmosphere?
so that the tools can remove pollution from the atmosphere after returning from space
so that the tools burn up in the atmosphere and don’t become space junk
so that the tools pollute the atmosphere instead of outer space
so that the tools can analyze the different gases that make up the atmosphere after returning from space
5. What was the passage mostly about?
different missions scientists are trying in space
the effects that tiny pieces of space junk could have on the earth
the problem of space junk and scientists’ attempts to solve this problem
the problem of trash on planet Earth
6. Read the following sentences: “In our opinion the problem is very challenging and it's quite urgent as well,'’ said Marco Castronuovo, an Italian Space Agency researcher who is working to solve the problem. One reason that it’s urgent is that countries are sending more and more objects into space. Many of these objects are tools that help people use their cell phones or computers.”
What does the word urgent most nearly mean?
easy to solve
unnecessary
needs immediate attention
minor
7. Choose the answer that best completes the sentence below.
Years of space exploration have left tons of “space junk,” _______ many scientists are trying to find a way to clean up outer space.
so
instead
because
similarly
8. What did the 2009 collision of a United States satellite and a Russian satellite cause?
(please use complete sentences)
9. What have the Germans done to help clean up space junk?
(use complete sentences)
10. Different countries have explored or are exploring different methods to clean up space junk. Explain why some methods may be more effective than others. Use evidence from the text to support your answer.
Don't Guess the answers i will give you the link to read the passage that goes along with the questions!
Answer:
1-B
2-A
3-D
4-B
5-C
6-C
7-A
8- The collision resulted in significant debris in low Earth orbit.
9-
10-
Step-by-step explanation:
10)
Which statement BEST describes how to find the distance between -5 and 15?!
Answer: Subtract -5 from 15, or 15- -5= 15+5. The distance would be 20.
Step-by-step explanation:
Answer:
The distance between -5 and 15 is 20.
Step-by-step explanation:
First find the distance between -5 and 0, which is 5. Then find the distance between 0 and 15, which is 15. Add the distances together, and you get 20.
hope this helps :)
Which has a greater volume? Cylinder A:r= 3m, h=1.2m cylinder B: d=4m, h=2.5m round your answer for the nearest tenths
Cylinder A has a greater volume of approximately [tex]\( 33.9 \, \text{cubic meters} \)[/tex].
To compare the volumes of the two cylinders, we'll use the formula for the volume of a cylinder, which is:
[tex]\[ V = \pi \times r^2 \times h \][/tex]
Let's calculate the volumes step by step for Cylinder A and Cylinder B:
Cylinder A:
Given:
- Radius [tex](\( r \)) = 3m[/tex]
- Height [tex](\( h \)) = 1.2m[/tex]
Using the formula:
[tex]\[ V_A = \pi \times (3^2) \times 1.2 \][/tex]
[tex]\[ V_A = \pi \times 9 \times 1.2 \][/tex]
[tex]\[ V_A = 10.8\pi \, \text{cubic meters} \][/tex]
Cylinder B:
Given:
- Diameter [tex](\( d \)) = 4m[/tex] (so, \( [tex]r = \frac{d}{2} = \frac{4}{2} = 2 \) m[/tex])
- Height [tex](\( h \)) = 2.5m[/tex]
Using the formula:
[tex]\[ V_B = \pi \times (2^2) \times 2.5 \][/tex]
[tex]\[ V_B = \pi \times 4 \times 2.5 \][/tex]
[tex]\[ V_B = 10\pi \, \text{cubic meters} \][/tex]
Now, to determine which cylinder has the greater volume, we compare [tex]\( V_A \)[/tex] and [tex]\( V_B \)[/tex]:
[tex]\[ V_A = 10.8\pi \, \text{cubic meters} \][/tex]
[tex]\[ V_B = 10\pi \, \text{cubic meters} \][/tex]
Since [tex]\( 10.8\pi > 10\pi \)[/tex], Cylinder A has the greater volume.
Therefore, Cylinder A has a greater volume, approximately [tex]\( 10.8\pi \)[/tex]cubic meters.
Let's calculate the approximate numerical value for [tex]\( 10.8\pi \)[/tex]:
[tex]\[ 10.8\pi \approx 10.8 \times 3.14 \approx 33.912 \][/tex]
Complete correct question:
Which has a greater volume?
