A ball is thrown from an initial height of 3 meters with an initial upward velocity of 30 m/s. The ball's height h (in meters) after seconds is given by the
following
h = 3+302-57
Find all values of tfor which the ball's height is 13 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
1 seconds
х
5
?
Initial
height
ground
Answers
[tex]h=3+30t-5t^2\implies 13=3+30t-5t^2\implies 0=-10+30t-5t^2 \\\\\\ 5t^2-30t+10=0\implies 5(t^2-6t+2)=0\implies t^2-6t+2=0[/tex]
now, it doesn't give us nice looking integers, so let's plug that into the quadratic formula.
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{1}t^2\stackrel{\stackrel{b}{\downarrow }}{-6}t\stackrel{\stackrel{c}{\downarrow }}{+2}=0 ~\hspace{10em} t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ t= \cfrac{ - (-6) \pm \sqrt { (-6)^2 -4(1)(2)}}{2(1)}\implies t=\cfrac{6\pm\sqrt{36-8}}{2}[/tex]
[tex]t=\cfrac{6\pm\sqrt{28}}{2}\implies t=\cfrac{6\pm\sqrt{2^2\cdot 7}}{2}\implies t=\cfrac{6\pm 2\sqrt{7}}{2}\implies t=\cfrac{2(3\pm 1\sqrt{7})}{2} \\\\\\ t=3\pm \sqrt{7}\implies t= \begin{cases} 3+\sqrt{7}\\ 3-\sqrt{7} \end{cases}\implies t\approx \begin{cases} 5.65\\ 0.35 \end{cases}[/tex]
Related Questions
A woman is 69 1/2 inches tall and her son is 66 2/9 inches tall. How much taller is the woman?
Answers
Answer:
Find The InterestRs1000 rateRs10%isRs1200
You just bought a new laptop and paid an initial payment of $150.00. You will make 12 payments of $69.50. How much will the computer cost if your state charges 6% sales tax on the total sale.
Answers
The computer will cost $924.96 after 6% tax.
Total cost of laptopThe initial payment of the laptop made = $150.00
The remaining balance that would be made = 12 × 69.50
=$834
Therefore total cost of laptop before tax = 834 + 150
= $984
But tax is 6% of total cost =
[tex] \frac{6}{100} \times 984[/tex]
[tex] \frac{5904}{100} [/tex]
= $59.04
Therefore, total cost of laptop after tax = 984 - 59.04
= $924.96
Learn more about costs of products here:
https://brainly.com/question/24494976
PLEASE HELP ASP!!!!!!!!!!!A birch tree that is 4 ft tall grows at a rate of 1 ft per year. A larch tree that is 6 ft tall grows at a rate of 0.5 ft per year.
Let the variable t represent time in years and let the variable h represent height in feet.
In how many years will the trees be the same height?
Which system of equations can be used to solve this problem?
{h=1+4th=0.5+6t
{h=4+th=6+0.5t
{h=5th=6.5t
{h=4−th=6−0.5t
Answers
Answer:
4 Years
Step-by-step explanation:
1:0.5 = 2:1
So, every two years, the birch tree grows 1 foot more than the larch tree
Currently, they are 2 feet apart, so in 4 years, they will be the same height
please helpppppppppppp
Answers
Answer:
[tex] \frac{x - 3}{x} [/tex]
Step-by-step explanation:
[tex]f(x) = \frac{1}{x} \: \: g(x) = x - 3 \\ \\ \implies \: (f•g)(x) = \frac{1}{x} (x - 3) \\ \\ = \frac{x - 3}{x} [/tex]
Please help me with this !!!
Answers
Step-by-step explanation:
sorry bro, ìdk dis answer
G.O.O.G.L.E IT....MAYBE YOU WILL FIND THE ANSWER...
PLEASE HELP ME QUICKKK, FIRST CORRECT PERSON GETS BRAINLIEST
Answers
Answer:
The answer is Tennesse
Step-by-step explanation:
because it raises the prices by $45.50
A construction crew has just finished building a road. The road is 8 kilometers long. If the crew worked for 3 1/3 days, how many kilometers of road did they build each day? ( Assume they built the same amount each day.) write your answer as a mixed number in simplest form.
