A candle burns at a constant rate of 2.5cm/h. The candle is 15cm tall when it is first lit. Let "t" represent the time is it burning in hours and let "h" represent the height of the candle in centimetres.

Answers

Answer 1

Answer:

The initial height of the candle is H = 15cm

The rate at which the candle burns is 2.5 cm per hour

Then after one hour, the height of the candle is:

h = 15cm - 2.5cm = 12.5cm

after two hours is:

h = 15cm - 2*2.5cm = 10cm

then, after t hours, the height of the candle is:

h = 15cm - (2.5cm/h)*t

now, the domain of h (or the range of the function) is:

h ∈ [0cm, 15cm]

when t = 0, h(0h) = 15cm

and the maximum value of t will be such that the candle is totally consumed:

h(t) = 0 = 15 - 2.5*t

t = 15/2.5 = 6

Then the domain of the function is:

t ∈ [0h, 6h]


Related Questions

I promise I will mark the brainiest

Answers

Answer:

[tex]\frac{9}{a - b}[/tex].

Step-by-step explanation:

a^2 - b^2 = 9

(a + b)(a - b) = 9

a + b = [tex]\frac{9}{a - b}[/tex].

ab = 3

a = 3/b

3/b + b = [tex]\frac{9}{\frac{3}{b} -b}[/tex]

3 + b^2 = [tex]\frac{9b}{\frac{3}{b}-\frac{b^2}{b} }[/tex]

3 + b^2 = [tex]\frac{9b}{\frac{3-b^2}{b} }[/tex]

3 + b^2 = [tex]9b * \frac{b}{-b^2 + 3}[/tex]

3 + b^2 = [tex]\frac{9b^2}{-b^2 + 3}[/tex]

(b^2 + 3)(-b^2 + 3) = 9b^2

-b^4 + 9 = 9b^2

b^4 + 9b^2 - 9 = 0

Let's say that b^2 = x

x^2 + 9x - 9 = 0

Hope this [somewhat] helps!

Answer:

Step-by-step explanation:

a²-b²=9

ab=3 then a=3/b

a²-b²=9

(a+b)(a-b)=9 ( the values has to b (3*3) or (9*1)

but since ab=3. so the value has to be (3*3)

(a+b)(a-b)=9

3*3=9

a+b=3

ab=3

What is the solution to this equation?
X +8=-3
A. x=-11
B. x= 11
c. x= -5
D. x = 5

Answers

Answer:

Option A

Step-by-step explanation:

x + 8 = -3

x + 8 - 8 = -3 - 8

x = - 11

Answer:

A. x= -11

Step-by-step explanation:

We want to solve for x. Therefore, we must get x by itself on one side of the equation.

x+8= -3

8 is being added to x. The inverse of addition is subtraction. So, subtract 8 from both sides of the equation.

x+8-8=-3-8

x= -3-8

x= -11

Now let’s check our solution. Plug -11 in for x in the original equation.

x+8=-3

-11+8=-3

-3=-3

This checks out, so we know our solution is correct and A. x= -11 is the correct choice.

Overnight the temperature in Alaska dropped from 3%
degrees Fahrenheit to twelve and a quarter degrees
Fahrenheit below zero. By how many degrees did the
cemperature drop overnight?**

A. 8 3/4 degrees
B. 9 3/4 degrees
C. 15 1/2 degrees
D. 15 3/4 degrees

Answers

Answer:

A. 8 3/4 degrees

Step-by-step explanation:

Alaska temperature dropped from 3 degrees Fahrenheit to twelve and a quarter degrees Fahrenheit below zero

12 1/4°F - 3°F

=8 3/4°F

The temperature dropped by 8 3/4°F

How many minutes are in 324 hours?​

Answers

Answer: 19440 minutes

Step-by-step explanation:

Hi there! Hopefully this helps!

--------------------------------------------------------------------------------------------------

Answer: There are 19440 minutes in 324 hours.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Since there are 60 minutes in each hour, we need to multiply the time value by 60. Like this:

324 x 60 = 19440.

