All categories

3 years ago

A candle is 6 inches tall and burns at a rate of one half an inch per hour. Write an equation to represent the situation.

Mathematics

2 answers:

Greeley [361]3 years ago

7 0

6=1/2h where 6 is the total hight, 1/2 is the rate of decrease, and h is the amount of hours the candle is burned.

Levart [38]3 years ago

5 0

Answer: $y=6-0.5x$

Step-by-step explanation:

Given : The initial height of candle = 6 inches

Amount of candle burn each hour = one half an inch per hour.

$=\dfrac{1}{2}\text{ inch per hour}$

Now , the height of candle = ( initial height ) -( Rate of burning) (Numb er of hours)

Let y be the height of the candle after x hours.

Then, the equation to represent the situation will be :

$y=6-\dfrac{1}{2}x\\\\\Rightarrow\ y=6-0.5x$

You might be interested in

A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

aleksklad [387]

The spider's movement is an illustration of a parabola.

The equation of a parabola is: $\mathbf{y = -\frac{1}{160}(x - 40) + 10}$
The focus of a parabola is: (40,-30)
The axis of symmetry is: $\mathbf{x = 40}$
The directrix is: $\mathbf{y = 50}$

<u>(a) The equation</u>

The spider passes through the origin.

So, we have:

$\mathbf{(x,y) = (0,0)}$

The spider jumps to a maximum height of 10mm, midway 80mm.

So, the vertex is:

$\mathbf{(h,k) = (40,10)}$

The equation of a parabola is:

$\mathbf{y = a(x - h)^2 + k}$

So, we have:

$\mathbf{0 = a(0 - 40)^2 + 10}$

Subtract 10 from both sides

$\mathbf{a(0 - 40)^2 =- 10}$

$\mathbf{1600a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{160}}$

Substitute $\mathbf{a =- \frac{1}{160}}$ and $\mathbf{(h,k) = (40,10)}$ in $\mathbf{(h,k) = (40,10)}$

$\mathbf{y = -\frac{1}{160}(x - 40) + 10}$

<u>(b) The focus, directrix and the axis of symmetry</u>

The focus of a parabola is:

$\mathbf{Focus= (h, k + p)}$

Where:

$\mathbf{p = \frac{1}{4a}}$

So, we have:

$\mathbf{p = \frac{1}{4 \times -1/160}}$

$\mathbf{p = -\frac{160}{4}}$

$\mathbf{p = -40}$

So, we have:

$\mathbf{Focus = (40,10-40)}$

$\mathbf{Focus = (40,-30)}$

The axis of symmetry is:

$\mathbf{x = h}$

So, we have:

$\mathbf{x = 40}$

The directrix is:

$\mathbf{y = k - p}$

$\mathbf{y = 10 + 40}$

$\mathbf{y = 50}$

Read more about parabolas at:

brainly.com/question/25237745

4 0

3 years ago

What is the answer to this math problem? 6=a/4+2

daser333 [38]

If you are solving for a the answer would be a=36.

Here's the process:

6=a/(4+2)

6(4+2)=a

24+12=a

36=a

6 0

3 years ago

Jasmine has 5 1/4 cups of frosting. She wants to put 3/8 cup of frosting on each cupcake she makes. About how many cupcakes can

Harlamova29_29 [7]

Oen cupcake = 3/8 cups

Number of cupcakes:

5 1/4 ÷ 3/8
= 21/4 ÷ 3/8
= 21/4 x 8/3
= 14

She can make 14 cupcakes.

4 0

3 years ago

A Ferris wheel holds up 48 people there are 823 people with tickets to ride the Ferris how many times will the Ferris wheel need

julia-pushkina [17]

Answer:

at least 18 times

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Joanne invited 21 friends to her

Bumek [7]

5 friends could got to the party
21-16=5

8 0

3 years ago