Answer:
1.056 seconds
Step-by-step explanation:
Solution:-
- When a ball is thrown vertically in air from a height of "so" from the ground at a velocity of " vo " it follows a parabolic trajectory. The ball undergoes its upward motion against gravity. Hence, it has negative acceleration of a = -g = -32 ft/s^2.
- When the balls reaches its maximum height in air, it starts its downward journey under the complete influence of gravity; hence, it accelerates with a = +g = 32 ft/s^2.
- The entire trajectory of the ball is governed by the constant acceleration "a" due to gravity and neglecting any other effects on the ball i.e air resistance.
- There are three kinematic equation of motion valid for any particle undergoing independent one dimensional motion with constant acceleration.
- For vertical trajectory the displacement "h" from the ground is given by the second kinematic equation of motion:
h - so = vo*t + 0.5*a*t^2
h = vo*t + 0.5*a*t^2 + so
Where the parameters are given as:
so = 2 feet
vo = 15 ft/s
a = - 32 ft/s^2
Therefore we have:
h = 15*t + 0.5*(-32)*t^2 + 2
h = -16t^2 + 15t + 2
- To determine the amount of time the ball is in air the displacement is given by the distance from the ground. The journey starts when the ball is thrown from height "so" and ends when it strikes the ground; hence, at h = 0 ft.
0 = -16t^2 + 15t + 2
0 = 16t^2 -15t - 2
- Use the quadratic formula to solve for time "t":
[tex]t = \frac{-b+/-\sqrt{b^2 - 4*a*c} }{2a} \\\\at^2 + bt + c = 0[/tex]
- Plug in the respective constants:
[tex]t = \frac{15+/-\sqrt{15^2 - 4*16*-2} }{32} \\\\ t = \frac{15+/-18.78829 }{32} \\\\t = 1.056 s[/tex]
- The total time for ball in air would be 1.056 seconds. ( Neglect the negative value of time )
Choose the graph that represents the linear equation 6x - 2y = 12. *
9
Answer: x-intercept = 2, y-intercept = -6
Step-by-step explanation:
To solve this problem, we must first convert 6x - 2y = 12 to slope-intercept form by getting y by itself.
1. 6x - 2y = 12
2. -2y = 12 - 6x
3. -2y/-2 = 12/-2 - 6x/-2
y = 3x - 6
Using our knowledge of what the slope-formula represents, we know that the -6 is the y-intercept.
To find the x-intercept, we set the formula equal to 0 instead of y and solve for x.
1. 0 = 3x - 6
2. 0 + 6 = 3x
3. 6/3 = 3x/3
x = 2
Which two of the following are continuous data?
A) concert attendance
B) age of a student
C) number of pens in a box
D) time taken to run 1 mile
Answer:
Age of a student (B) and Time taken you run 1 mile (D)
Step-by-step explanation:
Only the age of a student and the time taken to run 1 mile are continuous data.
What are the types of data?
The data is classified into majorly four categories:
Nominal data: Nominal Data is used to label variables without any order or quantitative value.Ordinal data: Ordinal data have natural ordering where a number is present in some kind of order by their position on the scale. Discrete data: The term discrete means distinct or separate. The discrete data contain the values that fall under integers or whole numbers.Continuous data: Continuous data are in the form of fractional numbers. It can be the version of an android phone, the height of a person, the length of an object, etc. Continuous data represents information that can be divided into smaller levels. The continuous variable can take any value within a range.As per the given definitions above we can state that Continuous data is (B) the Age of the students (D) the Time taken to run 1 mile
Therefore, the Answer is (B) and (D)
Learn more about data here:
https://brainly.com/question/10980404
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What is the area of the rectangle?
Answer:
Root square 25² - 15² = 20
Area = 20×15 = 300 cm²
Can u add me as Brainest pls?
I need help with question 10 please
Answer:
172
Step-by-step explanation:
13/40=x/528
40x=6864
x=172
A sporting equipment company wants to sell a new bicycle helmet. They have developed a function, shown below, where total profit, p, can be determined based on sale price, s.
What will be the total profit if the sale price of the helmet is $60?
