Andrew is an avid archer. He launches an arrow that takes a parabolic path.
The equation of the height of the arrow with respect to time is
y = -4.9x2 + 48x, where y is the height of the arrow in meters above
Andrew's bow and x is the time in seconds since Andrew shot the arrow.
Find how long it takes the arrow to come back to a height even with his bow
height.

Answers

Answer 1

Answer:

9.7959 sec

Step-by-step explanation:

For the arrow to reach the same height as the bow again, - 4.9x^2+48x=0, 48=4.9x, x=48/4.9=9.7959

Answer 2

The time arrow take to come back to a height even with his bow height is 9.79 seconds.

We have an equation of the height of the arrow with respect to time -[tex]y = -4.9x^{2} +48x[/tex] where y is the height of the arrow in meters above Andrew's bow and x is the time in seconds since Andrew shot the arrow.

We have to find out - how long it takes the arrow to come back to a height even with his bow height.

The motion of arrow in the above situation is an example of which type of motion?

It is an example of two - dimensional Projectile motion.

We have the function that depicts the variation of height of the arrow with respect to time given by -

[tex]y=-4.9x^{2} +48x[/tex]

To find the time taken by the arrow to come to a height even with his bow height, we should equate y = 0.

[tex]y=-4.9x^{2} +48x=0\\-4.9x(x-9.79)=0\\-4.9x=0\;\;\;and\;\;\;x-9.79=0\\x =0\;\;\;and\;\;\;x=9.79[/tex]

Time cannot be 0, hence the time arrow take to come back to a height even with his bow height is 9.79 seconds.

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Related Questions

Х
49°
X =
degrees
What do I do

Answers

Answer:

x = 139

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angle

x = 49 +90

x = 139

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

[tex] \bf \large \implies \: x \: = \: 49 \degree \: + \: 90 \degree[/tex]

[tex] \bf \large \implies \: x \: = \: 139 \degree [/tex]

Sally spent half of her allowance going to the movies. She washed the family
car and earned 6 dollars. What is her weekly allowance if she ended with
17 dollars ?

Answers

does it give the answer choice or is it a blank space?

Click the photo to solve the photo

Answers

Answer:

A=2

B=4

C=6

D=5

E=7

F=8

G=3

H=1

Step-by-step explanation:

explanation is in the picture!

b) Tìm ba cách viết số hữu tỉ -11/25 dưới dạng tổng của hai số hữu tỉ dương.

Answers

Bạn ơi tổng hai số hữu tỉ dương làm sao bằng âm được ạ? Bạn xem lại đề có sai không ạ ^^

What is the distance between (1, 9) and (1, -4)? Use the distance formula.

D=(x2-x1)2+(y2-y1)2

Answers

Answer:

D. 13

Step-by-step explanation:

You just have to plug in numbers then solve.

(1,9) and (1,-4). Every coordinate is placed as (x,y)

(1,9) is labeled as (x1, y1)

(1,-4) is labeled as (x2,y2)

Now plug in the numbers.

d= Square root of (1-1)^2 + (-4-9)^2

d= Square root of 1^2 +-13^2

d= Square root of 1+169

d= Square root of 170

d= 13.04

Rounded to a whole number, the answer is 13

Answer:

D

Step-by-step explanation:

you have to substitute the values in the distance formula,in this case x2 is 1,x1 is 1,y2 is -4 and y1 is 9

d=√(x2-x1)²+(y2-y1)²

=√(1-1)²+(-4-9)²

=√(0)²+(-13)²

=√169

=13

I hope this helps

Please help, the question is in the picture

Answers

Answer:

per = 18a         7a+2a+7a+2a

area = 14 [tex]a^{2}[/tex]      7a*2a

Step-by-step explanation:

Answer:

(i) 18a

(ii) 14[tex]a^2[/tex]

Step-by-step explanation:

i: 7a+7a+2a+2a

      14a+4a

         18a

ii: 7a*2a

     14a2

I hope this helps!

. Doanh nghiệp dự tính đầu tư góp vốn liên doanh với số tiền ban đầu là 500 trđ, trong vòng 4 năm, lãi suất dự kiến là 12%/năm. Tính tổng số lãi của hoạt động đầu tư liên doanh thu được sau khi kết thúc liên doanh ?

