Whats a open equation?

A circle has a circumference of 12. It has an arc of length 11.

riadik2000 [5.3K]

Answer:

The central angle is 330 degrees

Step-by-step explanation:

The arc length is equal to the circumference time the fractional part of the circle

arc length = circumference * x/360

11 = 12 * x/360

Divide each side by 12

11/12 = 12/12 *x/360

11/12 = x/360

Multiply by 360

11*360/12 = x /360 *360

330 = x

The central angle is 330 degrees

7 0

3 years ago

The graph h = −16t^2 + 25t + 5 models the height and time of a ball that was thrown off of a building where h is the height in f

Thepotemich [5.8K]

Answer:

part 1) 0.78 seconds

part 2) 1.74 seconds

Step-by-step explanation:

step 1

At about what time did the ball reach the maximum?

Let

h ----> the height of a ball in feet

t ---> the time in seconds

we have

$h(t)=-16t^{2}+25t+5$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

so

The x-coordinate of the vertex represent the time when the ball reach the maximum

Find the vertex

Convert the equation in vertex form

Factor -16

$h(t)=-16(t^{2}-\frac{25}{16}t)+5$

Complete the square

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}$

$h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}$

Rewrite as perfect squares

$h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

The vertex is the point $(\frac{25}{32},\frac{945}{64})$

therefore

The time when the ball reach the maximum is 25/32 sec or 0.78 sec

step 2

At about what time did the ball reach the minimum?

we know that

The ball reach the minimum when the the ball reach the ground (h=0)

For h=0

$0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}$

$16(t-\frac{25}{32})^{2}=\frac{945}{64}$

$(t-\frac{25}{32})^{2}=\frac{945}{1,024}$

square root both sides

$(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}$

$t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}$

the positive value is

$t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec$

8 0

3 years ago

How to solve inequalities

shepuryov [24]

Answer:An absolute value inequality is solved by re-writing it as compound inequality. For example.

|x+1| < 5

Since the value inside the absolute value brackets: (x+1) can be positive or negative, it is re-written as a compound inequality as the example below.

x+1 < 5

x+1 > - 5

solve for the range of values x can be

-6 < x < 4

Step-by-step explanation: How to solve inequalities

4 0

3 years ago

Solve these equations. Thanks.

Nutka1998 [239]

Answer:

1. 3.572 x 10^(-1)

2. 3.108 x 10^(6)

3. 5.31881533 x 10^(-6)

4. 4.18676122 x 10^(-1)

Hope this helps

8 0

2 years ago

Solve the equation. 2x+1/3+x-1/4=13/2

inessss [21]

The solution of the equation is x = 71 / 36.

<h3>How to solve an equation with one variable</h3>

Herein we have an equation with several rational constants and only one variable, x, which has to be cleared by using algebra procedures. The procedure is shown below:

2 · x + 1 / 3 + x - 1 / 4 = 13 / 2 Given

2 · x + x = 13 / 2 - 1 / 3 - 1 / 4 Compatibility with addition / Existence of additive inverse / Modulative property

3 · x = 71 / 12 Definitions of addition and subtraction / Distributive property

x = 71 / 36 Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Result

The solution of the equation is x = 71 / 36.

To learn more on equations: brainly.com/question/10413253

#SPJ1

4 0

1 year ago