Answer:
[tex] p(s) = -24s^2 +2200 s -18000[/tex]
If we use the valie of s =60 we have
[tex] p(60) = -24 (60)^2 +2200*60 -18000[/tex]
And after solve we got:
[tex] p(60)= -86400 +132000 -18000 =27600[/tex]
So then the best option for this case would be:
$27,600
Step-by-step explanation:
Using the following info in order to complete the problem:
p(s)=-24s^(2)+2200s-18000
$112,560
$27,600
$111,120
$236,400
$14,240
We have the following function given:
[tex] p(s) = -24s^2 +2200 s -18000[/tex]
If we use the valie of s =60 we have
[tex] p(60) = -24 (60)^2 +2200*60 -18000[/tex]
And after solve we got:
[tex] p(60)= -86400 +132000 -18000 =27600[/tex]
So then the best option for this case would be:
$27,600
Explain the significance of m and b in y = mx + b.
Answer:
the slope of the equation
A. 30.0 in
B. 7.5
C. 10.8
D. 27.6in
Answer:
A
Step-by-step explanation:
For which of the following graphs would it make sense to connect
the points?
a. a graph showing the amount of Karl's monthly rent
b. a graph showing the number of signatures on a petition
c. a graph of the temperature at each hour during the day
d. a graph showing the number of raffle tickets sold
I think that the correct answer to the question is A
This net can be folded to form a cube with a side length of 20 units. A cube has side lengths of 20 units. What is the surface area of the cube in square units? 1,400 square units 2,400 square units 4,800 square units 8,000 square units
Answer:
2400
Step-by-step explanation:
Answer:
2,400 square units / B
Step-by-step explanation:
Of the songs in Nicholas's music library, 1/2 are rock songs. Of the rock songs, 2/5 feature a guitar solo. What fraction of the songs in Nicholas's music library are rock songs that feature a guitar solo?
Answer:
1/10
Step-by-step explanation:
The ratio of yes votes to no votes was 5 to 7. If there were 10,092 total votes, how many yes votes were there?
Answer:
4,205
Step-by-step explanation:
5 + 7 = 12
10,092 ÷ 12 = 841
multiplier for the ratio is therefore 841.
5:7 is yes:no
since you want the number of yes votes, u take the 5 and multiply it by the multiplier found before.
5 × 841 = 4,205 yes votes.
Kevin won two goldfish at the county fair. He put them in a bowl with 2 liters of water. The next day, he bought a fish tank that holds 75 liters of water.How much more water does the tank hold than the bowl?
Answer:
UDCVUEGBCYEJJAJAJ
Step-by-step explanation:
does anyone know the answer for top and bottom? please help
Answer:
15/18=5/6
14/18=7/9
the last symbol
Step-by-step explanation:
Answer:
For the first part (the part on the top), you have to make the fractions have the same denominator. To do this, you must find the LCM (least common multiple) of 6 and 9. The LCM of 6 and 9 would be 18 because 6x3=18 and 9x2=18. Now, both of the denominators are 18. But we still have to change the numerators! To change the numerators, we must multiply them by the same numbers that we multiplied the denominators by. So for 5/6, we would multiply the 5 (the numerator) by 3 because that is what we multiplied the 6 by. 5x3=15. So now the first fraction, 5/6, is 15/18 (that's the answer). For 7/9, we still have to multiply the 7 (the numerator) by 2. 7x2=14. So now this fraction, 7/9, is 14/18 (that's the answer).
So basically what I was saying is that 5/6=15/18 and 7/9=14/18.
For the second part (the part on the bottom), you have to compare the fractions. It is difficult right now as it is written as 5/6 and 7/9. But remember what we did for the first part! Think about these fractions as 15/18 and 14/18. 15/18 is larger than 14/18. So the answer for the part on the bottom is 5/6 > 7/9.
Hope this helps! :)
An airplane took off and flew at an angle of elevation 12° with the ground. What was the approximate altitude of the airplane, (high how is the plane directly from the ground), after it had flown 8,000 meters (hypotenuse)?
Answer:
1663 m approx.
Step-by-step explanation:
We have a right triangle in which we know the hypotenuse and need to find the opposite side, so we use the sine function:
sin 12 = h / 8000
h = 8000 sin 12
= 1663 m approx.