Answers

i dont understand nun of that

You tried to get every semi truck to honk but only 7 did what fraction if semi trucks you saw honked

Answers

Answer:

I am so lost but if it's how many honk out of how many you saw I would assume 7/7

someone please help me with this question​

Answers

Answer:

Step-by-step explanation:

The diagram is given to you below. I could not change <C so that it was theta. So C = theta.

So C is the reference angle. Call it theta when you think of it. The diagram shows you how cos(C) must be set up.

The adjacent side is 7

The hypotenuse is 18

theta = C = cos-1(7/18) = 67.11

To the nearest degree 67.11 = 67

A kindergarten class had a total of 15 boys 9 girls , what is the ratio of girls to boys in that class ?

Answers

Answer:

9:15

girls : boys

Step-by-step explanation:

Answer:

9:15

Or 3:5 when reduced

Step-by-step explanation:

Write the expression 4^4(4^-7)(4) using a single
exponent.
4^-28
4^-4
4^-3
4^-2

Answers

Answer:

4^(-2)

Step-by-step explanation:

4^4(4^-7)(4)

We know that a^b * a^c = a^(b+c)

4^4(4^-7)(4^1)

4^(4+-7+1)

4^(-2)

HELP HURRY PLEASE i dont understanddd

Answers

Answer:

see image

Step-by-step explanation:

put a point on .5 on the x axis and a point on -3 on the y axis draw a line through them and shade the space under the line

Which answer shows 0.00897 written in scientific notation?
From what I heard it's not D​

Answers

Answer:

B

Step-by-step explanation:

The decimal number 0.00897 written in scientific notation is 8.97 ×10^3 and it has significant figures

Answer:

8.97 * 10⁻³

Step-by-step explanation:

0.00897 = [tex]\frac{8.97}{1000}=8.97 * 10^{-3}[/tex]

Place the decimal point after the first nonzero number.

Write the power of 10,

(i) If we move the decimal to the right, the power of 10 decrease by number of moves.

(ii) If we move the decimal to the left, the power of 10 increase by the number of moves

help me please and thank youu

Answers

Answer:

-3

Step-by-step explanation:

y - y1 = m(x - x1) m = slope

y - 5 = -3(x - 17) slope = -3

Answer:

-3

Step-by-step explanation:



** I NEED HELP PLEASE AND THANK YOU***

Instructions : X,Y,and Z are midpoints. Find the length of each segment.​

Answers

Answer:

MZ = 10

ZO = 10

MO = 20

XZ = 9

YZ = 7

Step-by-step explanation:

Triangles are all the same, proportionally.

X is midpoint of 14, so 7

Y for 18, so 9

Triangle with 10 is 7, 9, 10

Full triangle is double at 14, 18, MO

Since angle N is same angle, MO is double 10, so 20

Z is midpoint, so both halves are 10

Because of midpoints, XZ and YZ with 10 form same triangle as half triangle at 9, 7, and 10 respectively.

In a survey of women in a certain country the mean height was 62.9 inches with a standard deviation of 2.81 inches answer the followinv questions about the specified normal distribution

Answers

The question is incomplete. The complete question is :

In a survey of women in a certain country ( ages 20-29), the mean height was 62.9 inches with a standard deviation of 2.81 inches.  Answer the following questions about the specified normal distribution.  (a) What height represents the 99th percentile?  (b) What height represents the first quartile?  (Round to two decimal places as needed)

Solution :

Let the random variable X represents the height of women in a country.

Given :

X is normal with mean, μ = [tex]62.9[/tex] inches and the standard deviation, σ = [tex]2.81[/tex] inches

Let,

[tex]$Z=\frac{X - 62.9}{2.81}$[/tex] , then Z is a standard normal

a). Let the [tex]99th[/tex] percentile is = a

The point a is such that,

[tex]$P(X<a)=0.99$[/tex]

[tex]$P \left( Z < \frac{a-62.9}{2.81} \right) = 0.99$[/tex]

From standard table, we get : [tex]P( Z < 2.3263) =0.99[/tex]

∴ [tex]$\frac{(a-62.9)}{281} = 2.3263$[/tex]

  [tex]$a= (2.3263 \times 2.81 ) +62.9$[/tex]

     = 6.536903 + 62.9

     = 69.436903

     = 69.5 (rounding off)

Therefore, the height represents the [tex]99th[/tex] percentile = 69.5 inches.

b). Let b = height represents the first quartile.