A boat's value over time is given as the function f(x) and graphed below. Use A(x) = 400(b)x + 0 as the parent function. Which graph shows the boat's value decreasing at a rate of 40% per year? The graph starts on the left near the x-axis, and near the point negative 20 comma 5 curves upward to the right. The graph starts on the left near the horizontal line x equal 25, and near the point negative 20 comma 30, the graph curves upward to the right. The graph starts on the top left near the y-axis and moves downward to the right. The graph makes a sharp turn near the point 10 comma 2.5 and continues to the right along the x-axis. The graph starts on the top left near the y-axis and moves downward to the right. The graph makes a sharp turn near the point 5 comma negative 30 and continues to the right along the horizontal line x equals negative 25.

Answers

Answer:

C

Step-by-step explanation:

The required graph has been attached below which shows the boat's value decreasing at a rate of 40% per year.

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

A boat's value over time is given as the function f(x) and graphed below.  A(x) = 400(b)ˣ + 0 as the parent function.

Given that the boat's value decreases at a rate of 40% per year.

So after each year, the value becomes = 1 - 40% = 1 - 0.40 = 0.60 of the previous year.

So the equation becomes: A(x) = 400(0.60)ˣ + 0

Since, b = 0.60 < 1, so A(x) is a decreasing function. And for every value of x, A(x) > 0.

The attached graph meets these requirements.

Learn more about the graphs here:

brainly.com/question/16608196

#SPJ2

Waves with an amplitude of 2 feet pass a dock every 30 seconds. Write an equation for a cosine function to model the height of a water particle above and below the mean water line. Explain your steps.

Answers

Answer:

The cosine function to model the height of a water particle above and below the mean water line is h = 2·cos((π/30)·t)

Step-by-step explanation:

The cosine function equation is given as follows h = d + a·cos(b(x - c))

Where:

[tex]\left | a \right |[/tex] = Amplitude

2·π/b = The period

c = The phase shift

d = The vertical shift

h = Height of the function

x = The time duration of motion of the wave, t

The given data are;

The amplitude [tex]\left | a \right |[/tex] = 2 feet

Time for the wave to pass the dock

The number of times the wave passes a point in each cycle = 2 times

Therefore;

The time for each complete cycle = 2 × 30 seconds  = 60 seconds

The time for each complete cycle = Period = 2·π/b = 60

b = π/30 =

Taking the phase shift as zero, (moving wave) and the vertical shift as zero (movement about the mean water line), we have

h = 0 + 2·cos(π/30(t - 0)) = 2·cos((π/30)·t)

The cosine function is h = 2·cos((π/30)·t).

What is the simplified form of the following expression?
[tex]2 (\sqrt[4]{16x}) - 2 (\sqrt[4]{2y} ) + 3 (\sqrt[4]{81x} ) - 4 (\sqrt[4]{32y} )[/tex]

Answers

We have

[tex]16=2^4\implies\sqrt[4]{16}=2[/tex]

[tex]81=3^4\implies\sqrt[4]{81}=3[/tex]

[tex]32=2^5\implies\sqrt[4]{32}=2\sqrt[4]{2}[/tex]

So

[tex]2\sqrt[4]{16x}-2\sqrt[4]{2y}+3\sqrt[4]{81x}-4\sqrt[4]{32y}[/tex]

is equivalent to

[tex]2^2\sqrt[4]{x}-2\sqrt[4]{2y}+3^2\sqrt[4]{x}-8\sqrt[4]{2y}[/tex]

which reduces to

[tex]13\sqrt[4]{x}-10\sqrt[4]{2y}[/tex]

The following box plot shows the number of years during which 40 schools have participated in an interschool swimming meet: A box and whisker plot is drawn using a number line from 0 to 10 with primary markings and labels at 0, 5, 10. In between two primary markings are 4 secondary markings. The box extends from 1 to 6 on the number line. There is a vertical line at 3.5. The whiskers end at 0 and 8. Above the plot is written Duration of Participation. Below the plot is written Years. At least how many schools have participated for more than 1 year and less than 6 years?

Answers

Answer:

Step-by-step explanation:

The box encloses data between the two quartiles, namely at least half of the data.  If there are 40 schools, then half of them would be in the box, between 1 and 6.

see attached plot.