Nathan took his car in for service and repair. He had a coupon for 15% off. $261.36 $381.25 $77.52 Which amount is closest to Nathan's total costs after the 15% discount and 7% sales tax?
Answer:
Total amount to be paid = $655
Step-by-step explanation:
Given,
Total price before coupon is = 261.36 +381.25+77.52
= $720.13
Discount = 15%
Amount of discount = 15% of total amount
Amount of discount = [tex]\frac{15}{100} \times 720.13[/tex]
= $108.02
Remaining amount = Total amount - discount amount
Remaining amount = $720.13 - $108.02
= $612.11
Sales tax = 6%
Amount of sales tax = 6% of remaining amount
[tex]=\frac{6}{100} \times 612.11\\\\=42.85[/tex]
Amount to be paid = Remaining amount + sales tax
= 612.11 + 42.85
= 654.96
Rounding off to nearest whole number;
Total amount to be paid = $655
Dylan has a square piece of metal that measures 17 inches on each side. He cuts the metal along the diagonal, forming two right triangles. What is the length of the hypotenuse of each right triangle to the nearest tenth of an inch?
Answer:
24 Inch
Step-by-step explanation:
When the square piece of metal is cut along the diagonal, it forms two right triangles where each of the right triangle has legs of 17 inches.
To determine the length of the hypotenuse, we use the Pythagorean Theorem.
[tex]\text{Pythagoras Theorem}: Hypotenuse^2=Opposite^2+Adjacent^2\\Hypotenuse^2=17^2+17^2\\Hypotenuse^2=289+289\\Hypotenuse^2=578\\Hypotenuse=\sqrt{578} \\=24.04\\\approx 24$ inch ( to the nearest tenth of an inch)[/tex]
Answer:
24 square inches
Step-by-step explanation:
Find the area of the triangle.
b = 40 m
h=13.4 m
Answer:
[tex]268 {m}^{2} [/tex]
Step-by-step explanation:
[tex] \frac{1}{2} \times b \times h \\ \frac{1}{2} \times 40 \times 13.4 \\ = 268 {m}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What is the domain of the function f(x)=x^2+3x+5?
OA
all whole numbers
OB.
all positive real numbers
O c. all integers
OD. all real numbers
Answer:
all real numbers
Step-by-step explanation:
Answer:
The domain of this function is all real numbers
Step-by-step explanation:
Unless there is a domain restriction for the function, the domain of a function is all real numbers. This means that all we need to do is determine whether there is a domain restriction.
The things that cause a domain restriction are: an x in the denominator of a fraction like [tex]f(x)=\frac{1}{x}[/tex] or a radical like [tex]f(x)=\sqrt{1-x}[/tex]
As there are no variables in the denominator or a radical, we can conclude that the domain of this function is all real numbers.
Express x in term of y:x/7+2y=6
Answer:
You have to multiply the denorminator to both sides in order to make x the subject :
[tex] \frac{x}{7 + 2y} = 6[/tex]
[tex]x = 6(7 + 2y)[/tex]
Answer:
Given
x/7 + 2y = 6
Multiply through by 7 to clear the fraction
x + 14y = 42 ( subtract 14y from both sides )
x = 42 - 14y
Step-by-step explanation:
3. The temperature dropped 5 degrees each hour for 7 h. Use an integer to represent
the total change in temperature.
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14 in total
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thats all i came here for
Someone help please! I put A but I’m not sure if it’s correct.
Answer: B
21x^2-17x+2
Step-by-step explanation:
Which two expressions have the same value?
Answer:
a.
Step-by-step explanation:
i don't know the explanation step by step
Find the quotient: 8,441 ÷ 21 = ________. a. 400 r 12 b. 400 r 20 c. 401 r 12 d. 400 r 20
I Believe that the correct answer is option C) 401 r
8,441 ÷ 21 = 401.952380952
HOPE THIS HELPED!!!
If not please comment below
Write an equation to represent the following statement.
The sum of j and 47 is 55.
Answer:
J plus 47 = 55
If you need to find J
The value of J is
J=55-47
J=8
Step-by-step explanation
17. The length, breadth and height of a cuboid are doubled. What happens to its
surface area?
A.It is doubled.
B.It becomes four times.
C It becomes eight times.
D. (Nothing can be said with out knowing the dimensions of the cuboid.)
guys please tell the answer for this question....please.....
