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ASHA 777 [7]
3 years ago
14

Order the following numbers from least to greatest. square root of 7, -2.3, square root of 3, 5.1, -1/3. Please help! The last o

ne is a fraction not an equation.
Mathematics
2 answers:
aalyn [17]3 years ago
8 0

First of all, negative numbers will surely come before positive ones. So, let's compare -2.3 and -1/3.

One is a number, one is a fraction. You can either turn the fraction to number, or the number to fraction. The first option is surely easier: we have -1/3 = -0.333...

So, -1/3 is closer to 0 than -2.3, so we have -2.3 < -\frac{1}{3}

As for the positive numbers, we have to order \sqrt{7},\ \sqrt{3},\ 5.1. When dealing with positive numbers, it is true that x < y \implies x^2 < y^2. So, we can square the numbers to get rid of the roots: we have

3 = \sqrt{3}^2 < 7 = \sqrt{7}^2 < 26.01 = 5.1^2.

So, the ordered list is the following:

-2.3,\ -\frac{1}{3}, \sqrt{3},\ \sqrt{7},\ 5.1

dolphi86 [110]3 years ago
3 0
-2.3, -1/3, square root of 3, square root of 7, 5.1

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Solve for the variable: p - 4.2 = 2. Show your work
djverab [1.8K]

Answer:

p=6.2

Step-by-step explanation:

8 0
3 years ago
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Consider the following equation of the form dy/dt = f(y)dy/dt = ey − 1, −[infinity] &lt; y0 &lt; [infinity](a) Sketch the graph
kotegsom [21]

Complete Question:

The complete question is shown on the first uploaded image

Answer:

a) The graph of  f(y) versus y. is shown on the second uploaded image

b) The critical point is at y = 0  and the solution is asymptotically unstable.

c)The phase line is shown on the third uploaded image

d) The sketch for the several graphs of solution in the ty-plane  is shown on the fourth uploaded image

Step-by-step explanation:

Step One: Sketch The Graph of  f(y) versus y

Looking at the given differential equation

       \frac{dy}{dt} = e^{y} - 1 for -∞ < y_{o} < ∞

 We can say let \frac{dy}{dt} = f(y) =e^{y} - 1

Now the dependent value is f(y) and the independent value is y so to sketch is graph we can assume a scale in this case i cm on the graph is equal to 2 unit for both f(y) and y and the match the coordinates and after that join the point to form the graph as shown on the uploaded image.

Step Two : Determine the critical point

   To fin the critical point we have to set   \frac{dy}{dt} = 0

       This means e^{y} - 1 = 0

                          For this to be possible e^{y} = 1

                          which means that  e^{y} = e^{0}

                          which implies that y = 0

Hence the critical point occurs at y = 0

meaning that the equilibrium solution is y = 0

As t → ∞, our curve is going to move away from y = 0  hence it is asymptotically unstable.

Step Three : Draw the Phase lines

A phase line can be defined as an image that shows or represents the way an ODE(ordinary differential equation ) that does not explicitly depend on the independent variable behaves in a single variable. To draw this phase line , draw the y-axis as a vertical line and mark on it the equilibrium, i.e. where  f(y) = 0.

In each of the intervals bounded  by the equilibrium draw an upward

pointing arrow if f(y) > 0 and a downward pointing arrow if f(y) < 0.

      This phase line would solely depend on y does not matter what t is

On the positive x axis it would get steeper very quickly as you move up (looking at the part A graph).

For  below the x-axis which stable (looking at the part a graph) we are still going to have negative slope but they are going to be close to 0 and they would take a little bit longer to get steeper  

Step Four : Draw a Solution Curve

A solution curve is a curve that shows the solution of a DE (deferential equation)

Here the solution curve would be drawn on the ty-plane

So the t-axis(x-axis) is its the equilibrium  that is it is the solution

If we are above the x-axis it is going to increase faster and if we are below it is going to decrease but it would be slower (looking at part A graph)

5 0
3 years ago
Solve x:(x+4)/3=2<br> Will give points
sasho [114]

\frac{x + 4}{3}  = 2 \\  \\  \\  \text{ Multiply by 3 on both sides,  }\\  \\   \\ =  >  \frac{x + 4}{3}  \times 3 = 2 \times 3 \\  \\  \\  \\  =  > x + 4 = 6 \\ \\   \\  =  > x = 6 - 4 \\  \\  \\   =  > x = 2






Hence, value of x in the given equation is 2
8 0
3 years ago
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In the DBE 122 class, there are 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3
Sliva [168]

Answer:

i) it is not possible for the student to receive an A in the class

ii) 119 points

iii) 84points

Step-by-step explanation:

Total exam scores = 350points

homework scores of 7, 8, 7, 5, and 8

Let the third exam score =y

Exam scores = 81, 80, x

i) To know if the student would get an A in class, we would find the third exam score

(Scores received by a student)/ (total scores) = least of the grade percentage to get an A

(7 + 8 + 7 +5 + 8 + 81 + 80 + x)/350 = 0.9

(196+x)/350 = 0.9

196+x = 350 × 0.9

196+x = 315

x = 315-196

x = 119

119 > 100

Since the maximum grade for each of the exam score is 100points, it is not possible for the student to receive an A in the class.

ii) Since the least of the grade percentage that would guarantee an A is 0.9, the minimum score on the third exam that will give an A = 119points

iii) (Scores received by a student)/ (total scores) = least of the grade percentage to get a B

(7 + 8 + 7 +5 + 8 + 81 + 80 + x)/350 = 0.8

(196+x)/350 = 0.8

196+x = 350 × 0.8 = 280

x = 280-196

x = 84

The minimum score on the third exam that will give a B = 84points

3 0
3 years ago
Two shapes are shown below, one isosceles triangle and one rectangle. The dimensions can be represented by algebraic expressions
liberstina [14]

Answer:

Perimeter of Isosceles Triangle = 16 units

Step-by-step explanation:

Area of rectangle is given by the formula;

Area = 1/2 × base × height

From the diagram, base = 6x - 6 and height = 6x - 8

Thus,Area = 1/2 × (6x - 6) × (6x - 8)

Area = (3x - 3)(6x - 8) = 18x² - 42x + 24

Secondly, area of rectangle is given by;

Area = length x breadth

So, area of rectangle in question = (6x - 9)(3x - 2) = 18x² - 39x + 18

We are told both the area of the triangle and the rectangle are the same, so let's equate both areas;

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18x² will cancel out and rearranging, we have;

24 - 18 = 42x - 39x

6 = 3x

x = 6/3

x = 2

Plugging 2 for x for the height and base of the triangle, we have;

base = 6(2) - 6 and height = 6(2) - 8

Base = 6 and height = 4

So,let's find the slant height of the isosceles triangle.

Dividing the base by 2,we have; 6/2 = 3

So,using Pythagoras theorem, let the slant height be h, so we have;

h² = 3² + 4²

h² = 9 + 16

h² = 25

h = √25

h = 5

2 slant sides of isosceles triangle are the same. So perimeter = 5 + 5 + 6 = 16 units

8 0
3 years ago
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