Answers
Answer:
They built 2.4 kilometers each day
Step-by-step explanation:
8 divided by 3 1/2
Please answer this question thank you
Answers
Answer:
74
Step-by-step explanation:
What I'm getting at, is that you need to add all the hour sold cups up, and then double it because she expects to sell twice as much. 15 + 11 +5 +6 = 37, and 37 doubled is 74
Answer:
74 cups
Step-by-step explanation:
Total for today: 37
6 + 5 + 11 + 15 = 37
Tomorrow is twice of today
2(37) = 74
I hope this helps!
Mathematics need help with this paper
Answers
Answer:
5. x = 39°
6. x = 46°
7. x = 24°
8. x = 19°
Step-by-step explanation:
5.
Base angles are the same due to it being an isosceles triangle
Sum of angles in triangle = 180°
2x + 2x + (x - 15) = 1804x + x - 15 = 1805x - 15 = 1805x = 195x = 396.
Angle VZW and XZW are supplementary, meaning that they add up to 180°
3x + 17 + (x - 9) = 1803x + 17 + x - 9 = 1804x + 8 = 1804x = 184x = 46°7.
Sum of angles in a straight line add up to 180°
(2x - 4) + (3x + 5) + (2x + 11) = 1802x - 4 + 3x + 5 + 2x + 11 = 1807x + 12 = 1807x = 168x = 248.
All angles add up to 90°
x + (x + 4) + (3x - 9) = 90x + x + 4 + 3x - 9 = 905x - 5 = 905x = 95x = 19-Chetan K
Urgent, please reply as soon as possible! 30 points on brainly!
The above graph shows the acceleration of an object. use the information from the graph to answer the following question. During which section of the graph is there no acceleration? Explain why or why not.
Answers
Answer:
during section b
Step-by-step explanation:
the line is flat
Answer:
Yes beavause the graph goes up and then straight down
Step-by-step explanation:
can you answer my question?
Evaluate 7 1/6- 3 5/8
Answers
Answer:
3 13/24
Step-by-step explanation:
hope this helps you!
let's firstly convert the mixed fractions to improper fractions and then subtract.
[tex]\stackrel{mixed}{7\frac{1}{6}}\implies \cfrac{7\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{43}{6}} ~\hfill \stackrel{mixed}{3\frac{5}{8}}\implies \cfrac{3\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{29}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{43}{6}~~ - ~~\cfrac{29}{8}\implies \cfrac{(4)43~~ - ~~(3)29}{\underset{\textit{using this LCD}}{24}}\implies \cfrac{172~~ - ~~87}{24}\implies \cfrac{85}{24}\implies 3\frac{13}{24}[/tex]
Can someone please help me find out the answer to this question?
Answers
Answer:
A
Step-by-step explanation:
Hello!
The answer is attached with explanation. Please note me if you have any more questions.
Answer:
Letter A.
[tex] {f}^{ - 1} (x) = \frac{ x + 8}{9} [/tex]
Simplify the expression.
5(10 + g) + 14g + 4
A.
19g + 54
B.
9g + 44
C.
14g + 50
D.
15g + 15
Answers
Answer:
A. 19g+54
let me know if this helps :3
Step-by-step explanation:
Fraction………………..::::::
Answers
Answer:
0.45
Step-by-step explanation:
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{\dfrac{12}{25}\times\dfrac{15}{16}}[/tex]
[tex]\mathsf{= \dfrac{12\times15}{25\times16}}[/tex]
[tex]\mathsf{= \dfrac{180}{400}}[/tex]
[tex]\mathsf{= \dfrac{180\div5}{400\div5}}[/tex]
[tex]\mathsf{= \dfrac{36}{80}}[/tex]
[tex]\mathsf{= \dfrac{36\div4}{80\div4}}[/tex]
[tex]\mathsf{= \dfrac{9}{20}}[/tex]
[tex]\huge\textbf{Therefore, your answer is: \boxed{\mathsf{\dfrac{9}{20}}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]For homework Sarah had 45 English problems for spring break homework. If she can finish nine problems in an hour, how long will it take her to finish all the problems?
