A parallelogram has an area of x^2 + 9x

A football is thrown from the top of the stands, 50 feet above the ground at an initial velocity of 62 ft/sec and at an angle of

Anvisha [2.4K]

a. i. The parametric equation for the horizontal movement is x = 43.84t

ii. The parametric equation for the vertical movement is y = 50 + 43.84t

b. the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

<h2>a. Parametric equations</h2>

A parametric equation is an equation that defines a set of quantities a functions of one or more independent variables called parameters.

<h3>i. Parametric equation for the horizontal movement</h3>

The parametric equation for the horizontal movement is x = 43.84t

Since

the angle of elevation is Ф = 45° and
the initial velocity, v = 62 ft/s,

the horizontal component of the velocity is v' = vcosФ.

So, the horizontal distance the football moves in time, t is x = vcosФt

= vtcosФ

= 62tcos45°

= 62t × 0.7071

= 43.84t

So, the parametric equation for the horizontal movement is x = 43.84t

<h3>ii Parametric equation for the vertical movement</h3>

The parametric equation for the vertical movement is y = 50 + 43.84t

Also, since

the angle of elevation is Ф = 45° and
the initial velocity, v = 62 ft/s,

the vertical component of the velocity is v" = vsinФ.

Since the football is initially at a height of h = 50 feet, the vertical distance the football moves in time, t relative to the ground is y = 50 + vsinФt

= 50 + vtcosФ

= 50 + 62tsin45°

= 50 + 62t × 0.7071

= 50 + 43.84t

<h3>b. Location of football at maximum height relative to starting point</h3>

The location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

Since the football reaches maximum height at t = 1.37 s

The x coordinate of its location at maximum height is gotten by substituting t = 1.37 into x = 48.84t

So, x = 43.84t

x = 43.84 × 1.37

x = 60.0608

x ≅ 60.1 ft

The y coordinate of the football's location at maximum height relative to the ground is y = 50 + 48.84t

The y coordinate of the football's location at maximum height relative to the starting point is y - 50 = 48.84t

So, y - 50 = 48.84t

y - 50 = 43.84 × 1.37

y - 50 = 60.0608

y - 50 ≅ 60.1 ft

So, the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

Learn ore about parametric equations here:

brainly.com/question/8674159

5 0

2 years ago

The random variable X~(30,2^2) <br> Find p(X<33) <br> Find p(X>26)

Ostrovityanka [42]

Answer:

i) P(X<33) = 0.9232

ii) P(X>26) = 0.001

Step-by-step explanation:

Given that the mean of the Population = 30

Given that the standard deviation of the Population = 4

Let 'X' be the Normal distribution

i)

Given that the random variable X = 33

$Z = \frac{x-mean}{S.D}$

$Z = \frac{33-30}{2} = 1.5$ >0

P(X<33) = P( Z<1.5)

= 1- P(Z>1.5)

= 1 - ( 0.5 - A(1.5))

= 0.5 + 0.4232

P(X<33) = 0.9232

Given that the random variable X = 26

$Z = \frac{x-mean}{S.D}$

$Z = \frac{33-26}{2} = 3.5$ >0

P(X>26) = P( Z>3.5)

= 0.5 - A(3.5)

= 0.5 - 0.4990

= 0.001

P(X>26) = 0.001

5 0

3 years ago

Museum passes cost $5 for adults and $2 for children. One day the museum sold 1820 passes for profit of $6106. How many of each

Mariulka [41]

1,500 children, and 320 adults

2X + 9100 - 5X = 6100
x = 1500 (children passes sold)

1820-1500 = 320 (adult)

Mark brainliest please

4 0

3 years ago

Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself. A. Find the so

Dvinal [7]

Answer:

3x + 6 =27

Step-by-step explanation:

A. The solution is 7! First I Subtracted 6 from both sides of the equation, Then I Divided both sides of the equation by the same term. Then I got "7" from doing the following.

B. The solution is the x in the answer which is the amount of juice he poured.

"Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself"

tell me if i did something wrong

5 0

3 years ago

Read 2 more answers

Jennifer buys a block of clay for an art project. The block is shaped like a cube with edge lengths of 12 inches.

Gnoma [55]

Answer:

Volume of block Jennifer bought:

V = side^3 = 12 x 12 x 12 = 1728 (in3)

Volume of sphere Jennifer wanted to make:

V = (4/3) x pi x radius^3 = (4/3) x pi x (4/2)^3 = 33.5 (in3)

a, The number of spheres she can make:

N = 1728/33.5 = 51.58 = ~51

b, The area of remaining clay after she made a sphere:

A = 1728 - 33.5 = 1694.5 (in3)

Hope this helps!

:)

7 0

3 years ago

A parallelogram has an area of x^2 + 9x - 36.