Answer:

really hard to tell what the box plot is like without an attachment so im gonna help u find it out anyway

Step-by-step explanation:

basically when u look at a  box plot and the range the line in the middle is the median  and then the max the lowest range the lower quartile and then the higher quartile you can find ur anser, simply find the median first, find where the lower quartile is and then the lowest number in the group thats in betweeen 1 and 6

Write the rule for this sequence '32,16,8,4'

Answers

Step-by-step explanation:

This is a sequence of divide by 2 or half of the number so 32 16 8 4 2 1

What are two possible measures of the angle below? On a coordinate plane, 2 rays form an angle. One ray sits on the x-axis in quadrant 1 and another sits on the y-axis between quadrants 3 and 4. –90° and 630° –45° and 630° –90° and 225° –45° and 225°

Answers

Answer:

  –90° and 630°

Step-by-step explanation:

The described angle will be -90° plus any integer multiple of 360°. Possible values for the angle are ...

  -90° and 630°

_____

Angles are conventionally measured counterclockwise from the positive x-axis. The angle shown in the attachment is measured clockwise, so represents a negative 90° angle.

Answer:

–90° and 630°

Step-by-step explanation:

The answer above is correct.

Help me to solve this problem ASAP please, also {} is incorrect.

Answers

The answer is B I believe, hope this helps

Answer:

8/9

Step-by-step explanation:

2/3 + 1 / ( 2 2/5) - 1/x = 1/3 -  1 / ( 2 2/3)

Changing to improper fractions

2 2/5 = ((5*2+2) / 5 = 12/5

2 2/3 = ( 3*2+2) /3 = 8/3

2/3 + 1 / ( 12/5) - 1/x = 1/3 -  1 / ( 8/3)

1 over and improper fraction flips the improper fraction  1 / ( a/b) = b/a

2/3 + 5/12 - 1/x = 1/3 -3/8

Subtract 2/3 from each side

5/12 -1/x = 1/3 -2/3 -3/8

5/12 -1/x =  -1/3 -3/8

Subtract 5/12 from each side

-1/x =  -1/3 -3/8-5/12

Multiply each side by 24 to get rid of the fractions

-24/x = -24/3 -3*24/8 -5*24/12

-24/x = -8 -9 -10

-24/x = -27

Multiply each side by x

-24 = -27x

Divide by -27

-24/-27 =x

8/9 =x

Please answer this question now


Answers

Answer:

825 or 500

Step-by-step explanation:

Depends, if it is talking about just an up-down, it is 500, but if it is just distance in general, it would be 825 because 325+500=825

Hope this will help

Please answer the question correct only if you know the answer

Answers

Answer: g = 8.8

Use the law of cosines to solve for side g.

g^2 = e^2 + f^2 - 2*e*f*cos(G)

g^2 = 10^2 + 8^2 - 2*10*8*cos(57)

g^2 = 76.85775 ... make sure your calc is in degree mode

g = sqrt(76.85775)

g = 8.766855

g = 8.8

plzzz help me!! (question is attached)

Answers

Answer:

A, B, D, and E

Step-by-step explanation:

recall that the inverse functions verify the identity rule that one function applied on the other will render the identity "x". It is like launching a function from a value x, and then taking the trip back to the value that originated it.

Such also implies that the domain where you started becomes the Range of the function that makes the trip back. And of course, its reciprocal: The Range of the starting function becomes the Domain of the function that gets back.

Therefore, andswers A, B, D and E are correct answers

which expression is equivalent to 2(5)^4

Answers

Answer:

l0^4

2 (2)^4

I'm sorry if my answer is not helping

Una compañía sabe que si produce "x" unidades mensuales su utilidad "u" se podría calcular con la expresión: u(x)=-0.04x^2+44x-4000 donde "u" se expresa en dólares. Determine la razón del cambio promedio de la utilidad cuando el nivel de producción cambia de 600 a 620 unidades mensuales. Recuerde que la pendiente de la recta secante a la gráfica de la función representa a la razón de cambio promedio.

Answers

Answer:

The ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

Step-by-step explanation:

The question is:

A company knows that if it produces "x" monthly units its utility "u" could be calculated with the expression: u (x) = - 0.04x ^ 2 + 44x-4000 where "u" is expressed in dollars. Determine the ratio of the average change in profit when the level of production changes from 600 to 620 units per month. Remember that the slope of the secant line to the graph of the function represents the average rate of change.

Solution:

The expression for the utility is:

[tex]u (x) = - 0.04x ^ {2} + 44x-4000[/tex]

It is provided that the slope of the secant line to the graph of the function represents the average rate of change.