Answers
Answer:
5 hours
Step-by-step explanation:
assuming she works consecutively on these problems. if it takes 9 problems for 1 hour, and there are 45 problems, all that's needed to be done is 45/9, which is 5
What's the answer for 6m^2+18m+17=-3m^2+9
Answers
Answer:
m=−2/3 or m=−4/3
Step-by-step explanation:
Step 1: Subtract -3m^2+9 from both sides.
6m^2+18m+17−(−3m^2+9)=−3m^2+9−(−3m^2+9)
9m^2+18m+8=0
Step 2: Factor left side of the equation.
(3m+2)(3m+4)=0
Step 3: Set factors equal to 0.
3m+2=0 or 3m+4=0
m=−2/3 or m=−4/3
*PLEASE HELP* *IRRELEVANT ANSWERS WILL BE REPORTED AS SPAM*
A plane left Chicago at 8:00 A.M. At 1:00 P.M., the plane landed in Los Angeles, which is 1500 miles away. What was the average speed of the plane for the trip? (include units)
Find slope:
Then find the average speed of the plane for the trip
Answers
[tex]\\ \rm\hookrightarrow Avg\: Speed=\dfrac{Total\: distance}{Time}[/tex]
[tex]\\ \rm\hookrightarrow Avg\:Speed=\dfrac{1500}{5}[/tex]
[tex]\\ \rm\hookrightarrow Avg\:Speed=500mph[/tex]
Step-by-step explanation:
150/50=50
So 50mph is average speed
Formula Used :-Speed=Distance/Time
Lincoln High School has 84 teachers. 12 of the teachers teach math. Of the 32 females teachers, 6 teach math.
What is the probability that a teacher is a woman or teaches math? Express your answer as both a fraction and a percetage.
Answers
Probabilities are used to determine the chances of events
The probability that a teacher is a woman or teaches math is 45.24%
How to determine the probabilityThe given parameters are:
Teachers = 84
Math teachers = 12
Female teachers = 32
Female math teachers = 6
The number of female or math teachers is:
Female or math = Math + Female - Female math
So, we have:
Female or math = 12 + 32 - 6
Female or math = 38
The probability that a teacher is a woman or teaches math is:
[tex]Pr = \frac{38}{84}[/tex]
Simplify
[tex]Pr = \frac{19}{42}[/tex]
Express as percentage
[tex]Pr = 45.24\%[/tex]
Hence, the probability that a teacher is a woman or teaches math is 45.24%
Read more about probability at:
https://brainly.com/question/25870256
The citizens of a city were asked to choose their favorite pet. The circle graph shows how the citizens answered. If 65,000
citizens answered the question, how many chose Dogs or Snakes?
Answers
Answer:
Dogs: 14,300 people
Snakes: 3,900 people
Carmen is a professor at a local university. In collecting data on her Introduction to Business course for a year, she wants to calculate the z-score for a student who scores a 92 on the final exam. The mean and the standard deviation scores on the exam are 76 and 6, respectively. Calculate the z-score.
Answers
The z score of a student who scores a 92 on the final exam is 2.67.
Z scoreZ score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (x - μ) / σ
where x is the raw score, μ is the mean and σ is the standard deviation
Given that σ = 6, μ = 76. For a raw score of 92:
z = (92 - 76) / 6 = 2.67
The z score of a student who scores a 92 on the final exam is 2.67.
Find out more on Z score at: https://brainly.com/question/25638875
Player Aled a baseball league in runs batted in for the 2005 regular season. Player B, who came in second to player A, had 18 fewer runs batted in for the 2005 regular
season. Together, these two players brought home 232 runs during the 2005 regular season. How many runs batted in did player A and player Beach account for?
CE
Player A had runs and player B had runs batted in for the 2005 regular season.
