What are the diminshens of a cube with the volume of 216?

The levels of mercury in two different bodies of water are rising. In one body of water the initial measure of mercury is 0.05 parts per billion (ppb) and is rising at a rate of 0.1 ppb each year. In the second body of water the initial measure is 0.12 ppb and the rate of increase is 0.06 ppb each year.

Which equation can be used to find y, the year in which both bodies of water have the same amount of mercury?

A) 0.05 – 0.1y = 0.12 – 0.06y

B) 0.05y + 0.1 = 0.12y + 0.06

C) 0.05 + 0.1y = 0.12 + 0.06y

D) 0.05y – 0.1 = 0.12y – 0.06

Answer:

Option C: 0.05 + 0.1y = 0.12 + 0.06y

Step-by-step explanation:

In the first body, the initial measure of mercury is 0.05 parts per billion (ppb) while it's rising at a rate of 0.1 ppb each year. We are told to use y for the number of years.

Thus, amount of mercury for y years in this first body is;

A1 = 0.05 + 0.1y

Now, for the second body, we are told that;the initial measure is 0.12 ppb and the rate of increase is 0.06 ppb each year.

Thus, amount of mercury for y years in this second body is;

A2 = 0.12 + 0.06y

Since we want to find the year in which both bodies of water have the same amount of mercury. Thus, it means;

A1 = A2

Thus;

0.05 + 0.1y = 0.12 + 0.06y

7 0

3 years ago

A water ballon is launched straight up. The balloons flight is modeled by the function h(t)=16t^2+192t

lubasha [3.4K]

Answer:Step by Step Solution

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Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

h*(t)-(16*t^2+192*t)=0

STEP

1

:

Equation at the end of step 1

ht - (24t2 + 192t) = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

ht - 16t2 - 192t = t • (h - 16t - 192)

Equation at the end of step

3

:

t • (h - 16t - 192) = 0

STEP

4

:

Theory - Roots of a product

4.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

4.2 Solve : t = 0

Solution is t = 0

Equation of a Straight Line

4.3 Solve h-16t-192 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line h-16t-192 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when h = 0 the value of t is 12/-1 so this line "cuts" the t axis at t=-12.00000

t-intercept = 192/-16 = 12/-1 = -12.00000

Calculate the X-Intercept :

When t = 0 the value of h is 192/1 Our line therefore "cuts" the h axis at h=192.00000

h-intercept = 192/1 = 192.00000

Calculate the Slope :

Slope is defined as the change in t divided by the change in h. We note that for h=0, the value of t is -12.000 and for h=2.000, the value of t is -11.875. So, for a change of 2.000 in h (The change in h is sometimes referred to as "RUN") we get a change of -11.875 - (-12.000) = 0.125 in t. (The change in t is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 0.125/2.000 = 0.062

Geometric figure: Straight Line

Slope = 0.125/2.000 = 0.062

h-intercept = 192/1 = 192.00000

t-intercept = 192/-16 = 12/-1 = -12.00000

t = 0

Step-by-step explanation:

7 0

2 years ago

Is 45.6 a irrational number!!???

notsponge [240]

No

Mark brainliest please

Hope this helps you

6 0

2 years ago