Cylinder A: r = 3m, h = 1.2m.
Cylinder B: d = 4m, h = 2.5m.
Round your answer to the nearest tenth.
Cylinder A has a greater volume.
To find the volume of a cylinder, we use the formula:
[tex]\[ V = \pi r^2 h \]For Cylinder A:- Radius \( r = 3 \) meters- Height \( h = 1.2 \) meters\[ V_A = \pi (3)^2 \times 1.2 \]\[ V_A = \pi \times 9 \times 1.2 \]\[ V_A = 10.8 \pi \][/tex]
For Cylinder B:
[tex]- Radius \( r = \frac{d}{2} = \frac{4}{2} = 2 \) meters- Height \( h = 2.5 \) meters\[ V_B = \pi (2)^2 \times 2.5 \]\[ V_B = \pi \times 4 \times 2.5 \]\[ V_B = 10 \pi \]Now, let's compare the volumes:\[ V_A = 10.8 \pi \]\[ V_B = 10 \pi \][/tex]
Since [tex]\( 10.8 \pi > 10 \pi \)[/tex], Cylinder A has a greater volume.
Rounded to the nearest tenth, the volume of Cylinder A is approximately 33.9 cubic meters, and the volume of Cylinder B is approximately 31.4 cubic meters.
HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
how are we supposed to help with that
Step-by-step explanation:
use your snip tool on your computer and connect them
Answer:
Use the numbers that they gave you..
Step-by-step explanation:
It's not that hard
A) A counterclockwise rotation
B) A reflection over the y-axis
C) A reflection over the x-axis
D) A counterclockwise rotation of 90 degrees about the origin
Answer:
C) A reflection over the x-axis
Step-by-step explanation:
It shows the reflection but over the x-axis.
The equation which represents x, the width of the border is 2 left-bracket (12 + 2 x) + (15 + 2 x) right-bracket = 74. What is the width of the border?
Answer:
2 1/2
Step-by-step explanation:
If you do the step by step calculation:
Step 1: Simplify both sides of the equation.
2(12+2x+15+2x)=74
(2)(12)+(2)(2x)+(2)(15)+(2)(2x)=74(Distribute)
24+4x+30+4x=74
(4x+4x)+(24+30)=74(Combine Like Terms)
8x+54=74
8x+54=74
Step 2: Subtract 54 from both sides.
8x+54−54=74−54
8x=20
Step 3: Divide both sides by 8.
8x divide by 8 and that is 20 divided by 8
leaves you with the answer 5/2.
If you then turn the improper fraction into a mixed fraction you get 2 and one half.
Answer= 2 1/2 or "a" DEPENDS ON WHAT QUIZ YOU HAVE
Peace!
Michael is training for a marathon. In his first week he plans to run 8 miles. Which path should he take?
Answer: B
Step-by-step explanation: Usa Pept
Final answer:
Michael's 8-mile training run should be on a path that is enjoyable and reflective of the marathon environment, helping to build endurance and maintain motivation.
Explanation:
Michael is training for a marathon and plans to run 8 miles in his first week. The appropriate path for him would depend on several factors including scenery, difficulty level, and whether the path is traffic-free. A key aspect of marathon training as illustrated through the personal story shared is a gradual increase in mileage and a lifestyle change towards constant movement. Michael's marathon training should ensure that his 8 miles are manageable and reflect the incremental changes in habits he's aiming for.
When selecting a path, Michael might consider one that is reflective of the marathon environment, which could include terrain similar to the race he plans to participate in, or he might choose a path known for its relaxing scenery to make the run enjoyable and maintain motivation. Regardless of the exact path taken, the focus should be on building endurance through consistent and enjoyable running experiences.
How does the volume of a square pyramid change if the base area is quadrupled and the height is reduced to 1/9 of its original size
Final answer:
The volume of a square pyramid changes by a factor of 4/27 when the base area is quadrupled and the height is reduced to 1/9 of its original size.
Explanation:
The volume of a square pyramid can be found using the formula:
Volume = (1/3) * Base Area * Height
If the base area is quadrupled, it means the new base area is 4 times the original.
