A sphere has a radius of 12 centimeters.

Consider the function f(x)= 1-|x-1|+|x+1| for -3<x<3. Recall that the absolute function can be represented as a piece wise

Kruka [31]

By the definition for the absolute value,

$|x-1|=\begin{cases}x-1&\text{for }x\ge1\\-(x-1)&\text{for }x$
$|x+1|=\begin{cases}x+1&\text{for }x\ge-1\\-(x+1)&\text{for }x$

So for the compound function $f(x)=1-|x-1|+|x+1|$ , there are three intervals to consider. What happens when $x$ ? when $-1\le x$ ? when $x\ge1$ ?

You have

$f(x)=\begin{cases}1-(-(x-1))+(-(x+1))=-1&\text{for }x$

8 0

3 years ago

From base camp, a hiker walks 3.5 miles west and 1.5 miles north. Another hiker walks 2 miles east and 0.5 miles south. To the n

levacccp [35]

Answer:

The hikers are 5.9 miles apart.

Step-by-step explanation:

Let O represents the base camp,

Suppose after walking 3.5 miles west, first hiker's position is A, then after going 1.5 miles north from A his final position is B,

Similarly, after walking 2 miles east, second hiker's position is C then going towards 0.5 miles south his final position is D.

By making the diagram of this situation,

Let D' is the point in the line AB,

Such that, AD' = CD

In triangle BD'D,

BD' = AB + AD' = 1.5 + 0.5 = 2 miles,

DD' = AC = AO + OC = 3.5 + 2 = 5.5 miles,

By Pythagoras theorem,

$BD^2 = BD'^2 + DD'^2$

$BD = \sqrt{2^2 + 5.5^2}=\sqrt{4+30.25}=\sqrt{34.25}\approx 5.9$

Hence, the hikers are 5.9 miles apart.

8 0

3 years ago

A woman is 10 times as old as her daughter. In 8 years she will be 4 times as old as her daughter. How old is the mother now?

jeka57 [31]

Answer:

Mom is 40 and her daughter is 4; in eight years, mom will be 48 and her daughter will be 12.

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Please help me with my math

Taya2010 [7]

3x + 22 is the equation that represents the perimeter of the triangle. 4x + 10 is the perimeter of the rectangle. Setting the two equal:

$3x + 22 = 4x + 10$

and collecting like terms:

$x=11$

We find that the perimeter of both shapes is equal to 11 units.

8 0

3 years ago

Help I have to turn this in. In a couple hours

Gelneren [198K]

28. Surface Area

This is some sort of house-like model so for every face we see there's a congruent one that's hidden. We'll just double the area we can see.

Area = 2 × ( [14×9 rectangle] + 2[15×9 rectangle]+[triangle base 14, height 6] )

Let's separate the area into the area of the front and the sides; the front will help us for problem 29.

Front = [14×9 rectangle] + [triangle base 14, height 6]

= 14×9 + (1/2)(14)(6) = 14(9 + 3) = 14×12 = 168 sq ft

OneSide = 2[15×9 rectangle] = 30×9 = 270 sq ft

Surface Area = 2(168 + 270) = 876 sq ft

Answer: D) 876 sq ft

29. Volume of an extruded shape is area of the base, here the front, times the height, here 15 feet.

Volume = 168 * 15 = 2520 cubic ft

Answer: D) 2520 cubic ft

6 0

3 years ago