David drops a ball from a bridge at an initial height of 100 meters.

(a) What is the height of the ball to the nearest tenth of a meter exactly 3 seconds after he releases the ball?

(b) How many seconds after the ball is released will it hit the ground?

Answers

Answer 1
(a) 55.9 m

(b) About 4.518 seconds.

_____
A graphing calculator can be helpful for these.
David Drops A Ball From A Bridge At An Initial Height Of 100 Meters.(a) What Is The Height Of The Ball
Answer 2
The general formula is:
[tex]y = y_{o} + v_{o}t - \frac{1*g*t^{2} }{2} [/tex] -- (A)

Where g = 9.8 m/s/s
[tex]v_{o}[/tex] = 0
[tex]y_{o}[/tex] = 100

a)
Time=t=3s.
Plug-in the values in (A)
y = 100 -(1/2*9.8*3*3)
y = 100-44.1 = 55.9m

Height of the ball exactly after 3 seconds = 55.9m.

b)
At ground, y=0; Plug-in values in (A):
A=> 0 = 100 - (1/2* 9.8 * [tex]t_{2}[/text])
Therefore t = + 4.52 s and - 4.52 seconds.

As t cannot be negative, therefore:
Time when ball hits the ground = 4.52s

-i

Related Questions

The cost of a single ticket depends on the number of tickets, t, purchased in a group, as represented by the function C(t).

C(t) = $18.50 1 <_t < 12
$16.00 12<_t < 20
$14.50 20<_t

What is the total cost for 20 tickets?
A.)$14.50
B.)$16.00
C.)$290.00
D.)$320.00

Answers

The total cost for 20 tickets:
20 · 14.50 = $290.00
Answer: C ) $290.00

Answer:

C. $290

Step-by-step explanation:

We see that,

The cost of the single ticket is given by,

[tex]C(t) =\left\{\begin{matrix} 18.50, &1\leq t\leq 12 \\ 16.00, & 12\leq t\leq 20\\ 14.50, & 20\leq t\end{matrix}\right.[/tex],

where t = number of tickets.

As, we have,

When t = 20, the value of C(t) is $14.50.

That is, the cost of 20 tickets = 20 × 14.50 = $290.

Thus, the total cost of 20 tickets is $290.

Please help! what is y+7=-1/7(x+4) in slope intercept form?

Answers

we know that
the equation of a line in slope intercept form is--------------> y=mx+b
where
m-----------> is the slope
b-----------> is the y-intercept  point when x=0

y+7=-1/7(x+4)---------> y+7=(-1/7)x-4/7
y+7=(-1/7)x-4/7------> y=(-1/7)x-4/7-7------> y=(-1/7)x-(53/7)

the answer is
y=(-1/7)x-(53/7)-------------> this is the equation of a line in slope intercept form
m=(-1/7)=-0.14
b=(-53/7)=-7.57
y=-0.14x-7.57

see the attached figure

Identify the initial amount a and the growth factor b in the exponential function a(x) =680•4.3^

Answers



         f(x)  =  680   (   4   )³
                      a         b

Multiply the binomials (x - 8) (x + 8)

Answers

(x - 8) (x + 8)
= x^2 - 8x + 8x -64
= x^2 - 64

What is an equation of a line that is perpendiculauation is 2y=3x-10 and passes through -6,1?

Answers

There's a bit of a neat trick for doing these. You swap the x- and y-coefficients and negate one of them. You use the methods of translating functions to translate the answer to the point of interest. For example, you use (x -h) and (y -k) in place of (x, y) when you want the line to go through (h, k).

3(y -1) = -2(x +6)

A garden has four sides that are all the same length. Each side measures x+4 units. The garden's perimeter is 112 units. What is the value of x? Enter your answer in the box.

Answers

we know that
the garden's perimeter is 112 =[(x+4)+(x+4)+(x+4)+(x+4)]  

112=4*[x+4]------------ > 112/4=x+4
x=(112/4)-4=28-4=24 units

the answer is x=24 units

Answer: x=24 :)

Step-by-step explanation:

write fifty-seven and one hundred forty-two thousandths in standard form.

Answers

57,142 because it says standard

Fifty-seven and one hundred forty-two thousandths in standard form is 57.142, which is the conventionally written numeric form without placeholder zeroes.

