All categories

3 years ago

What is the vertex of each function

Mathematics

1 answer:

cricket20 [7]3 years ago

7 0

Answer:

Step-by-step explanation:

note :

f(x) =a(x-h)²+k

the vertex is : (h,k)

continu .........

You might be interested in

A force of 7 lb is required to hold a spring stretched 9 in. beyond its natural length. How much work W is done in stretching it

Ymorist [56]

144 joules is the work W done in stretching it from its natural length to 13 in beyond its natural length

Force F=10 lb

From the hookes Law

$F=kx$

Therefore, calculate k for the spring for

$10=k(\frac{4}{12}) = > k=\frac{120}{4}=30$

Work done in stretching a spring through a length dx is

$dW=F.dx = > dW=kxdx$

For calculating the work done for stretching the spring to x=6in=(6/12)feet beyond the natural length, Integrate over the limits of x=0 to x=1/2

Therefore,

$\int_{0}^{W}dW=\int_{0}^{0.5}kxdx = > W=\frac{1}{2}k[x^2]_{0}^{0.5}=\frac{1}{2}30 \times (0.5)^2=\frac{30}{8}$

That is,

$W=\frac{15}{4} ft-lb\\$

The answer that is given is for stretching the spring to 4 inches.

Mass of 10 m of chain length is 80kg. This implies, Mass per unit meter length of the chain is

$m_{l}=\frac{80}{10}=8kg/m$

Consider a small length dx of the chain at the end point A. Work done in lifting the small length dx over the height of x meters is

$dW=(8g)dx \times x=8gxdx$

Now, integrate over the the value of x from

x=0 when end of the chain A is on the ground

x=6 when end of the chain A reaches 6 m above the ground

That is,

$\int_{0}^{W}dW=\int_{0}^{6}8gxdx=8g [\frac{x^2}{2}]_{0}^{6}=4g(6^2-0^2)$

$W=4g \times 36=144g \ Joules$

Hence,144 joules is the work W done in stretching it from its natural length to 13 in beyond its natural length

Learn more about Integration here brainly.com/question/2263647

#SPJ4

7 0

2 years ago

Andrei had cinnamon-scented jar candle that burned for 303030 hours and a berry-scented pillar candle that burned for 888888 hou

enyata [817]

The cinnamon-scented jar candle brunt faster.

<h3>What does relative speed means ?</h3>

Relativity means observing some action with different perspective.

Suppose you are moving in a bus at 100 km/hr and you are reading a book.To an observer which you are passing by you and the book he observes moving at a speed of 100 km/hr.But for you the book is not moving at all because both you and the book is moving at a speed of 100 km per hour.

According to the given question Andrei had cinnamon-scented jar candle that burned for 303030 hours and a berry-scented pillar candle that burned for 888888 hours.

From the given data of burning hours we can observe that berry-scented pillar candle that burned for 888888 hours which is more that of Andrei had cinnamon-scented jar candle that brunt for 303030 hours because

30303030 < 888888.

Learn more about relative speed here :

brainly.com/question/15687499

#SPJ4

5 0

1 year ago

Who is your favorite y-o-u-t-u-b-e-r

Sladkaya [172]

Answer:

dream

Step-by-step explanation:

why not

7 0

3 years ago

Read 2 more answers

At the market, 9 apples cost $4.00. How much does 10 apples cost?

ycow [4]

Answer:

$6.25

Step-by-step explanation:

Each apple is 2.25

6 0

3 years ago

A DEF has vertices D(-5,-1), E (3, 3), and F (1,-5). Find the equation of the altitude through F in

Tems11 [23]

Answer:

y = -2x -3

Step-by-step explanation:

- the altitude trough F is a perpendicular line to the line DE

- find slope of line DE

D ( x2 = -5, y2 = -1); E (x1 = 3, y1 = 3)

slope m = (y2-y1) / (x2-x1) = (-1-3) / (-5-3) = -4/ -8 = 1/2

-find equation of the altitude trough F

lines that are perpendicular have the slope negative reciprocal (negative reciprocal of 1/2 is -2)

y= -2x +b , for point F(1, -5)

-5 = -2*1 +b, add 2 to both sides

-5 +2 = b, combine like terms

-3 =b

equation of the altitude trough F is y = -2x -3

4 0

3 years ago