How should the decimal point in 6.093 be moved to determine the product of 1,000 × 6.093?

Between 0 degrees Celsius and 30 degrees Celsius, the volume V (in cubic centimeters) of 1 kg of water at a temperature T is giv

Ira Lisetskai [31]

Answer:

T = 3.967 C

Step-by-step explanation:

Density = mass / volume

Use the mass = 1kg and volume as the equation given V, we will come up with the following equation

D = 1 / 999.87−0.06426T+0.0085043T^2−0.0000679T^3

= (999.87−0.06426T+0.0085043T^2−0.0000679T^3)^-1

Find the first derivative of D with respect to temperature T

dD/dT = $\dfrac{70000000\left(291T^2-24298T+91800\right)}{\left(679T^3-85043T^2+642600T-9998700000\right)^2}$

Let dD/dT = 0 to find the critical value we will get

$\dfrac{70000000\left(291T^2-24298T+91800\right)}$ = 0

Using formula of quadratic, we get the roots:

T = 79.53 and T = 3.967

Since the temperature is only between 0 and 30, pick T = 3.967

Find 2nd derivative to check whether the equation will have maximum value:

$-\dfrac{140000000\left(395178T^4-65993368T^3+3286558821T^2+2886200857800T-121415215620000\right)}{\left(679T^3-85043T^2+642600T-9998700000\right)^3}$

Substituting the value with T=3.967,

d2D/dT2 = -1.54 x 10^(-8) a negative value. Hence It is a maximum value

Substitute T =3.967 into equation V, we get V = 0.001 i.e. the volume when the the density is the highest is at 0.001 m3 with density of

D = 1/0.001 = 1000 kg/m3

Therefore T = 3.967 C

3 0

2 years ago

Which real-world scenario can be described by the algebraic expression 4w? withdrawing w dollars from the bank and giving 4 doll

ANTONII [103]

Answer:

It's B

Step-by-step explanation:

3 0

2 years ago

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What is the probability that a point chosen at random in the rectangle is also in the blue triangle? A triangle inside of a rect

Oduvanchick [21]

Alright, lets get started.

Two sides of the rectange are 14 and s.

So, the area of the rectange would be =

A triangle is cut from the rectangle.

The height of the triangle is =

The base of the triangle is = 14

So area of the triangle would be =

area of the triangle would be =

So, the area of shaded region = area of rectange - area of triangle

the area of shaded region =

As per given in question, area of shaded region is 84, hence

..........equation

So, this is the equation for s : Answer

Hope it will help :)

5 0

2 years ago

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Harold measures the heights in inches of the new plants that are growing in his greenhouse. He records the lengths shown below a

viva [34]

Answer:

The least value plotted on the line plot is 18.0

The greatest value plotted on the line plot is 22.0

The height of inches occurs the most often is 19.5 with 3 times

Step-by-step explanation:

A line plot is a graph that shows frequency (the number of times the data value occur) of data along a number line.

The line plot has dots plotted on it over each value of the number line.

8 0

2 years ago

use the point-slope equation to identify the slope and the coordinates of a point on the line y – 4 = 1/2 (x – 1). the slope of

mihalych1998 [28]

Answer:

The slope of the line is $\dfrac{1}{2}$ and a point on the line is $(1, 4)$

Step-by-step explanation:

The general point slope of line passing through $(x_1,y_1)$ and having slope as m.

$y-y_1=m(x-x_1)$

The given equation of the straight line,

$y-4=\dfrac{1}{2}(x-1)$

Comparing this to the general equation we get the point as $(1, 4)$ and slope as $\dfrac{1}{2}$

7 0

2 years ago

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