The number fifty-seven and one hundred forty-two thousandths in standard form is written as 57.142. The standard form of writing numbers is also known as conventional notation, which means writing out the number as it is normally seen and used. To convert a number into standard form, you place the decimal point after the last non-zero digit and write out the number without any placeholder zeroes.

factor the equation.

Answers

x² - 11x + 18

find factors of x² and 18 that will give you -11x

x² - 11x + 18
x               -9
x               -2

(x - 9)(x -2) is your answer

if you are finding the x, place each parenthesis equal to zero

x - 9 = 0
x - 9 (+9) = 0 (+9)
x = 9

x - 2 = 0
x - 2 (+2) = 0 (+2)
x = 2

x = 2, 9


hope this helps

Can someone help me? Any mathematicians? I'll give you the brainliest and points

Answers

Answer:
Choice A
Min value: -4
Domain: All real numbers
Range: All real numbers greater than or equal to -4

---------------------------------------------------------------------------------
---------------------------------------------------------------------------------

The given equation y = 2(x-3)^2-4 is in the form y = a(x-h)^2 + k

a = 2 is the leading coefficient
since the leading coefficient is positive, the graph opens upward meaning this graph has a min value (instead of a max). Since we know it doesn't have a max, we can rule out choice B and choice C

The min value is the value of k, which in this case is k = -4. At this point, we can see the answer is choice A. Recall that (h,k) is the vertex which is either the highest or lowest point. 

Adding on more confirmation that the answer is choice A, the domain is in fact the set of all real numbers. We can replace x with any number want to get some output value for y. There are no restrictions since we don't have to worry about dividing by zero or taking the square root of a negative number.

The range is the set of y values such that y >= -4. Basically y is either -4 or larger than -4. This comes from the fact that y = -4 is the smallest output possible (aka the min value mentioned earlier)

A rectangle is 25 inches long and 13 inches wide. What is the area of the rectangle?

Answers

Length x width = area of a rectangle

Therefore,

25 x 13 = 325

The answer is 325 inches squared.

Hope this helps! Good luck! :D

Answer:

GUYS HE MEANT 2/5 AND 1/3

Step-by-step explanation:

THE REAL ANSWER IS 2/15

Area of rectangle is given by:

where

A is the area of rectangle

l is the length of the rectangle

w is the width of the rectangle

As per the statement:

a rectangle is 2/5 inches long and 1/3 in wide

and  inches

then using area formula we have;

Simplify:

inches square.

Therefore, the area of rectangle is  square inches.

Jessica paid $13.24 for a 3.41-pound bag of shrimp at one store. The following week, she paid $18.99 for a 4.96-pound bag at another store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent.

Answers

Answer:  1st answer is 3.88 lastly the 2nd is 3.83

Step-by-step explanation:

The bag with price $18.99 for a 4.96-pound bag is best to buy.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Jessica paid $13.24 for a 3.41-pound bag of shrimp at one store.

So, Jessica paid for one pound of shrimp = 13.24/ 3.41

                                                                     = $3.88

                                                                      = $3.9      

and, he paid $18.99 for a 4.96-pound bag at another store.

So, she paid for one pound = 18.99/4.96

                                              = $3.8286

                                              = $3.8

Hence, the bag with price $18.99 for a 4.96-pound bag is best to buy.

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Francis have 5 more dollars than Julia together they have at most $45 let X represent the amount of money francis has. Which inequality can be used to find the possible amounts of money that francis has?

Answers

x=francis  y=julia

the answer is francis has $27.5 and julia has $17.5 you find this by 45 and dividing it by 2 then get on half and add 5 and with the other half subtract five

If f(x) is a linear function, what is the value of n?

Answers

Answer:

Option C. 13

Step-by-step explanation:

Since f(x) is a linear function then we can rewrite the function in the form of an equation y = mx + c

where m is the slope of a line.

Since line passes through two points (3, 7), (9, 16)

Therefore m = (16 - 7)/(9 - 3) = 9/6 = 3/2

Now we know a point (16, 26.5) also lie on the line so by putting the values of m, x, and y in the equation.

y = 3x/2 + c

26.5 = 3×16/2 + c

c = 26.5 - 24 = 2.5

So the equation is y = 3x/2 + 5/2

y = 1/2(3x + 5)

If a point (7, n) lies on the line then

n = 1/2(3×7 + 5) = 1/2(21 + 5) = 26/2 = 13

Therefore n = 13 is the answer.