If the height is reduced to 1/9 of its original size, it means the new height is 1/9 of the original.
Therefore, the change in volume can be calculated as:
Change in Volume = (1/3) * (4 * Original Base Area) * (1/9 * Original Height)
Simplifying the expression, we get:
Change in Volume = (4/27) * Original Volume
Help me please find the area of the room
Answer:
Cut the room into a rectangle and a trapezoid vertically. Then just use the rectangle and trapezoid area formulas to solve.
Step-by-step explanation:
It should work because this is how I find the area of most irregular shapes.
Answer:
To find the area you would first break the shape down into smaller regular shapes. In this case it would be a rectangle and trapezium. Then the next step to working out the area is to work out the area of one of the shapes. In this example i would start with the rectangle as it would be easier. The formula for the area of the rectangle would be length multiplied by the width. Then hold on to the answer. After you would work out the area of the trapezium. The formula for the area of a trapezium is: [tex]\frac{a+b}{2} *height[/tex]. To work this out you would add the lengths of the top line and the bottom line and divide them by 2. Then you would multiply that by the height of the trapezium. After you would add the area of the rectangle and the area of the trapezium and this will give you the total area.
1) Divide the shape into smaller regular shapes.
2) Find the area of the rectangle.
3) Find the area of the trapezium.
4) Add the two areas together.
Find the slope of (-2,1),(-5,5)
Answer: m = - 4/3
Step-by-step explanation:
The formula to find slope is m = y2 - y1 / x2 - x1.
So for this problem I did 1 - 5 / -2 - (-5) which equals -4/3
A rectangle has an area of (x - 17x + 72) square units. Since the area of a rectangle is determined using the formula, A =
kw, what could be the length and width of the rectangle?
length = (x - 8) units and width = (x - 9) units
length = (x + 9) units and width = (x + 8) units
length = (x-6) units and width= (x - 12) units
length = (x + 12) units and width = (x + 6) units
Answer:
Step-by-step explanation:
x² - 17x + 72 = 0
Sum = -17
Product = 72
Factor = 8 , 9
x² - 17x + 72 = 0
x² - 8x -9x + (-8)*(-9) = 0
x(x - 8) -9(x -8) = 0
(x - 8 ) (x - 9) = 0
Length = (x - 8) units
Width = (x - 9) units
Keenan has 28 CDs and 44 DVDs. What is the ratio of DVDs to CDs?
The ratio of DVDs to CDs in Keenan's collection is 11:7, after simplifying the original ratio of 44:28 by dividing both terms by their greatest common divisor, which is 4.
Keenan has a collection of 28 CDs and 44 DVDs. To find the ratio of DVDs to CDs, we divide the number of DVDs by the number of CDs. This gives us:
Ratio of DVDs to CDs = Number of DVDs / Number of CDs
Ratio of DVDs to CDs = 44 / 28
Now, we can simplify this by dividing both numbers by the greatest common divisor (GCD), which is 4 in this case:
44 / 4 = 11
28 / 4 = 7
So, the simplified ratio is 11:7.
Therefore, the ratio of DVDs to CDs in Keenan's collection is 11:7.
Solve: 512^x-2/(1/64)^3x=512
Answer:
The correct answer is x=1
Step-by-step explanation:
Answer:
x = 1
Step-by-step explanation:
Expand and combine like terms.
(x+3)(x+4)
Answer:
x^2 +7x+12
Step-by-step explanation:
(x+3)(x+4)
FOIL
first x*x= x^2
outer: 4x
inner:3x
Last 3*4=12
Add together
x^2+3x+4x+12
Combine like terms
x^2 +7x+12
Brahmagupta's book is the oldest text representing zero
as a number, using the symbol 0. Why was this a
mathematical breakthrough?
Answer:
Understanding zero as a number represented by the symbol 0 enabled mathematicians to have a representation of nothing. Having a digit to represent zero enables mathematics to be more abstract, and allows more complex problems to be solved.
If the area of the circle is 97.9 units squared, what is the radius?
Answer:
r = 5.58
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
97.9 = 3.14 r^2
Divide each side by 3.14
97.9/3.14 =3.14 /31.4 r^2
31.17834395 = r^2
Take the square root of each side
sqrt(31.17834395) = sqrt(r^2)
5.583757153 = r
HELP!!! PLEASE!!! NOW!!!!!! ASAP!!!!
