All categories

3 years ago

Write the equations after translating the graph of y = | 1/2 x−2|+3 one unit up

Mathematics

2 answers:

Sunny_sXe [5.5K]3 years ago

8 0

Answer:

$\huge\boxed{y=\bigg|\dfrac{1}{2}x-2\bigg|+4}$

Step-by-step explanation:

f(x) + n - translation n units up

f(x) - n - translation n units down

f(x + n) - translation n units to the left

f(x - n) - translation n units to the right

We have

$y=\bigg|\dfrac{1}{2}x-2\bigg|+3\to f(x)=\bigg|\dfrac{1}{2}x-2\bigg|+3$

translation 1 unit up (f(x) + 1)

$f(x)+1=\bigg(\bigg|\dfrac{1}{2}x-2\bigg|+3\bigg)+1=\bigg|\dfrac{1}{2}x-2\bigg|+3+1\\\\=\bigg|\dfrac{1}{2}x-2\bigg|+4$

tresset_1 [31]3 years ago

7 0

Answer:

[1/2x-2]+4

Step-by-step explanation:

add one to the end

You might be interested in

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

Can someone help me with this please?!

posledela

Answer:

x < 6

Step-by-step explanation:

1) -5x > -30

2) divide both sides by -5

3) flip the sign as we divided inequality by a negative

4) x < 6

7 0

2 years ago

Derek works 40 hours as a skycap. he earns $2.50 per hour plus tips. in one week, he earned $250.00 in tips. what was derek's to

wel

He works 40 hrs....at 2.50 per hr...thats (40 * 2.50) = 100 bucks salary
he earned $ 250 in tips..

salary + tips = total income
100 + 250 = t
350 = t...so his total income add up to $ 350 <==

6 0

3 years ago

What is 275.9 × 10−4 in standard form?

lisov135 [29]

Answer:

-2755

Step-by-step explanation:

4 0

3 years ago

A homeowner has two different sets of triangular tiles, green tiles and blue tiles. Which of these would prove that the green an

ICE Princess25 [194]

I need a picture to answer the question sorry