MATHEMATICS COLLEGE

If $11000 yields $1100 over 5 years, what is the interest rate?

Answers

Answer 1

Answer:

Answer:

1.92449%

Step-by-step explanation:

Simple Interest Rate Formula: A = P(1 + r)ⁿ

Step 1: Define variables

Principle amount P = 11000

Total amount A = 11000 + 1100 = 12100

Years n = 5

Step 2: Substitute and Evaluate for r

12100 = 11000(1 + r)⁵

11/10 = (1 + r)⁵

1.01924 = 1 + r

r = 0.019245

Step 3: Convert to percentage

0.019245 × 100 = 1.92449%

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Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation for the sphere of radius 5 centered at the origin incylindricalcoordinates.(b) Write an equation for a cylinder of radius 1 centered at the origin and running parallel to thez-axis inspherical coordinates.

Answers

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

$(x-a)^(2)+(y-b)^(2)+(z-c)^(2)=p^(2)$

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

$a=b=c=0,p=5$

That is, the equation of the sphere in cartesian coordinates is,

$(x-0)^(2)+(y-0)^(2)+(z-0)^(2)=5^(2)$

$\Rightarrow x^(2)+y^(2)+z^(2)=25$

Now, the cylindrical coordinate system is represented by $(r, \theta,z)$

The relation between cartesian and cylindrical coordinates is given by,

$x=rcos\theta,y=rsin\theta,z=z$

$r^(2)=x^(2)+y^(2),tan\theta=(y)/(x),z=z$

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

$r^(2)+z^(2)=25$

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

$(x-a)^(2)+(y-b)^(2)=p^(2)$

Here, it is given that the center is at origin & radius is 1. That is, here, we have, $a=b=0,p=1$ . Then the equation of the cylinder in cartesian coordinates is,

$x^(2)+y^(2)=1$

Now, the spherical coordinate system is represented by $(\rho,\theta,\phi)$

The relation between cartesian and spherical coordinates is given by,

$x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi$

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

$(\rho sin\phi cos\theta)^(2)+(\rho sin\phi sin\theta)^(2)=1$

$\Rightarrow \rho^(2) sin^(2)\phi cos^(2)\theta+\rho^(2) sin^(2)\phi sin^(2)\theta=1$

$\Rightarrow \rho^(2) sin^(2)\phi (cos^(2)\theta+sin^(2)\theta)=1$

$\Rightarrow \rho^(2) sin^(2)\phi=1$ (As $sin^(2)\theta+cos^(2)\theta=1$ )

Note that $\rho$ represents the distance of a point from the origin, which is always positive. $\phi$ represents the angle made by the line segment joining the point with z-axis. The range of $\phi$ is given as $0\leq \phi\leq \pi$ . We know that in this range the sine function is positive. Thus, we can say that $sin\phi$ is always positive.

Thus, we can square root both sides and only consider the positive root as,

$\Rightarrow \rho sin\phi=1$

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is $r^(2)+z^(2)=25$

(b) The equation of the given cylinder in spherical coordinates is $\rho sin\phi=1$

Trapezoid W X Y Z is rotated about point A 180 degrees clockwise to form trapezoid W prime X prime Y prime Z prime. Trapezoid W prime X prime Y prime Z prime is reflected across the line of reflection m to form trapezoid W double-prime X double-prime Y double-prime Z double-prime.Analyze the diagram. What is the composition of transformations that was applied to map WXYZ to W''X''Y''Z''?

The first transformation was a

.

The second transformation was a

Answers

The first transformation was a rotation about point A.

The second transformation was a reflection across line M.

What is a rotation?

In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By critically observing the diagram which illustrates the sequence of transformations, we can logically deduce that the first transformation was a clockwise rotation about point A by 180 degrees.

Furthermore, the second transformation that maps W'X'Y'Z' to W''X''Y''Z'' is a reflection across the line of reflection M.

Read more on transformation here: brainly.com/question/15832612

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Complete the steps to factor the polynomial by grouping. P(x) = x3 + 5x2 – x – 5 P(x) = x2 (x + ) – (x + 5) P(x) = (x2 – )(x + 5) P(x) = (x – )(x + 1)(x + )

Answers

Answer:

$p(x)=(x+5)(x-1)(x+1)$

Step-by-step explanation:

we are given polynomial as

$p(x)=x^3+5x^2-x-5$

We can group first two terms and last two terms

$p(x)=(x^3+5x^2)-x-5$

We can factor out -1 from last two terms

$p(x)=(x^3+5x^2)-1* (x+5)$

We can see that x^2 is common in first two terms

so, we can factor out x^2 from first two terms

$p(x)=x^2(x+5)-1* (x+5)$

we can see x+5 is in both terms

so, we can factor out x+5

$p(x)=(x+5)(x^2-1)$

we can also factor it as

$p(x)=(x+5)(x-1)(x+1)$

Answer:

P(x)=x^2(x+5)-(x+5)

P(x)=(x^2-1) (x+5)

P(x)=(x-1) (x+1) (x+5)

Step-by-step explanation:

In the sixth grade class at Madison Middle School, for every 6 students, 4 of them play at least one sport. If there are 270 students on the sixth grade class, how many of them play at least one sport? a) 39
b) 180
c) 11
d) 405

Answers

Answer:

B is the answer

Step-by-step explanation:

Because we can make 4/6 into 2/3 and 2/3 of 270 is 180

Kurt's truck uses 10 gallons of gas to travel 140miles. He has 5 gallons in the tank. How much more gas will he need to drive 322 miles

Answers

Answer:

18 gallons

Step-by-step explanation:

Step 1:

140 : 10 = x : 5 Equation / Ratio

Step 2:

10x = 700 Multiply

Step 3:

x = 70 Divide

Step 4:

322 miles - 70 miles To find how many miles are needed to get to 322

Step 5:

252 miles ÷ 14 To find the amount of gas / Divide

Answer:

18 gallons more

Hope This Helps :)

(2 + 3i) + (4 - 6i) equal?

Answers

Answer:

Yes indeed, at least I'm pretty sure.

Step-by-step explanation:

4 is half of 2, and 3 is half of 6. you could write them as equal, just like 1/2 and 2/4 fractions.

Answer:

6-3i

Step-by-step explanation:

First, you need to get rid of perenthesis. Use destributuve property to do so.

Then, add the add the same types of integers(whole numbers and numbers with variables)

after that, you get your answer!

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