the volum of the wood in a tree varries directly as height and the square of length

Answers

Answer 1

Answer:

The volume of wood in a tree varies directly with the height and the square of the length of the tree. This means that if we increase the height of the tree, the volume of wood in the tree will also increase, and if we increase the length of the tree, the volume of wood will increase by the square of that increase.

This relationship can be expressed mathematically as:

V = khl^2

Where V is the volume of wood in the tree, h is the height of the tree, l is the length of the tree, and k is a constant of proportionality.

This relationship is based on the assumption that the cross-sectional area of the tree remains constant, and that the volume of wood in the tree is directly proportional to the height and the square of the length of the tree.

Related Questions

Solve the equation 5 (x + 1) = 5x

Answers

[tex]\textbf{Heya !}[/tex]

✏[tex]\bigstar\textsf{Given:-}[/tex]✏

an equation = [tex]\sf{5(x+1)=5x}[/tex]

✏[tex]\bigstar\textsf{To\quad find:-}[/tex]

x = ?

✏[tex]\bigstar\textsf{Solution \quad steps:-}[/tex] ✏

first use the distributive property

[tex]\sf{\longmapsto{ 5x+5=5x}[/tex]

subtract both sides by 5x

[tex]\sf{\longmapsto{0x+5=0}[/tex] (strange expression right)

[tex]\sf{\longmapsto 0=-5}[/tex] (whattt ?!)

the above statement's false, so the equation has no solutions

`hope that was helpful to u ~

What is
3/2^2 equal to

Answers

Answer: SQUARE ROOT OF 8

Step-by-step explanation: 2^3^1/2 is SQUARE ROOT OF 8. GOD BLESS

- FRIEND TO DINO

The length of the major axis of the ellipse below is 14, and the length of the
red line segment is 3. How long is the blue line segment?

Answers

Answer:

Step-by-step explanation:

The focal length is 14, and thus the sum of the lengths of the blue and red segments is also 14.

In a one tail hypothesis where you only in the lower tail, what is the p-value if

Answers

P-Value becomes 0.8599 when (z < 1.08).

According to the statement

We have given that the Z-stat value is 1.08 and we have to find the P value with the help of Z-stat value.

So,

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

and we know that

The P-Value is calculated by converting your statistic (such as mean / average) into a Z-Score.

So, If the z-stat is 1.08, the p-value for a left-tail test is the probability that (z < 1.08), which is 0.8599.

So, P-Value becomes 0.8599 when (z < 1.08).

Learn more about P-VALUE here https://brainly.com/question/4621112

#SPJ1

The diameter of a pipe is normally distributed, with a mean of 0.8 inch and a variance of 0.0004. What is the probability that the diameter of a randomly selected pipe will exceed 0.84 inch? (You may need to use the standard normal distribution table. Round your answer to three decimal places.) . Hint: take the square root of the variance to find the standard deviation.

Answers

The probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

What is probability?

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

How to determine the probability?

The given parameters are:

Mean = 0.8

Variance = 0.0004

Calculate Standard deviation using

σ = √σ²

This gives

σ = √0.0004

Evaluate

σ = 0.02

Calculate the z-score at x = 0.84 using

z = (x - [tex]\bar x[/tex])/σ

This gives

z = (0.84 - 0.8)/0.02

Evaluate

z = 2

The probability is then represented as:

P(x > 0.84) = P(z > 2)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.84) = 0.977

Hence, the probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

Answers

Answer: 5

Step-by-step explanation:

Because there are 35 when you add yourself so u subtract 30 to get 5

There would be 4 people left in the garden.

34 - 30 = 4.

Subtraction of Numbers

Subtraction is a mathematical operation that involves taking away one number from another to find the difference between them. For the question, At first, there were 34 people in the garden and later 30 people were no longer alive in the garden, so the difference between 30 people and 34 people is 4.

Subtraction is the opposite of addition, and it is used to measure the distance between two values on the number line.

Subtraction is represented by minus Sign (-). For example, subtracting 5 from 10 gives you a difference of 5 (10 - 5 = 5).

