A tree initially measured 2712
feet tall. Over the next 312
years, it grew to a final height of 3512
feet. During those 312
years, what was the average yearly growth rate of the height of the tree?

Answer:

18 units

Step-by-step explanation:

Area = length * width (A = L * w)

So, in order to find the length when given the width and area, you have to divide the area by the width.

432 / 24 = 18

I hope this helps! Have a lovely day!! :)

The Surface region of the cylinder that has a 3 cm radius is 8.4π cm²

The area or region that an object’s surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has. There are numerous shapes and dimensions in geometry, including spheres, cubes, cuboids, cones, cylinders, etc. Each form has its own volume and surface area.

Given, The surface area of a right cylinder with a diameter of 8 cm is 60π cm².

From the general formula for the Surface area of the cylinder

Area = 2πrh + 2πr²

or

Area = 2πr²(h/r + 1)

Where

r = radius of the base

h = height of the Cylinder

in our case

r = 8/2 = 4 cm

Thus,

60π = 2πrh + 2πr²

60π = 2πr²(h/r + 1)

(h/r + 1 ) = 60π/ 2π4²

(h/r + 1) = 15/8

Also given there is another similar Cylinder that has a radius of 1.5 cm or a diameter of 3 cm.

Since it's similar to the First cylinder thus "h/r" would be the same for both of them.

Thus,

The surface area of the second cylinder = 2πr²(h/r + 1)

The surface area of the second cylinder = 2π *  1.5² * 15/8

The surface area of the second cylinder = 8.4π

Therefore, the Surface area of the cylinder that has a 3 cm radius is 8.4π cm².

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Answer:

A. It was decreasing by -138,629.44 barrels

B. 26 years of time

Step-by-step explanation:

Due to the length of this question solution, I was unable to type it. The answer is contained in the attachment.

A. At 1200000

Bt = 1200000

-1/6ln2 x 1200000

Solve this using a calculator

= -138,629.4361

So the amount of oil is decreasing by -138,629.44 barrels

The value of the given equation the value of x : (3 , -10)

Definitions: A quadratic equation is a second-order polynomial equation in some kind of a single variable x ax2+bx+c=0. Because it is a second-order polynomial problem, the fundamental theorem of fundamental algebra guarantees therefore it has at least one solution.

the student haven't solved the equation properly he has not expanded the equation:

According to the given data:

The given equation is f(x) = (x - 3)² - 10

(x - 3)² - 10 = 0

this could be expand and write as:

x² + 9 -6x - 10 = 0

x² -6x -1 = 0

The vertex of an up-down facing parabola of the form y=ax^2+bx+c is Xv.

The parabola params are:

a=1, b=-6, c=-1

\(\:x_v=-\frac{b}{2a}\)

\(x_v=-\frac{(-6)}{2 \cdot 1}\)

Xv = 3

Putting x = 3 to get the value of y

we get:

y = -10

(3 , -10)

The value of the given equation the value of x : (3 , -10)

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We need to find two relations, and use them to find the value of y when z = 15.

We will see that the value of y in that case is 4,860.

We know that y  varies inversely with the square of  x, also y  is also proportional to the cube of  z

Then we can write:

y = k/x^2

y = c*z^3

We also know that:

When x = 3, y = 80.

Replacing that in the first equation to find the value of k:

80 = k/3^2

80 = k/9

80*9 = k = 720

We also know that when x = 2, z = 5

From the first relation we have:

y = 720/2^2 = 720/4 = 180

Now we replace this in the equation of y and z:

y = c*z^3

180 = c*5^3

180 = c*125

180/125 = c = 1.44

Now we need to calculate y when z = 15, then we just need to replace z by 15 in the equation for y and z:

y = 1.44*(15)^3 = 4,860.

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The standard definition of the equation of a parabola is given as follows:

y = ax² + bx + c.

The leading coefficient a determines how wide the parabola is, as lower values of a are associated with a wider parabola.

The equation for this problem is:

y = x².

With a = 1, hence the rules are given as follwos:

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Answer:

62.5inches because if it has to be shorter than 63.5 inches tall it would be 62.5inches tall

Answer:

zach ran 31680 feet over the weekend.

Step-by-step explanation:

1 mile = 5280, so 6 x 5280 = 31680

743₁₆ = 7 • 16² + 4 • 16¹ + 3 • 16⁰

743₁₆ = 1792 + 64 + 3

743₁₆ = 1859

Answer:

2.99 meters

Step-by-step explanation:

Answer:

There's only one solution x = 2

Thr solution x = 1 is an extraneous solution.

Step-by-step explanation:

\( \frac{1}{x - 1} + \frac{2}{x} = \frac{x}{x - 1} \\ \frac{2}{x} = \frac{x}{x - 1} - \frac{1}{x - 1} \\ \frac{2}{x} = \frac{x - 1}{x - 1} \\ \frac{2}{x} = 1 \\ 2 = x\)

Answer:

There is only one solution: x = 2.