Answer:
D.
Step-by-step explanation:
Try any example and double
you will find that A is incorrect
B) incorrect
C incorrect
D is my answer.
Expand 4(-2x - 3)
Factorise 5n + 15
シ︎❤︎✰✌︎
Look at the attached picture
Hope it will help you
Good luck on your assignment
Have a great day...
a rectangle is reduced by a scale factor of 1/4 which choices show the ratio of the area hurry because i need this for a test
Aleecha107Junior Moderator
Answer:
The area would be 1 : 16 ratio, of the smaller rectangle to the larger one.
Step-by-step explanation:
I used a rectangle with the side length of 1 to model this for me. You can choose any number, but 1 is easy to multiply.
If the original rectangle had a side length of 1 and 1, the area would be 1.
If you reduce the size to 1/4th of the size, the area would be 0.0625, or 1/16th of the original.
I hope this helped!
Someone help me with this please
Answer:
60 88
Step-by-step explanation:
khn566
Answer:
60 and 88
Step-by-step explanation:
Mark spent $73.43 on some CDs. He purchased 7 CDs. What was the price of each CD?
Answer:
$10.49
Step-by-step explanation:
if the problem doesn't account for tax, 73.43 divided by 7 is 10.49
Ms. Ahmed has a rectangular garden where she grows tomatoes. The length of her garden is represented by t + 4 and the width by 2t - 1. Express the area of Ms. Ahmed's garden as a polynomial in standard form. If the area of Ms. Ahmed's garden is 56 ft2, what are the dimensions of the garden?
Answer:
Area of the garden in standard form:
Area = (2t^2) + 7t - 4
The dimension of the garden is 8ft × 7ft
Step-by-step explanation:
Length of the rectangular garden, L = t+4
Width of the garden, B = 2t - 1
Area = length * width
Area = (t+4) * ( 2t-1)
Area = (2t^2) + 7t - 4..….......(1)
If the Area = 56 ft^2
Substitute Area into (1)
56 = (2t^2) + 7t - 4
(2t^2) + 7t - 60 = 0
(2t^2) - 8t + 15t - 60 = 0
2t(t - 4) + 15(t - 4) = 0
(2t+15) (t-4) = 0
Let 2t + 15 =0
t = -7.5
Let t - 4 = 0
t = 4
* When t = -7.5
Length, L = -7.5 + 4 = -3.5 ft
Width, B = 2(-7.5) -1 = -16 ft
Since length and breadth cannot be negative, t = -7.5 is not possible
** When t = 4
Length, L = 4+4 = 8 ft
Width, B = 2(4) - 1 = 7 ft
Therefore, the dimension of the garden is 8ft × 7ft
Answer:
The dimension is 8ft by 7ft
Step-by-step explanation:
Given data
Length l = [tex](t+4)[/tex]
Width w= [tex](2t-1)[/tex]
the area is expressed as [tex]A= length * width[/tex]
[tex]A= (t+4)*(2t-1)\\A= t(2t-1) +4(2t-1)\\A= 2t^{2}-t+8t-4\\[/tex]
collecting like terms we have
[tex]A= 2t^{2} +7t-4[/tex]
hence our expression for area is [tex]A= 2t^{2} +7t-4[/tex]
given that the area is [tex]56ft^{2}[/tex] to solve for the sides we need to first solve fot t
equating the expression for area to 56 we can solve for t
[tex]A= 2t^{2} +7t-4= 56[/tex]
taking the constant term to the other side and solve we have
[tex]A= 2t^{2} +7t-4-56\\A= 2t^{2} +7t-60\\[/tex]
we can substitute two factors for 7t that when multiplied we give -60 and when added we give 7 these factors are 15 and -8
[tex]A= 2t^{2} +7t-60\\\\A= 2t^{2} -8t+15t-60\\2t^{2} -8t+15t-60=0\\\\2t(t-4) +15(t-4)= 0\\2t+15=0, (t-4)= 0\\2t=-15, t= -7.5\\t= 4[/tex]
t=4 hence the length is
[tex](t+4)\\(4+4)= 8ft\\[/tex]
hence the width is
[tex](2t-1)\\(2*4-1)= (8-1)= 7ft[/tex]