1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Makovka662 [10]
3 years ago
10

Please help find the formulas for these!! ASAP!!!

Mathematics
1 answer:
Ilya [14]3 years ago
6 0

Answer:

a)\ f(x)=\left\{\begin{array}{cccc}-x+2&for&x\in(0,\ 2]&/0

b)\ f(x)=\left\{\begin{array}{cccc}-3x-3&for&x\in(-1,\ 0]&/-1

Step-by-step explanation:

These are graphs of piecewise functions.

Each part is a graph of the linear function.

The slope-intercept form of an equation of a line:

y=mx+b

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept → (0, b)</em>

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

========================================

<h2>a)</h2>

Part 1:

Points (0, 2) → <em>b = 2</em>, and (2, 0).

Calculate the slope:

m=\dfrac{0-2}{2-0}=\dfrac{-2}{2}=-1

Put the value of <em>m</em> and <em>b</em> to the equation of a line:

(1)\ y=-1x+2=-x+2

Part 2:

Points (2, 1) and (5, 0).

Calculate the slope:

m=\dfrac{0-1}{5-2}=\dfrac{-1}{3}=-\dfrac{1}{3}

Put the value of the slope and the coordinates of the point (5, 0) to the equation of a line:

0=-\dfrac{1}{3}(5)+b

0=-\dfrac{5}{3}+b         <em>add 5/3 to both sides</em>

\dfrac{5}{3}=b

Therefore we have:

y=-\dfrac{1}{3}x+\dfrac{5}{3}

The domain of the function is (0, 2] and (2, 5].

Formula of the piecewise function:

f(x)=\left\{\begin{array}{cccc}-x+2&for&x\in(0,\ 2]&/0

============================================================

<h2>b)</h2>

We solve the same as in a) in Part 1

Part 1:

(-1, 0), (0, -3) → <em>b = -3</em>

m=\dfrac{-3-0}{0-(-1)}=\dfrac{-3}{1}=-3

y=-3x-3

Part 2:

(0, 3) → <em>b = 3</em>, (2, -1)

m=\dfrac{-1-3}{2-0}=\dfrac{-4}{2}=-2

y=-2x+3

Domain: (-1, 0] and (0, 2].

f(x)=\left\{\begin{array}{cccc}-3x-3&for&x\in(-1,\ 0]&/-1

You might be interested in
Josslyn has nickels and dimes in her pocket. The number of nickels is three more than seven times the number of dimes let d repr
vfiekz [6]
7d+3Explanation

to solve this we need to translate into math terms, so

Step 1

a) let d represents the number of dimes

let n represents the number of nickles

so

re write the expressions

\begin{gathered} number\text{ of dimes=d} \\ seven\text{ times the number of dimes = 7d} \\  \end{gathered}

The number of nickels is three more than seven times the number of dimes in other words you have to add 7 to seven times the number of dimes to obtain the number of nickles

hence

n=7d+3

therefore , the expression for the number of nickles is

7d+3

I hope this helps you

3 0
1 year ago
Two numbers are opposites are 12 units apart. What are the two numbers? Answer smaller number, larger number
Ugo [173]

Answer:

-6, 6

Explanation:

-6 - 6 = -12

8 0
2 years ago
A car rental agency has 150 cars. The owner finds that at a price of $48 per day, he can rent all the cars. For each $2 increase
hram777 [196]
Given that for each <span>$2 increase in price, the demand is less and 4 fewer cars are rented.

Let x be the number of $2 increases in price, then the revenue from renting cars is given by
(48 + 2x) \times (150 - 4x)=7,200+108x-8x^2.

Also, given that f</span><span>or each car that is rented, there are routine maintenance costs of $5 per day, then the total cost of renting cars is given by
5(150-4x)=750-20x

Profit is given by revenue - cost.
Thus, the profit from renting cars is given by
</span><span>(7,200+108x-8x^2)-(750-20x)=6,450+128x-8x^2

For maximum profit, the differentiation of the profit function equals zero.
i.e.
</span><span>\frac{d}{dx} (6,450+128x-8x^2)=0 \\  \\ 128-16x=0 \\  \\ x= \frac{128}{16} =8

The price of renting a car is given by 48 + 2x = 48 + 2(8) = 48 + 16 = 64.

Therefore, the </span><span>rental charge will maximize profit is $64.</span>
3 0
3 years ago
A grain silo has the shape of a right circular cylinder surmounted by a hemisphere. If the silo is to have a volume of 505π ft3,
Romashka-Z-Leto [24]

Answer:

radius   x  = 3 ft

height   h = 23,8  ft

Step-by-step explanation:

From problem statement

V(t)  = V(cylinder) + V(hemisphere)

let x be radius of base of cylinder (at the same time radius of the hemisphere)

and h the height of the cylinder, then:

V(c)  = π*x²*h       area of cylinder = area of base + lateral area

                                              A(c)  = π*x²  +   2*π*x*h

V(h) = (2/3)*π*x³   area of hemisphere   A(h)  =   (2/3)*π*x²

A(t)  =  π*x²  +   2*π*x*h +   (2/3)*π*x²

Now A as fuction of x    

total volume   505  = π*x²*h  +  (2/3)*π*x³

h = [505 - (2/3)* π*x³ ]  /2* π*x    

Now we have the expression for A as function of x

A(x) =  3π*x² + 2π*x*h     A(x) = 3π*x² + 505  - (2/3)π*x³

Taking derivatives both sides

A´(x) =  6πx -  2πx²              A´(x) =  0         6x  - 2x²  = 0

x₁  =  0  we dismiss

6 - 2x = 0

x = 3     and   h = [505 - (2/3)* π*x³]/2* π*x

h  =  (505 - 18.84) / 6.28*3

h  = 23,8  ft

7 0
3 years ago
What is the answer to 10 to the 2nd power times 5/2 is ?
katrin2010 [14]
Answer: 250
10 times itself or 10^2 = 100
(100)(5)=500
500/2= 250
5 0
3 years ago
Other questions:
  • What is the value of 6 in the number of 46.026
    11·1 answer
  • A = 1/2(a + b)h for h
    11·1 answer
  • 1.5 as a mixed number and 1.5 as a improper fraction
    10·2 answers
  • Find the greatest rational number r such that the ratios 8/15 ÷r and 18/35 ÷r are whole numbers.
    15·1 answer
  • Find the distance between the two points.<br> 8. (-1,0), (-8, 4)
    5·1 answer
  • BRAINLIEST! will give BRAINLY! can someone please explain, I don't understand how to do this.
    10·1 answer
  • Can someone help me with this
    7·2 answers
  • Another Question in my test
    11·1 answer
  • Find the distance between the points (-2, -4) and (-6, -8). Round your answer to to the nearest tenth.
    5·1 answer
  • Shelly paid $2.00 per kg for the item that weighs 25% of the total weight of the 4 items calculate the amount of money she paid
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!