Which expression is not equivalent to 3x – 2?

A. x + x – 1 – 1 + x
B. 2x + 2 + x
C. 3 – x + 2x – 5 + 2x
D. 4x – 4 – x + 2

Answers

The expression which is not equivalent to the given expression is 2x + 2 + x. Hence, option B is correct.

What is an expression?

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given information in the question,

The given expression is,

3x - 2

Now, one by one check with given options,

A. x + x - 1 - 1 + x = 3x - 2, So, it is correct.

B. 2x + 2 + x = 3x + 2, So, it is incorrect.

C. 3 - x + 2x - 5 + 2x = 3x + 2, So, it is correct

D. 4x - 4 - x + 2 = 3x + 2, So, it is correct.

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b

just got it right on edge

Which pair of measurements is not equivalent?
450 mm, 4.5 m
250 cm, 2.5 m
4 km, 4,000 m
1.2 cm, 12 mm

Answers

450 mm doesn't equal 4.5 m.

450 mm = 45 cm
45 cm = 0.45 m
0.45 doesn't equal 4.5

Hope this helps!

Final answer:

The pair of measurements that is not equivalent is 450 mm and 4.5 m.

Explanation:

When comparing pairs of measurements, it's important to convert them to the same unit before making a comparison. Let's examine the pairs to determine which one is not equivalent:

450 mm is convertible to meters by dividing by 1000, as there are 1000 millimeters in a meter, giving us 0.45 m. This is not equal to 4.5 m.250 cm is convertible to meters by dividing by 100, since there are 100 centimeters in a meter, resulting in 2.5 m. Hence, 250 cm and 2.5 m are equivalent.4 km converts to meters by multiplying by 1000, as there are 1000 meters in a kilometer, resulting in 4000 m. Therefore, 4 km and 4000 m are equivalent.1.2 cm is convertible to millimeters by multiplying by 10, as there are 10 millimeters in a centimeter, giving us 12 mm. So, 1.2 cm and 12 mm are equivalent.

The non-equivalent pair is 450 mm and 4.5 m. All other pairs are equivalent after conversion.

please help with another math question

Answers

Given system of equations:
2y=4x+20 Eq 1
4y=6x+24 Eq 2
Divide both sides of equation 1 by 2.
y=2x+10
Substitute value of y in equation 2.
4(2x+10)=6x+24
8x+40=6x+24
2x+40=24
2x=-16
x=-8
Put value of x in y=2x+10
y=2(-8) + 10
y=-16+10
y=-6

Answer : (-8,-6)

The length of a rectangle is 4 cm longer than the width. if the perimeter of the rectangle is 20 centimeters, what is the area of the rectangle?

Answers

P=2(w)+2(l)

length=x+4
width=x

2(x)+2(x+4)=20
use the distributive property

2x+2x+8=20
combine like terms

4x+8=20
subtract 8 from both sides

4x=12
divide both sides by 4 to isolate x

x=3

Length=x+4=3+4= 7
Width= 3

According to the above graph, which industry will have 25% more growth than health services over the period from 2000 to 2010?

Answers

It is c. b is wrong.

Industry which will have 25% more growth than health services over the period from 2000 to 2010 is Computer and data processing.

What is data?

In computing, data is information that has been translated into a form that is efficient for movement or processing.

Given that, a graph titled top 10 Industries with Fastest Growth and Salary Employment 2000 to 2010.

Here,

Health services, 57;

Personnel supply services, 49;

Warehousing and storage, 45;

Water and sanitation, 45;

Computer and data processing, 86;

Management and public relations, 42;

Cable television services, 51;

Residential care, 64;

Business services, 43;

Equipment rental and leasing, 42.

So, according to the given data the highest record is given by computer and data processing.

Therefore, industry which will have 25% more growth than health services over the period from 2000 to 2010 is Computer and data processing.

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"Your question is incomplete, probably the complete question/missing part is:"

A graph titled Top 10 Industries with Fastest Growth and Salary Employment 2000 to 2010 showing percent change for the following: health services, 57; personnel supply services, 49; warehousing and storage, 45; water and sanitation, 45; computer and data processing, 86; management and public relations, 42; cable television services, 51; residential care, 64; business services, 43; equipment rental and leasing, 42.

According to the above graph, which industry will have 25% more growth than health services over the period from 2000 to 2010?

