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3 years ago

What is the sum of the geometric series t=1

1 answer:

7 0

In order for an infinite geometric series to have a sum, the common ratio r must be between −1 and 1. ... To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.

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A construction worker needs to put a rectangular window in the side of a building. He knows from measuring that the top and bott

Sliva [168]

Answer: 5 feet

Step-by-step explanation: A rectangle is a quadrilateral with 4 sides. The opposite sides are parallel and have the same length.

Top and bottom of the window are opposite, so they have the same measure of 3 feet.

One length of the window is 5 feet. Since the last side is opposite to the length of the window, it has the same length, i.e., its value is 5 feet.

7 0

2 years ago

WILL GIVE BRAINLIEST!!!!!!!

Liula [17]

Hints on solving trigonometry problems:

If no diagram is given, draw one yourself.

Mark the right angles in the diagram.

Show the sizes of the other angles and the lengths of any lines that are known

Mark the angles or sides you have to calculate.

Consider whether you need to create right triangles by drawing extra lines. For example, divide an isosceles triangle into two congruent right triangles.

Decide whether you will need Pythagorean theorem, sine, cosine or tangent.

Check that your answer is reasonable. The hypotenuse is the longest side in a right triangle.

How to use the tangent ratio to find missing sides or angles?

Example:

5 0

3 years ago

Solve for m p=2m+2w what does m=

Alika [10]

$p=2m+2w \ \ |-2w \\ \\ p-2w=2m +2w -2w \\ \\ p-2w =2m \ \ |:2 \\ \\m=\frac{p}{2}-\frac{2w}{2}\\ \\m=\frac{p}{2}-w$

8 0

3 years ago

Question down below about linear equations and grapghing.

Alik [6]

The system of equations is -x + y = 4 and -2x + y = 0

<h3>How to create the system of linear equations?</h3>

To do this, we make use of the following ordered pairs

(4, 8)

The above point represents April 2008.

Let the system of equations be

mx + ny = 4

2mx + ny = 0

Substitute (4, 8) for x and y in the above equations.

4m + 8n = 4

8m + 8n = 0

Subtract both equations

4m - 8m = 4

This gives

-4m = 4

Divide by 4

m = -1

Substitute m = -1 in 8m + 8n = 0

-8 + 8n = 0

This gives

8n = 8

Divide by 8

n = 1

So, the system of equations is -x + y = 4 and -2x + y = 0

<h3>The graph of the system of equations</h3>

The system of equations is -x + y = 4 and -2x + y = 0

See attachment for the graph of the system of equation

<h3>Prove that the solution is (4, 8)</h3>

The above is represented in the (a) part of this solution

Verify that the solution is (4, 8)

We have:

-x + y = 4 and -2x + y = 0

Substitute (4, 8) for x and y in the above equations.

-4 + 8 = 4 --- true

-2*4 + 8 = 0 --- true

Both equations are true

Hence, the system of equations have been verified

Read more about system of equations at:

brainly.com/question/14323743

#SPJ1

6 0

1 year ago

Show that if the vector field F = Pi + Qj + Rk is conservative and P, Q, R have continuous first-order partial derivatives, then

olchik [2.2K]

Answer:

It is proved that $\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}, \frac{\partial P}{\partial z}=\frac{\partial R}{\partial x}, \frac{\partial Q}{\partial z}=\frac{\partial R}{\partial y}$

Step-by-step explanation:

Given vector field,

$F=P\uvec{i}+Q\uvec{j}+R\uvec{k}$

Where,

$P=f_x=\frac{\partial f}{\partial x}, Q=f_y=\frac{\partial f}{\partial y}, R=f_z=\frac{\partial f}{\partial z}$

To show,

$\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}, \frac{\partial P}{\partial z}=\frac{\partial R}{\partial x}, \frac{\partial Q}{\partial z}=\frac{\partial R}{\partial y}$

Consider,

$\frac{\partial P}{\partial y}=\frac{\partial}{\partial y}(\frac{\partial f}{\partial x})=\frac{\partial^2 f}{\partial y\partial x}=\frac{\partial^2 f}{\partial x\partial y}=\frac{\partial }{\partial x}(\frac{\partial f}{\partial y})=\frac{\partial Q}{\partial x}$

$\frac{\partial P}{\partial z}=\frac{\partial}{\partial z}(\frac{\partial f}{\partial x})=\frac{\partial^2 f}{\partial z\partial x}=\frac{\partial^2 f}{\partial x\partial z}=\frac{\partial }{\partial x}(\frac{\partial f}{\partial z})=\frac{\partial R}{\partial x}$

$\frac{\partial Q}{\partial z}=\frac{\partial}{\partial z}(\frac{\partial f}{\partial y})=\frac{\partial^2 f}{\partial z\partial y}=\frac{\partial^2 f}{\partial y\partial z}=\frac{\partial}{\partial y}(\frac{\partial f}{\partial z})=\frac{\partial R}{\partial y}$

Hence proved.

4 0

3 years ago