Then the ratio of the average change in profit when the level of production changes is:

[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]

Compute the values of u (x₁) and u (x₂) as follows:

x₁ = 600

[tex]u (x_{1}) = - 0.04x_{1} ^ {2} + 44x_{1}-4000[/tex]

         [tex]= - 0.04(600) ^ {2} + 44(600)-4000\\=-14400+26400-4000\\=8000[/tex]

x₂ = 620

[tex]u (x_{2}) = - 0.04x_{2} ^ {2} + 44x_{2}-4000[/tex]

         [tex]= - 0.04(620) ^ {2} + 44(620)-4000\\=-15376+27280-4000\\=7904[/tex]

Compute the average rate of change as follows:

[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]

                                      [tex]=\frac{7904-800}{620-600}\\\\=\frac{-96}{20}\\\\=-\frac{24}{5}\\\\=-24:5[/tex]

Thus, the ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

U
Which statements are true about x? Select three
options
B
XEBUC
Oxenc
OXEAUC
Oxeanc
ΕχεΑ
с​

Answers

Answer:

A, B, C

Step-by-step explanation:

x is in the intersection of sets B and C, in set B, in set C, in the union of sets B and C, in the union of sets A and C

Answer: A, B, C

Answer:

[tex]\huge\boxed{x\in\bigg(A\cup C\bigg)}[/tex]

[tex]\huge\boxed{x\in\bigg(B\cup C\bigg)}\\\\\boxed{x\in\bigg(B\cap C\bigg)}[/tex]

Step-by-step explanation:

Look at the picture

In a school, the ratio of students of class 9 to that of class 10 is 3:2. 30% of the students of class 9 and 10%of the students of class 10 were elected to the school student committee. What fraction of the total number of students of the two classes was selected to the school student committee?

Answers

Answer:

22% of the two classes were elected to the student committee

Step-by-step explanation:

Given

class 9 : class 10 = 3:2 = 60% : 40%

Total fraction = 60% * 30% + 40% * 10% = 18% + 4% = 22%

Completing the square........... (+25 points+!) Someone please help:)

Answers

Answer:

D)

[tex]5 \times {10}^{ - 12} [/tex]

Step-by-step explanation:

velocity(v) = distance/time

but distance =

[tex]3 \times {10}^{ - 4} [/tex]

and velocity =

[tex]6 \times {10}^{7} [/tex]

[tex]6 \times {10}^{7} = \frac{3 \times {10}^{ - 4} }{time} [/tex]

[tex]time = \frac{3 \times {10}^{ - 4} }{6 \times {10}^{7} } [/tex]

[tex]time = 5 \times {10}^{ - 12} [/tex]

10.
Find the length of the arc on a circle of radius r intercepted by a central angle 0.
r=20 cm,
e
1/4 radian

Answers

Answer:

Length of arc = 5 cm (Approx)

Step-by-step explanation:

Given:

Radius of circle = 20 cm

Angle = 1/4 radian

Find:

Length of arc

Computation:

Angle in degree = 1/4 radian × 180°π

Angle in degree = 1/4 × 180°  / 22/7

Angle in degree = 14.31° Approx

Length of arc = (Ф / 360)2πr

Length of arc = (14.31 /360)2(22/7)(20)

Length of arc = 4.997 cm

Length of arc = 5 cm (Approx)

Represent the expression
(4 x 1,000) + (3 x 100) + (6 x
1/100) + (7x1000)
as a decimal number.

Answers

Answer:

The answer is 11 300.06

[tex](4 \times 1000) + (3 \times 100) + (6 \times \frac{1}{100}) + (7 \times 1000) [/tex]

[tex] = 4000 + 300 + \frac{6}{100} + 7000[/tex]

[tex] = 11 \: 300 + 0.06[/tex]

[tex] = 11 \: 300.06[/tex]

{b(1)=-2 {b(n)=b(n-1)-7 What’s the 3rd term?

Answers

Answer: the answer is b(5)

Step-by-step explanation:

To find the third term work backwards and plug it in. That was when you plug the solution of b(n-1) everything fits.