The solution x = 1 is an extraneous solution.

Step-by-step explanation:

I hope this helps :)

Answer:

56tt8989899999999×-×554545--455356788:988

Answer:

True

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to show that the point (4, -4) is on the graph of x² +y² = 32, and you want the tangent and normal lines at that point.

The point is on the curve because when x = 4 and y = -4 the resulting statement is 16 +16 = 32, which is a true statement.

The tangent to a circle is most easily found by first considering the normal. The normal line will be the line through the point on the circle and the center of the circle. Here, the center is (0, 0). The slope of the normal line is ...

  m = y/x = -4/4 = -1

The tangent line's slope is the opposite reciprocal of this:

  m = -1/(-1) = 1

The point-slope form of the equation for the tangent line is ...

  y -k = m(x -h) . . . . . equation for line with slope m through point (h, k)

  y -(-4) = 1(x -4) . . . . . equation for line with slope 1 through point (4, -4)

  x -y = 8 . . . . . . . . . . add 4-y to put in standard form

The equation of the tangent line is x - y = 8.

In the section above, we found the slope of the normal line is -1. We also noted that the normal line goes through the point (0, 0). Then the point-slope form of the normal line is ...

  y -0 = -1(x -0)

  y = -x

The equation of the normal line is y = -x.

__

Additional comment

The normal line can also be written as x + y = 0.

The tangent line can also be written as y = x -8.

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Answer:

4/3 or 1 1/3

Step-by-step explanation:

To find slope, we subtract the y-values (9 - 5), then divide the difference we find from that by the difference of the x-values (6 - 3). So, let's go ahead and do that now. First, what's 9 - 5? Well, the answer is 4. Next, we have to divide this value by 6 - 3, which is equivalent to 3. Then, we divide the two numbers - what is 4 ÷ 3? Well, we can represent this as 4/3, or 1 1/3. Hopefully that's helpful - if you have any questions on that, let me know! :)

Answer:

Slope is 4/3

Step-by-step explanation:

Slope or gradient can be found by using several formulas. For this situation, we can use rate of changes between two points also known as rise over run or changes in y over change so in x.

The formula of slope between two points can be expressed as several equations, expressions, etc such as:

\(\displaystyle \large{m=\frac{dy}{dx}=\frac{y_2-y_1}{x_2-x_1} =\frac{\Delta y}{\Delta x}\) where m is a variable representing the slope.

Since we are given two points, we are going to use the y2-y1 over x2-x1 formula.

Let (3,5) be (x1,y1,) and (6,9) be (x2,y2) thus the slope is \(\displaystyle \large{m=\frac{y_2-y_1}{x_2-x_1} =\frac{9-5}{6-3} =\frac{4}{3}\)

Therefore the slope of two points is 4/3.

__________________

Let me know in comment if you have any questions.

Answer:

a) 7.5 meters b) 588.75

Step-by-step explanation:

To calculate the volume you need to multiply the 3 values together so

3x5x0.5 = 7.5

That is the volume

Then you got to multiply that by 78.50 to get the answer for b

78.50x7.5 =588.75

The width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.

What is width in rectangle ?

In a rectangle, the width refers to the measurement of the shorter side of the rectangle, which is perpendicular to its length.

Let x be the width of the blanket in inches. Then the length of the blanket is x + 18 inches.

The area of the blanket is given by:

Area = Length x Width

5760 sq inches = (x + 18) inches * x inches

Expanding the right-hand side and solving for x, we get:

\(x^2 + 18x - 5760 = 0\)

We can solve this quadratic equation using the quadratic formula:

\(x = (-b \pm \sqrt{(b^2 - 4ac)}) / 2a\)

where a = 1, b = 18, and c = -5760. Plugging in these values, we get:

\(x = (-18 \pm \sqrt{(18^2 - 4(1)(-5760))}) / 2(1)\)

\(x = (-18 \pm \sqrt{(18^2 + 23040)}) / 2\)

x ≈ 67.42 or x ≈ -85.42

Since the width cannot be negative, the width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.

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Answer:

43% probability of being moderate

Step-by-step explanation:

Since the formating is a little messed up, I assumed that the first column was liberal, second was moderate, and the third was conservative.

The graph that shows the new position of the rectangle after a translation is; Option C

When it comes to transformation in mathematics, there are different types such as reflection, dilation, rotation, translation.

Now, we are dealing with translation which is defined as a transformation of a shape in a plane that preserves the length, which tells us that the object is transformed without getting its dimensions affected.

In this case, we see the rectangle in the graph and we can conclude that the translation of the rectangle shows the correct translation would be the second option because it shows that the length is preserved without getting its dimensions or shape altered.