Answers
Answer:
ok so we trying to find out how many each batted so lets make this a system of equation
first we now that combined they are 232 so
a+b=232
then we now that b is 18 less then a so
a-18=b
the system of equation is
a+b=232
a-18=b
so we now what b is so we can just plug that in
a+a-18=232
2a-18=232
2a=250
a=125
then we can just plug this back in
125+b=232
b=107
a=125
b=107
Hope This Helps!!!
8≥−6x−x^2
find Inequality for X
Answers
Inequality for X.......:)
Please help, thanks in advance
Answers
Answer:
D. [tex]\frac{45a^{16}c^{34}}{b^{27}}[/tex]
Step-by-step explanation:
Here you are...
Hope this helps! Brainliest would be much appreciated! Have a great day! :)
6) Suppose you put $200 in a savings account. The account earns simple interest at an
annual rate of 10%. You earned $100 in interest. How many years did you keep the
money in your savings account?
Answers
====================================================
Work Shown:
i = P*r*t
100 = 200*0.10*t
100 = 20t
20t = 100
t = 100/20
t = 5
Please help me I will give you brainliest!
Answers
Answer:
data set 1 - y=x*3.5 data set 2 - y=x*3
Step-by-step explanation:
=======
#14-#19
help would rlly be great! i'm struggling rlly hard
Answers
Answer:
14. ∠UVS = 63.6°
15. ∠TWU = 90°
16. ∠TUV = 116.4°
17. UW = √111 ≈ 10.5
18. SU = 2√111 ≈ 21.1
19. VT = 34
Step-by-step explanation:
The relevant relations for a rhombus are ...
diagonals bisect each other at right angles, dividing the figure into 4 congruent right trianglesthe diagonals bisect the vertex anglesadjacent vertex angles are supplementary__
14.Angle UVS is double the measure of angle UVW. 2×31.8° = 63.6°.
angle UVS = 63.6°
__
15.As we said above, the angles where the diagonals cross are right angles.
angle TWU = 90°
__
16.Angle TUV is supplementary to angle UVS. 180° -63.6° = 116.4°
angle TUV = 116.4°
__
17.UW is found using the Pythagorean theorem.
UW² +TW² = TU²
UW² = TU² -TW² = 20² -17² = 111
UW = √111 ≈ 10.536
__
18.The whole diagonal is twice the measure of half of it. SU = 2×UW
SU = 2√111 ≈ 20.071
__
19.The whole diagonal is twice the measure of half of it. 2×17 = 34
VT = 34
Given the lengths of two sides of a triangle, write an inequality to indicate between which two numbers the length of the third side must fall. 8 and 13
Answers
Answer:
13-8<3rd<13+8 so
5<3rd<21
Step-by-step explanation:
The theorem of Angles-Sides Inequalities.
I got this question too in RSM
Answer: 5 and 21
Step-by-step explanation: look below
6.82×105 minus 3.11×104
Answers
Answer:
Simplify the expression.
answer :
392.66
Step-by-step explanation:
Answer:
392.66
Step-by-step explanation:
Our equation at first is (6.82x105) - (3.11x104)
We first multiply 6.82 and 105 and we get 716.1
Now our equation is 716.1 - (3.11x104)
Now we multiply 3.11 and 104 and we get 323.44
We now subtract 716.1-323.44 and we get our final answer of…
392.66!
Please award brainliest if possible!
Chase and Sara went to the candy store. Chase bought {6}6 pieces of fudge and {3}3 pieces of bubble gum for a total of ${18.00}18.00. Write an equation using {f}f for cost of fudge and {g}g for cost of gum. (No spaces, just numbers and symbols.)
Answers
Hopefully this helps you
Read the story. The Bridgetown Youth Group had their annual pancake breakfast yesterday. At the breakfast, there were 5 blueberry pancakes eaten for every 6 plain pancakes eaten. Pick the diagram that models the ratio in the story. If 108 plain pancakes were eaten, how many blueberry pancakes were eaten? blueberry pancakes
Answers
Answer:
90
Step-by-step explanation:
Firstly, you divide 108 by 6, since 108 can't be divided by 5, and 108 divided by 6 gives you 18. Then you multiply 18 by 5, which gives you 90. Boom.
Answer: the answer is 90
Step-by-step explanation: