Simplify (15x^2 - 24x + 9) divided (3x

Find the 110 term of the sequence -7, 3, 13, 23, ...

Evgesh-ka [11]

First, find the nth term
To do this, find the term to term difference...
A
-7 and 3 = 10
3 and 13 = 10
13 and 23 = 10

As the difference is 10, we now write out the 10 times table

10, 20, 30, 40

The next step is to work out how to get from the sequence to the 10x table
B
-7 - 10 = -17
3 - 20 = -17
13 - 30 = -17
23 - 40 = -17

Now use the answer from each section in the general formula
x = An + B
This could also be written as ?n + ?
Using our numbers, this becomes 10n - 17

Now use the formula to work out the 110th term
(10 x 110) - 17
1100 - 17 = 1083

7 0

3 years ago

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

Law Incorporation [45]

Answer:

Step-by-step explanation:

To solve this problem, we will use the following two theorems/definitions:

- Given a vector field F of the form (P(x,y,z),Q(x,y,z),W(x,y,z)) then the divergence of F denoted by $\nabla \cdot F = \frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}}+\frac{\partial W}{\partial z}$

- (Gauss' theorem)Given a closed surface S, the following applies

$\int_{S} F\cdot \vec{n} dS = \int_{V} \nabla \cdot F dV$

where n is the normal vector pointing outward of the surface and V is the volume bounded by the surface S.

Let us, in our case, calculate the divergence of the given field. We have that

$\nabla \cdot F = \frac{\partial}{\partial x}(x)+\frac{\partial}{\partial y}(2y)+ \frac{\partial}{\partial z}(5z) = 1+2+5 = 8$

Hence, by the Gauss theorem we have that

$\int_{S} F\cdot \vec{n} dS = \int_{V} 8 dV = 8\cdot\text{Volume of V}$

So, we must calculate the volume V bounded by the cube S.

We know that the vertices are located on the given points. We must determine the lenght of the side of the cube. To do so, we will take two vertices that are on the some side and whose coordinates differ in only one coordinate. Then, we will calculate the distance between the vertices and that is the lenght of the side.

Take the vertices (1,1,1) and (1,1-1). The distance between them is given by

$\sqrt[]{(1-1)^2+(1-1)^2+(1-(-1)^2} = \sqrt[]{4} = 2$ .

Hence, the volume of V is $2\cdot 2 \cdot 2 = 8$ . Then, the final answer is

$\int_{S} F\cdot \vec{n} dS =8\cdot 8 = 64$

5 0

3 years ago

The formula for the circumference, C, of a circle with radius r is given.

kolezko [41]

The formula for the circumference, C, of a circle with radius r is given.

C=2pi

Amanda made a circular toy hoop using a plastic tube. The circumference of the hoop is 125.6 inches. What is the radius of the hoop? Use 3.14 for pi.

The answer is
D.
40 inches

8 0

3 years ago

What number us 17 less than the product of 7 and 11

m_a_m_a [10]

77 is the product of 7 and 11 (Multiply them)

77 - 17 = 60

Hope this helped!

3 0

3 years ago

A group of friends were working on a student film with a budget of $700, which they

Westkost [7]

Answer:

76%

Step-by-step explanation:

First do 700 - 168 which is 532

Next we see that 700 is 100% in this scenario

Then we will use the value we seek as ‘x’

So, x% = 532

We can put the two equations, 100%/x% = 700/532

they both have LHS

We can take the inverse from both sides yields

Therefore, the answer is 76%

8 0

2 years ago

Simplify (15x^2 - 24x + 9) divided (3x - 3) =