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Answer:

cos A=   36/45

        = 0.8

Step-bcoy-step explanation:

1) 1/4+1/2

We need to convert the fractions.

1/4 is fine.

1 x 2=2

2 x 2=4

1/4+2/4=3/4

2) a+a

a can be written as 1a.

1a+1a=2a

I can't see photos and he doesn't know 3 or 4 and i'm confused on 5.

a=?

Hope it helps?

Answer:

2. 2a

3. a^4

4. a^5

5. 1

9. 125

10. 1875

I believe most of these are correct

The value of the quotient is - 27

To determine the quotient, first, we have

(1/2)(-27Divided by 1/3) 2/3

Multiply the numerator and denominator

=

\( \frac{ - 162}{6} \)

Then divide the numerator by the denominator, we get

= - 27

Thus, the value of the quotient is - 27

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Answer: The probability of Dana selecting a hockey card will be a 4/36 or 1/9.

Work:

1.I added all of the cards together.

2.I saw that the number of hockey cards was 4 and divided it by 36 (the total number of cards)

3.Simplified

The different sums are possible are 18.

As, the number of different sums possible is given by the equation:

Number of different sums = n x m

In other words, we multiply the number of outcomes for the first spinner by the number of outcomes for the second spinner to get the total number of unique sums.

So, the different sums are possible

= 2 x 3 x 3

= 18

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Given statement solution is :-

1) Gather your electricity bills from the period before the summer break.

2) Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

3) Research or locate the power consumption information for each appliance.

4) Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

5) After the summer break, collect your electricity bill for the corresponding period.

6) Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

To conduct a comparative study of consecutive electric bills and analyze the impact of a reduction plan, you can follow the steps below:

Examine your electricity bills of pre-summer break:

Gather your electricity bills from the period before the summer break.

Look for details such as total energy consumption (in kilowatt-hours or kWh), billing period, and the cost per unit of electricity.

List the various electrical appliances used in your home:

Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

Find out the power consumption and duration for each device in use:

Research or locate the power consumption information for each appliance.

This information is typically provided on the appliance itself or in the user manual.

Note down the power rating of each device in watts (W) or kilowatts (kW).

Estimate the average duration each device is used daily in hours (e.g., 2 hours for a television, 8 hours for a refrigerator).

Calculate the estimated electricity consumption and cost:

Multiply the power rating (in kW) of each device by its average daily usage (in hours) to find the daily energy consumption (in kWh).

Multiply the daily energy consumption by the number of days in the billing period to get the total energy consumption for that period.

Multiply the total energy consumption by the cost per unit of electricity to calculate the estimated cost for each appliance.

Sum up the estimated costs for all appliances to get the total estimated electricity bill.

Make an energy reduction plan and determine implementation:

Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

Unplugging devices when not in use.

Determine the feasibility of implementing these energy reduction measures in your home.

Re-examine your electricity bill of post-summer break:

After the summer break, collect your electricity bill for the corresponding period.

Calculate the actual energy consumption and cost using the same method as in step 4.

Compare the actual post-summer break bill with the estimated pre-summer break bill.

Note any changes in energy consumption and cost, and analyze the effectiveness of your energy reduction plan.

Document your reduction plan and changes in the bill:

Write a report summarizing your findings and observations.

Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

By following these steps, you can conduct a comparative study of consecutive electric bills, analyze the effectiveness of your energy reduction plan, and track changes in energy consumption and costs.

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Answer:

-Picture attached-

Step-by-step explanation:

The gradient would be 4, with a rising graph and the y-intercept would be 1. I attached a picture of the graph, hope it helps.

Answer:

The average repair cost per saw for the past month is 20.

The bound of error of estimation is ±10.

Step-by-step explanation:

a) Data and Calculations:

Industry        No.of saws   Total repair cost   Average

                                           for past month

1                            3                        50           16.67

2                           7                        110           15.71

3                          11                       230          20.91

4                          9                        140           15.56

5                          2                         60           30

6                         12                       280           23.33

7                         14                       240           17.14

8                          3                         45           15

9                          5                        60           12

10                         9                      230           25.56

11                          8                       140           17.50

12                         6                       130           21.67

13                         3                        70           23.33

14                         2                        50           25

15                         1                          10           10

16                        4                         60           15

17                       12                       280           23.33

18                        6                        150           25

19                        5                         110           22

20                       8                        120           15

Total               130                    2,565           19.73

Average = Sum of the total repair cost for past month divided by the number of saws repaired

= 19.73 (2,565/130)

= 20

The bound on error of estimation = the difference between the upper bound of the interval and the calculated mean

= 30 - 20

= 10

The lower bound = 10

The bound of error is also = (30 -10)/2 = 10

Answer:

10 months

$500

Step-by-step explanation:

Option 1

Option 2

Both options reveal same amount:

Cost of notebook: