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3 years ago

a ball is thrown vertically upward from the ground with an initial velocity of 60 ft/sec. how high will the ball go?

Mathematics

1 answer:

vazorg [7]3 years ago

3 0

Answer:

The ball will go to maximum height of 56.25 meters.

Step-by-step explanation:

It is given that, a ball is thrown vertically upward from the ground. Initial velocity of the ball, v = 60 ft/sec

Initial height is 0 as the ball is thrown from ground. The equation of projectile is given by :

$h(t)=-16t^2+vt+h$

h = 0

$h(t)=-16t^2+60t$ ..............(1)

We need to find the maximum height reached by the ball. For maximum height,

$\dfrac{dh(t)}{dt}=0$

$\dfrac{d(-16t^2+60t)}{dt}=0$

t = 1.875 seconds

Put the values of t in equation (1). So,

$h(t)=-16(1.875)^2+60(1.875)$

h(t) = 56.25 meters

So, the ball will go to maximum height of 56.25 meters. Hence, this is teh required solution.

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The expression below is scientific notation for what number?<br> 6.1 x 10^6

arlik [135]

Scientific notation is a way to write compactly numbers with lots of digits, either because they're very large (like 2393490000000000000000000), or very small (like 0.0000000000356).

We use powers of ten to describe all those leading/trailing zeros, so that we con concentrate on the significat digits alone.

In your case, the "important" part of the number is composed by the digits 6 and 1, all the other digits are zero. But how many zeroes? Well, let's do the computation.

Every power of 10, $10^n$ is written as one zero followed by n zeroes, so we have

$10^6 = 1000000 \implies 6.1 \times 10^6 =6.1 \times 1000000$

Multiplying a number by $10^n$ means to shift the decimal point to the right and/or add trailing zeroes n times. So, we have to repeat this process six times. We shift the decimal point to the right one position, and then add the five remaning zeroes. The result is thus

$6.1 \times 1000000 = 6100000$

4 0

3 years ago

Someone please help me

Mars2501 [29]

Answer:

x=-1,-2

Step-by-step explanation:

Multiply the given equation with (x+1) on both sides. We'll get,

x+2/x=-3

or,x^2+2=-3x

or,x^2+3x+2=0

or,x^2+2x+x+2=0

or,x(x+2)+1(x+2)=0

or,(x+2)(x+1)=0

or,x=-2,-1

4 0

3 years ago

A class photo is being taken of six students, sitting in a row. Three of the students are Jamie, Marshall, and Susan, and Jamie

irina [24]

Answer:

2 different arrangments

6 0

3 years ago

Indicate the equation of the given line in standard form. Show all your work for full credit. the line containing the median of

alukav5142 [94]

Answer:

* The equation of the median of the trapezoid is 10x + 6y = 39

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line whose end points are (x1 , y1) , (x2 , y2) is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- The mid point of the line whose end point are (x1 , y1) , (x2 , y2) is

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

- The standard form of the linear equation is Ax + BC = C, where

A , B , C are integers and A , B ≠ 0

- The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

- It has two properties:

# It is parallel to both bases

# Its length equals half the sum of the base lengths

* Lets solve the problem

- The trapezoid has vertices R (-1 , 5) , S (! , 8) , T (7 , -2) , U (2 , 0)

- Lets find the slope of the 4 sides two find which of them are the

parallel bases and which of them are the non-parallel bases

# The side RS

∵ $m_{RS}=\frac{8-5}{1 - (-1)}=\frac{3}{2}$

# The side ST

∵ $m_{ST}=\frac{-2-8}{7-1}=\frac{-10}{6}=\frac{-5}{3}$

# The side TU

∵ $m_{TU}=\frac{0-(-2)}{2-7}=\frac{2}{-5}=\frac{-2}{5}$

# The side UR

∵ $m_{UR}=\frac{5-0}{-1-2}=\frac{5}{-3}=\frac{-5}{3}$

∵ The slope of ST = the slop UR

∴ ST// UR

∴ The parallel bases are ST and UR

∴ The nonparallel sides are RS and TU

- Lets find the midpoint of RS and TU to find the equation of the

median of the trapezoid

∵ The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

∵ The midpoint of RS = $(\frac{-1+1}{2},\frac{5+8}{2})=(0,\frac{13}{2})$

∵ The median is parallel to both bases

∴ The slope of the median equal the slopes of the parallel bases = -5/3

∵ The form of the equation of a line is y = mx + c

∴ The equation of the median is y = -5/3 x + c

- To find c substitute x , y in the equation by the coordinates of the

midpoint of RS

∵ The mid point of Rs is (0 , 13/2)

∴ 13/2 = -5/3 (0) + c

∴ 13/2 = c

∴ The equation of the median is y = -5/3 x + 13/2

- Multiply the two sides by 6 to cancel the denominator

∴ The equation of the median is 6y = -10x + 39

- Add 10x to both sides

∴ The equation of the median is 10x + 6y = 39

* The equation of the median of the trapezoid is 10x + 6y = 39

7 0

3 years ago

Miguel has 12 chocolate chip cookies, 6 lemon cookies and 17 strawberry cookies. Write a fraction that indicates how many cookie

Anon25 [30]

Answer:

Step-by-step explanation:

This problem is on fraction

given data

chocolate chip cookies= 12

lemon cookies = 6

strawberry cookies= 17

the total cookies is = 12+6+17

=35 cookies

Therefore the fraction that indicates the lemon cookies is

=the number of lemon cookies/total cookies

=6/35

Hence the fraction lemon is 6/35

8 0

2 years ago