MATHEMATICS COLLEGE

Will Mark Brainliest! What are the coordinates of point A?(–2, –6)

(–6, –2)

(–6, –3)

(–3, –6)

Answers

Answer 1
Answer:

Step-by-step explanation:

the first one -2,-6 .......

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How many rational numbers are there between - 5 and - 4?​
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X + y + w = b2x + 3y + z + 5w = 6z + w = 42y + 2z + aw = 1For what values a, b (constants) is the system:(a) inconsistent?(b) consistent w/ a unique sol'n?(c) consistent w/ infinitely-many sol'ns?

What is the solution of the system of equationsy-x=5 and y=x² +5?
1) (0,5) and (1,6)
2) (0,5) and (-1,0)
3) (2.9) and (-1,4)
4) (-2,9) and (-1.4)

Answers

You can basically just plug in the values. “1) (0,5) and (1,6)” is correct.

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

Question 1x + 6 = 23 x = ____

Question 2
Solve.
x - 7 = 12 x = ___

Question 3
Solve. Round your answer to the nearest tenth.

4x = 13 x = ____

Question 4
Solve. Round your answer to the nearest tenth.

3x + 1 = 15

Answers

Answer:

1. x=17

2. x=19

3. x=3

4. x=4

Answer:

question 1:

3/11

question 2:

-  7/11

Step-by-step explanation:

in

Given that the measurement is in centimeters,find the area of the circle to the nearest tenth.(Use 3.14 for pi)A)28.3
B)56.5
C)88.7
D).254.3

Answers

Answer:

D) 254.3

Step-by-step explanation:

The formula for the area of a circle is πr^2

so it would be, 3.14 x 9 x 9= 254.34

then just round your answer to the nearest tenth to get 254.3

Hope this helps! Let me know if you need help with anything else!

Mary wants to buy a new house but needs money for the down payment. Her parents agree to lend her money at an annual rate of 2%, charged as simple interest. They lend her $6000 for 3 years. She makes no payments except the one at the end of that time. Answer the following questions. If necessary, refer to the list of financial formulas. (a) How much total interest will Mary have to pay?
(b) What will the total repayment amount be (including interest)? X

Answers

Answer:

a) Simple interest paid = $360

b) Total repayment amount = $6360

Step-by-step explanation:

It is given that:

Principal, P = $6000

Rate of interest, R = 2%

Time, T = 3 years

(a) Total interest paid:

Formula for Simple Interest is given as:

S.I. = (P * R * T)/(100)

Putting the values of P, R and T to find out Simple Interest:\n\Rightarrow S.I. = (6000 * 2 * 3)/(100)\n\Rightarrow S.I. = \$360

(b) Total repayment amount:

We know that formula for total amount is given as:

Amount = Principal + Simple Interest

Amount = 6000 + 360 = $6360

So, total repayment amount = $6360

So, the answers are:

a) Simple interest paid = $360

b) Total repayment amount = $6360

What is the average of the data in the line plot

Answers

Hey there!

The “average” is your “total” or your “mean” of a data set. To find out the average you have to ADD the total numbers in your data & DIVIDE it by the amount of numbers you have in your data.

EXAMPLE:

SET:

10, 20, 30, 40, 50, 60

EQUATION: 10 + 20 + 30 + 40 + 50 + 60 / 6

10 + 20 + 30 + 40 + 50 + 60 / 6

= 30 + 30 + 40 + 50 + 60 / 6

= 60 + 40 + 50 + 60 / 6

= 100 + 50 + 60 / 6

= 150 + 60 / 6

= 210 / 6

= 35

Thus, the mean is: 35

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)
The average can be found by adding each of the pieces of data on the plot and then dividing it by how ever many pieces of data there are

ie=
 100+300+800=1200
1200/3=400
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