A. Equipment rental and leasing

B. Residential care

C. Computer and data processing

D. None of these

Andy is buying carpet squares for his living room. the length of the room is 20 feet, and the width is 16 feet. each carpet square covers 4 square feet. how many carpet squares will andy need to purchase to cover the room

Answers

Answer:

andy needs 80 carpet squares

Step-by-step explanation:

Final answer:

To cover the living room, multiply the room's length by its width to get the area in square feet (320 square feet), then divide by the area that one carpet square can cover (4 square feet), resulting in 80 carpet squares needed.

Explanation:

To calculate the number of carpet squares needed to cover Andy's living room, we start by finding the area of the room. The area is the product of the length and the width, so we multiply the room's dimensions: 20 feet (length) by 16 feet (width). This calculation gives us an area of 320 square feet. Next, we divide the total area by the area that each carpet square can cover. Since each square covers 4 square feet, we divide 320 square feet by 4 square feet per square to determine the number of squares needed:

320 square feet ÷ 4 square feet/square = 80 squares.

Therefore, Andy will need to purchase 80 carpet squares to cover the living room.

helpppppppppppppppppppppppppp

Answers

Answer:
The last choice is the correct one

Explanation:
We can solve this question using "difference between squares" which has the following general rule:
a^2 - b^2 = (a+b)(a-b)

For the given question:
p^4 - 16 = (p^2 - 4)(p^2 + 4)

Now, p^2 - 4 can be further factorized using difference between squares, therefore:
p^4 - 16 = (p-2)(p+2)(p^2 + 4)

Hope this helps :)

Alina has one-quarter of a dollar for parking money. Which amount is equivalent to her parking money?

Answers

This answer would be .25, otherwise known as 25 cents

How many pounds of cashew nuts worth 75 cents a pound must be mixed with 10 pounds of pecans worth $1.50 a pound to make a mixture worth $1.00 a pound? Which of the equations could be used to solve for p, the pounds of cashew nuts? 75p + 150(10) = 100(p + 10) 75(p + 10) + 150(10) = 100(p + 10) 75p + 150 = 100(p + 10)

Answers

Answer:

  75p + 150(10) = 100(p + 10)

Explanation:

Mixture problems such as this can be solved by writing an equation that expresses the total cost of the mixture in terms of the costs of the constituents.

Here, the cost (in cents) of p pounds of cashews will be 75p. The cost (in cents) of the 10 pounds of pecans at $1.50 per pound will be 150(10). The total cost of p+10 pounds of the mixture is desired to be 100(p+10).

The equation of the 1st selection is appropriate. It tells that the prices of the contributing nuts add to give the price of the mixture, just as you want:

  75p + 150(10) = 100(p+10)

The correct equation to solve for the pounds of cashew nuts, denoted as p, that must be mixed with pecans to get a mixture worth $1.00 a pound is: 75p + 150(10) = 100(p + 10).

We are trying to determine how many pounds of cashew nuts that are worth 75 cents a pound must be mixed with 10 pounds of pecans worth $1.50 a pound to create a mixture worth $1.00 a pound. Let's denote the pounds of cashew nuts needed as p. The respective values of each type of nut are included in calculating the total value of the mix. Therefore, the value of the cashews (at 75 cents per pound) plus the value of the pecans (at $1.50 per pound) should equal the value of the desired mixture (at $1.00 per pound). The correct equation to use would be:

75p + 150(10) = 100(p + 10)

To solve for p, we multiply the cost per pound by the weight for each type of nut, then equate this to the cost per pound of the mixture multiplied by the total weight of the mixture. After solving this equation for p, we will know the required pounds of cashew nuts.

Is this tangent to the circle?

Answers

Hello,

Yes since (2*6.4)²+9.6²=256=16²
Angle A=90°
if you are asking about AB, Then in order to be a tangent to the circle the m(A) should be equal to 90 degrees. So we have to test it, if measure of angle "A" is 90 or not. Since the 3 sides lengths were given, I guess they want you to use Pythagorean theorem which says the following:
[tex] hyp^{2}= adj^{2}+opposite^{2}[/tex]
hypotenuse in here is the 16 unit length side, the adjacent is AB and  the opposite is the diameter with length of 6.4  unit length.
if [tex] 16^{2} = 6.4^{2}+9.6^{2}[/tex] then m(A)= 90 degrees and it will be a tangent.
[tex]16^{2}=256[/tex]
[tex]6.4^{2} + 9.6^{2}=40.96+92.16=133.12 [/tex] 
so the theorem is not applicable in this situation so the [tex]m(A) \neq 90 degrees[/tex]
therefore AB is not a tangent

The math test scores of Mrs. Hunter's class are shown below.48, 56, 68, 72, 72, 78, 78, 80, 82, 84, 88, 88, 88, 90, 94, 98, 100 What is the range of the scores?