Answer:

b(3)=-16

Step-by-step explanation:

We have to figure out the second term

b(2)=b(1)-7

b(2)=-2-7

b(2)=-9

and now the third one

b(3)=b(2)-7

b(3)=-9-7

b(3)=-16

find the slope y=2x+5

Answers

Answer:

slope is 2

Step-by-step explanation:

the equation of linear is y=mx+b, where m is the slope

therefore, m=2 which means the slope is 2

Answer:the slope is 2

Step-by-step explanation:

the equation y=mx+b represents m as the slope.

Go step by step to reduce the radical. 288 ​

Answers

Step-by-step explanation:

hope this helps if not well im rlly srry lol

Find the product.

(6xyz4)(5xy3)

PLEASE HELP!!! ASAP!!

Answers

Answer:

[tex]30x^2y^4z^4[/tex]

Step-by-step explanation:

If we multiply 6x by 5x, we get [tex]30x^2[/tex].

If we multiply y by [tex]y^{3}[/tex], we get [tex]y^{4}[/tex].

z stays the same, since it's not being multiplied by anything.

Hope this helped!

Answer:

Step-by-step explanation:

Multiply each term:

30x^2y^4z^4

Plz mark me brainliest!!

(Dividing polynomials ick!) Please help I'm failing summer class:)

Answers

Answer:

The answer is 9 (D).

Step-by-step explanation:

Hope this helps!

Please answer this question now

Answers

Since HJ is tangent to circle G, it forms a right angle with the radius that intersects it.

This means HG and HG are perpendicular and we have a right angle.

We have a (right) triangle with angle measurements 43 and 90, and we want to find the value of the last angle.

All the angles in a triangle must add up to 180, thus we can create the following equation to find the measurement of the last angle:

[tex]180-90-43[/tex]

[tex]=47[/tex]

The measure of angle G is 47 degrees. Let me know if you need any clarifications, thanks!

Answer:

<G = 47 degrees

Step-by-step explanation:

For this problem, we need to understand two things.  This tangent on the circle, with a line drawn to the center, forms a right angle at H.  Additionally, the sum of the angles of a triangle is 180.  Now with these two things, let's solve.

<G = 180 - (43 + 90)

<G = 180 - 133

<G = 47 degrees

Hope this helps.

Cheers.

Need help, there are also two more questions to answer after those but I couldn’t put them in the picture, they are semicircle and radius. Thanks

Answers

Answer:

arc KL=minor arc

arc LJK=major arc

Step-by-step explanation:

so minor arc is a arc which is larger than a semicircle .

a major arc is a circle having measure less than radians.

In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown.
Choose True Or False for each statement

Answers

Answer:rut

Step-by-step explanation:

What is the answer now in two minutes

Answers

Answer:

m<R=48.2 to the nearest tenth

Step-by-step explanation:

1. sin(m<T)=2/3

m<T=arcsin(2/3)=41.81 degrees

m<R=180-90-m<T=180-90-41.81=48.19 degrees

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A newspaper advertisement for Cashmere Closet states "This Saturday 9 a.m., 1 Red Cashmere Scarf, worth $299.95 $10.00 First Come First Served." Which of the following statements is false? A. The ad is clear and specific about what was being offered and asked for in exchange. B. The ad lacks intent to constitute an offer. C. The number of people who have the power of acceptance is limited. Gingrich Corporation issued $2,000,000 in bonds on January 1, 2020. The bonds have a coupon rate of 1.5% and pay interest semi-annually on July 1st and January 1st. The bonds have a 10 year term. The market rate at the issue date is 3.9%. What amount of interest expense will be recorded on July 1, 2020 (the first interest payment) The amount of safety time needed to protect a particular path in a project is less than the sum of the safety times required to protect the individual activities making up the path. a. True b. False Which sentence would make the best thesis statement? Giraffes are tall, interesting animals.Flamingos are pink birds that eat with their heads upside down.Although insects are thought of as pests, they perform several vital functions in our ecosystems.The peregrine falcon of North America is the fastest known bird, with diving speeds of over 250 mph. In the search to determine if car 1 is slower to accelerate than car 2, the mean time it takes to accelerate to 30 miles per hour is recorded (Note: a car is slower to accelerate if it takes more time to accelerate). Twenty trials of the acceleration time for each car are recorded, and both populations have normal distributions with known standard deviations. What are the hypotheses used in this test Unscramble the words and phrases to write a sentence. 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What will be the final speed of an electron released from rest at the negative plate? Express your answer to two significant figures and include the appropriate units V=_________