Answer:
y < -5
Step-by-step explanation:
19 > -6 - 5y
add 6 to both sides
25 > - 5y
divide by -5
-5 > y
Answer:
y>-5.
Step-by-step explanation:
Solved it don't really know how to explain it. :/
Which situation shows a constant rate of change? Why?
A. The amount raised by a booster club compared w/ the number of raffle tickets sold
B. The weight of a kitten compared w/ its age in months
C. The height of a paper airplane over time
D. The number of goals scored in a soccer game compared w/ the minutes played
The situation that shows a constant rate of change the amount raised by a booster club compared w/ the number of raffle tickets sold.
A constant rate of change occurs when there is a consistent relationship between two variables, where a change in one variable consistently leads to a corresponding change in the other variable.
Here the booster club selling raffle tickets, a constant rate of change can be observed between the number of tickets sold and the amount of money raised by the club.
As the booster club sells more raffle tickets, the amount of money they raise increases.
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Ted borrowed $100 from 2 years at a 10% interest rate. How much interest will he pay on the loan? What will be the total amount due at the end of the loan?
Answer:
Interest = $20
Amount due = $120
Step-by-step explanation:
This is a Simple Interest problem. Simple interest is given as:
I = (P * R * T) / 100
Where I = interest
P = principal or amount loaned
R = rate of interest
T = time elapsed
Ted borrowed $100 from 2 years at a 10% interest rate.
This means that P = $100, R = 10%, T = 2 years.
Hence, the interest will be:
I = (100 * 10 * 2) / 100
I = 2000 / 100
I = $20
The interest after two years will be $20.
Therefore, the total amount due at the end of the loan is:
A = P + I
A = 100 + 20 = $120
The amount due is $120.
Which statement is true about the effect of the 2-page introduction chapter?
The outlier of 2 increases the median page count.
The outlier of 2 increases the mean page count.
The outlier of 2 decreases the median page count.
The outlier of 2 decreases the mean page count.
Answer:
D
Step-by-step explanation:
The outlier of 2 decreases the mean page count.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
If the outlier is included in the calculation of the median and mean, then it will affect the measures of central tendency.
However, if the outlier is excluded from the calculation, then it will not affect the measures of central tendency.
If the 2-page introduction chapter is an outlier on the higher side of the distribution, the outlier of 2 increases the mean page count more than the median page count.
If the 2-page introduction chapter is an outlier on the lower side of the distribution, the outlier of 2 decreases the mean page count more than the median page count.
therefore, The outlier of 2 decreases the mean page count.
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Complete question:
Evaluate f(-3) for f(x) = 2x.
Group of answer choices
8
1/8
-8
-6
the inequality s > or = 92 represents the score s that jared must earn on his test to get a A on his report card. give two possible answers scores that jared could earn to get the A
Final answer:
Two test scores that fulfill the inequality s ≥ 92 are 92 and 95, meaning that Jared can get an A on his report card with either of those scores.
Explanation:
The inequality s ≥ 92 represents the score (s) that Jared must earn on his test to get an A on his report card. Since the inequality includes the 'greater than or equal to' symbol (≥), two possible test scores that Jared could earn to get an A would be 92 and any other number greater than 92, for instance, 95.
What are all kinds of triangle
A triangle is a three-sided two-dimensional shape that can be classified based on side lengths and angle measurements. There are various types of triangles, including equilateral, isosceles, scalene, acute, right, obtuse, equiangular, and right-angled isosceles triangles.
Explanation:A triangle is a three-sided two-dimensional shape. It is a polygon, which is a closed figure with straight sides. Triangles can be classified based on their side lengths, such as equilateral (all sides are equal), isosceles (two sides are equal), and scalene (no sides are equal). They can also be classified based on their angle measurements, such as acute (all angles are less than 90 degrees), right (one angle is 90 degrees), and obtuse (one angle is greater than 90 degrees). Additionally, there are special types of triangles like equiangular triangles (all angles are equal) and right-angled isosceles triangles (one angle is 90 degrees and two sides are equal).