It is given by :

[tex]P( X < b) =0.25[/tex]

[tex]$P \left( Z < \frac{(b-62.9)}{2.81} \right) = 0.25$[/tex]

From the standard normal table,

[tex]P( Z < -0.6745) =0.99[/tex]

∴ [tex]$\frac{(b-62.9)}{2.81}= 0.6745$[/tex]

[tex]$b=(0.6745 \times 2.81) +62.9$[/tex]

  = 1.895345 + 62.9

   = 64.795345

   = 64.8 (rounding off)

Therefore, the height represents the 1st quartile is 64.8 inches.

find the value of x.

Answers

Answer: x=35

Step-by-step explanation:

To find the value of x, we can use the Pythegorean Theorem because this is a right triangle.

Pythagorean Theorem: a²+b²=c²

[tex]12^2+x^2=(x+2)^2[/tex]             [exponent and distribute]

[tex]144+x^2=x^2+4x+4[/tex]       [subtract both sides by 144]

[tex]x^2=x^2+4x-140[/tex]             [subtract both sides by x²+4x]

[tex]-4x=-140[/tex]                       [divide both sides by -4]

[tex]x=35[/tex]

Now, we know that x=35.

The mean age of 5 women in an office is 35 years old.
The mean age of 5 men in an office is 24 years old.
What is the mean age (nearest year) of all the people in the office?

Answers

Answer:

29.5

Step-by-step explanation:

(5×35)+(5×24)/10

175+120/10

295/10

=29.5

If 55% people in a city like Cricket, 30% like Football and the remaining like nother games, then what per cent of the people like other games? If the total people is 60 lakh, find the exact number who like each type of games Answer it fast, no spam please



write in notebook ​

Answers

[tex]\large{\dag\:{\underline{\underline{\frak{\pmb{\red{Answer:-}}}}}}}[/tex]

Cricket = 55%Football = 30%Other games = Remaining (?)

So, the percent of people who like other games equals:

= 100 – (55 + 30)

= 100 – 85

= 15%

If the total no. of. people is 60,00,000:

★ Cricket

= 60,00,000 × 55/100

= 33,00,000

★ Football

= 60,00,000 × 30/100

= 18,00,000

★ Other sports

= 60,00,000 × 15/100

= 9,00,000

HELPPP PYTHAGOREAN THEOREM

Answers

Answer:

60

Step-by-step explanation:

We can use the Pythagorean theorem since this is a right triangle

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

a^2+25^2 = 65^2

a^2 +625 = 4225

a^2 = 4225-625

a^2=3600

Taking the square root of each side

sqrt(a^2) = sqrt(3600)

a = 60

Answer:

Step-by-step explanation:

Hypotenuse: 65

Leg: 25

Let Hypotenuse be c, and leg be a

[tex]a^{2}[/tex] + [tex]b^{2} = c^{2}[/tex]

[tex]a^{2} + 25^{2} = 65^{2}[/tex]

[tex]a^{2} + 625 = 4225\\[/tex]

[tex]a^{2}[/tex] = 4225 - 625

[tex]a^{2}[/tex] = 3600

3600 is the exponential value of a, meaning we need to apply the opposite of squaring to get the value of b. Which is square rooting.

a = [tex]\sqrt{3600\\}[/tex]

a = 60

Therefore a is equal to 60 feet

Triangle QRP is congruent to triangle YXZ. What is the perimeter of triangle YXZ?
What is the perimeter of triangle YXZ?

Answers

Answer:

Perimeter of XYZ = Perimeter of QRP

Step-by-step explanation:

Since congruent then

P of XYZ = P of QRP

Please hurry I will mark you brainliest

Answers

Answer:

q = 1/4

Step-by-step explanation:

-5/4 - (-1/4) = -1

-1/(q-1/2) = 4

-1 = 4(q-1/2)

-1 = 4q - 2

1 = 4q

q = 1/4

Fifteen years from now, Atli’s age will be 4 times his current age. What is his current age?