Answers

the range would be the difference between the highest and the lowest score

Highest = 100

lowest = 48

range = 100 - 48 = 52
the answer is 52. You get the range by taking the greatest and the least number and subtract

The ratio of the numerator to the denominator of a fraction is 2 to 3. If both the numerator and the denominator are increased by 2, the fraction becomes 3/4 . What is the original fraction? Which of the following systems of equations can be used to solve the problem? n + 4 = 3 and d + 5 = 4 3n - 2d = 0 and 4n + 2 = 3d + 2 3n = 2d and 4n + 8 = 3d + 6

Answers

n/d = 2/3   ------------------->  3n = 2d

(n + 2)/(d + 2) = 3/4  ------> 4n + 8 = 3d + 6

The answer is C, 3d = 2d and 4n + 8 = 3d + 6

–13.5a + 34.12b + 65.5a – 32.5b – 35.8a

A.
32.5a + 20.47b
B.
16.2a + 1.62b
C.
–18.7a – 26b
D.
1.62a + 16.2b

Answers

Answer:

the answer is C

Step-by-step explanation:

Answer:

The Answer is not C

Step-by-step explanation:

if you simplify your problem, it should not come out as C. if so, you did it wrong.

Which of the following terminating decimals is equivalent to -1 3/4
?

Answers

It would be - 1.75. Hope it helps! :)

Answer:

→ The decimal expansion of rational number is either terminating or non terminating repeating.

→If the denominator of rational number is of the form [tex]2^a \text{or} 5^b \text{or} 2^a \times 5^b [/tex] , then the decimal terminates.

   [tex]\rightarrow -1 \frac{3}{4}=\frac{-7}{4}\\\\=-1.75[/tex]

What is the length of the side of a cube that has a surface area of 864 in2
A.11in
B.12in
C.13in
D.14in

Answers

Let
b-----------> length of the side of cube

we know that

the area surface of cube=6*b²
A=6*b²=864 in²----------------> b=√(864/6)=12 in

the answer is b=12 in

A reporter for the local news station wants to know how the citizens of the area feel about the current gas prices. The reporter decides to gather this information by conducting a survey at the local golf course.

Part A

Determine if the chosen sample is random or not random for the population and give and explanation why.

Part B

Come up with two different ways a random sample could be collected for this population.

Answers

The reporter wants to get a random (or representative) sample of the citizens in the area. That means that he wants the people he selects to reflect those that live in the area. If half the people in the area are men, then we expect more or less half of those he asks to be men, for example.

PART A
While it is not entirely clear if the members of the golf club are representative of those in the area (one might be in an area where most folks golf), it is probably unlikely. Most people do not golf and (I am being very stereotypical here) most golfers are men. So the people he asks might be more likely to be men than those in the area, as an example.

PART B
To get a random sample, the reporter could instead knock on the door of 3 houses on every block in the area and ask the inhabitants of these houses about the gas prices. We, of course, don't know how big the area is or how feasible it is to knock on 3 doors per block, but here we are likely to get a random sample.

Another method could be to take a list of residents from the area and contact every 5th name on the list. In this way the people selected are random and more likely to be representative of those in the area.

If the typical balance on Lucy's credit card is $650 and the interest rate (APR) on her credit card is 18%, how much in interest would you expect Lucy to be charged in a typical month?

Answers

(18%\12)x650=9.75 18 divide by 12 times 650

General Idea:

[tex] Amount \; Charged \; in \; a \; Month \; = \; Monthly \; Interest \; Rate \; \times Typical \; Creditcard\; Balance\\ \\ [/tex]

[tex] Amount \; Charged \; in\; a\; month =\frac{18\%}{12} \times 650 \; = 0.015\times650=9.75 [/tex]

Conclusion:

Amount of interest that Lucy to be charged in a typical month is $9.75

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