Answers

Answer:

he is three i think

Step-by-step explanation:

if the cost of 5 dozen of copies is rupees 60 what is the cost of 33 such copies​

Answers

Answer: Rs 33

Step-by-step explanation:

Cost of 5 dozen copies = Rs 60

Total copies in 5 dozen = 5×12

= 60

Cost of each copy = 60/60

= Rs 1 per copy

Cost of 33 copies = 33×1

= Rs 33

Therefore cost of 33 such copies is Rs 33

please click thanks and mark brainliest if you like :)

60/5
= 12
So 12 rupees per copy
33x12 = 396 rupees
So the answer is 396 rupees

Given the function g(x) = x^2 + 5x + 14, determine the average rate of change
of the function over the interval 1 < x < 7.

Answers

Answer:

13

Step-by-step explanation:

The average rate of change is

f(7) - f(1)

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

7-1

f(7) = 7^2 + 5*7 +14 = 49 +35 +14=98

f(1) = 1^2 +5(1)+14 = 1+5+14=20

98-20

--------

7-1

78/6

13

A group has more than $120 to spend. The inequality 5x + 20 > 120 represents the cost to rent a hall for a conference, where x represents the number of hours the group can rent the hall. Which of the following is the solution for this situation?

Answers

Answer:

x>20

Step-by-step explanation:

You want to try and get the x alone so

5x + 20 > 120

     -20     -20  Subtract 20 from each side

5x        > 100

5x/5    > 100/5 Divide 5 from each side

       x  > 20

f The difference of 8 and 3 is multiplied by one-quarter of the sum of 7 and 5 37 vedanta Excel in Mathematics​

Answers

Answer:

15

Step-by-step explanation:

first find f which is (8-3) × ( 1/4 × 7 + 5)

simplify

5 × (1/4 ×12)

5 × 3

15 is thw answer

what is the solution to Y=-2x²+4x+8
Y=-4x+16

Answers

Hi there!

[tex]\large\boxed{(2, 8)}[/tex]

Solve by setting the two equations equal to each other:

-2x² + 4x + 8 = -4x + 16

Move all terms to one side:

-2x² + 4x + 4x + 8 - 16 = 0

Simplify:

-2x² + 8x - 8 = 0

Factor out a negative 2 from each term:

-2(x² - 4x + 4) = 0

Factor:

-2(x - 2)² = 0

Set the factor equal to 0 to solve:

(x - 2)² = 0

x - 2 = 0

x = 2

Substitute this value of x into an equation to find the shared y value:

y = -4(2) + 16 = 8

Find the shortest side of a triangle whose perimeter is 64 if the ratio of two of its sides is 4:3 and the third side is 20 less than the sum if the other two

Answers

Answer:

The shortest side of the triangle is 18

Step-by-step explanation:

Let the sides the triangle be x, y and z.

From the question, the perimeter of the rectangle is 64, that is

x + y + z = 64 ...... (1)

Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)

The third side, z, is 20 less than the sum of the other two, that is

z + 20 = x + y ...... (3)

Substitute equation (3) into (1)

Then,

z + 20 + z = 64

2z +20 = 64

2z = 64 - 20

2z = 44

z = 44/2 k

z = 22

From equation (3)

z + 20 = x + y

Then, k

22 + 20 = x +y

42 = x + y

x = 42 - y ...... (4)

Substitute this into equation 2

3x = 4y

3(42-y) = 4y

126 - 3y = 4y

4y + 3y = 126

7y = 126

y = 126/7

y = 18

Substitute this into equation (4)

x = 42 - y

x = 42 - 18

x = 24

∴ x = 24, y = 18 and z = 22

Hence, the shortest side of the triangle is 18.

Find the vertical asymptotes of the function (x-1)(x-3)^2(x+1)^2/(x-2)(x+2)(x-1)(x+3)​

Answers

Answer:

x=2, x=-2, x=-3

Step-by-step explanation:

-check if anything simplifies

(x-1)(x-3)²(x+1)² / (x-2)(x+2)(x-1)(x+3), simplify (x-1)

(x-3)²(x+1)² / (x-2)(x+2)(x+3)

-make the denominator 0 to find the asymptotes

(x-2)(x+2)(x+3) = 0

(x-2) =0 gives x = 2 asymptote

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

(x+3) = 0 gives x=- 3 asymptote

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