Learn more about subtraction of Numbers here

https://brainly.com/question/28467694

#SPJ3

convert this into a standard number
[tex]10^{12}[/tex]

Answers

10^12 in standard number is 1000000000000

How to convert the number?

The number is given as:

[tex]10^{12[/tex]

Expand the expression

[tex]10^{12} = 10 * 10 * 10 * 10 *10 * 10 * 10 * 10*10 * 10 * 10 * 10[/tex]

Evaluate the product

[tex]10^{12} = 1000000000000[/tex]

Hence, 10^12 in standard number is 1000000000000

Answers

The probability that the mean fill is more than 84.8 ounces is 0.39358

How to determine the probability that the mean fill is more than 84.8 ounces?

From the question, the given parameters about the distribution are

Mean value of the set of data = 84.5Standard deviation value of the set of data = 1.1The actual data value = 84.8

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (84.8 - 84.5)/1.1

Evaluate the difference of 84.8 and 84.5

z = 0.3/1.1

Evaluate the quotient of 0.3 and 1.1

z = 0.27

The probability that the mean fill is more than 84.8 ounces is then calculated as:

P(x > 84.8) = P(z > 0.27)

From the z table of probabilities, we have;

P(x > 84.8) = 0.39358

Hence, the probability that the mean fill is more than 84.8 ounces is 0.39358

Answers

Por restricciones de longitud no es posible resumir las respuestas asociadas a esta pregunta, invitamos cordialmente a leer la explicación para mayores detalles sobre el análisis de secciones cónicas.

¿Cómo analizar ecuaciones de secciones cónicas?

Según la geometría analítica, existen cinco tipos de secciones cónicas: (i) Circunferencia, (ii) Parábola, (iii) Elipse, (iv) Hipérbola, (v) Recta. 2) a) La ecuación estándar de la circunferencia se caracteriza con el centro (h, k) y la longitud del radio (r):

(x - h)² + (y - k)² = r²

(x - 2)² + (y + 1)² = 4²

b) La longitud del radio de la circunferencia se obtiene por el teorema de Pitágoras sobre la longitud del segmento CP:

r = √[(4 - 1)² + (6 - 3)²]

r = √(3² + 3²)

r = 3√2

(x - 1)² + (y - 3)² = 18

3) a) El eje focal forma parte del eje de simetría de la parábola. La ecuación estándar de la parábola es:

4 · p · x = y²

Donde p es la distancia entre el foco y el vértice.

Si tenemos que (x, y) = (2, 4), entonces la ecuación de la parábola es:

4 · p · 2 = 4²

p = 2

8 · x = y²

Las coordenadas del foco de la parábola son de la forma (x, y) = (h + p, k):

F(x, y) = (2, 0)

Ahora se determinan los extremos del lado recto: (x = 2)

8 · 2 = y²

y = ± 4

Los extremos del lado recto son (2, 4) y (2, - 4), cuya longitud de segmento es 8 unidades.

b) El eje focal forma parte del eje de simetría de la parábola. La ecuación estándar de la parábola es:

4 · p · x = y²

Si tenemos que (x, y) = (6, 3), entonces la ecuación de la parábola es:

4 · p · 6 = 3²

p = 8 / 3

(32 / 3) · x = y²

Las coordenadas del foco son F(x, y) = (8 / 3, 0).

Ahora se determinan los extremos del lado recto: (x = 6)

(32 / 3) · 6 = y²

y = ± 8

Los extremos del lado recto son (6, 8) y (- 6, - 8), cuya longitud de segmento es 16 unidades.

4) a) Tenemos una ecuación estándar de la forma 4 · p · y = x². A continuación, hallamos todas las variables requeridas:

x² = 8 · y

p = 2

Directriz: y = - 2, Foco: F(x, y) = (0, 2), Longitud del lado recto: 4

b) Tenemos una ecuación estándar de la forma 4 · p · x = y². A continuación, hallamos todas las variables requeridas:

y² = - (3 / 2) · x

p = - 3 / 8

Directriz: x = 3 / 2, Foco: F(x, y) = (- 3 / 2, 0), Longitud del lado recto: 3.

5) En esta parte debemos manipular algebraicamente las ecuaciones hasta su forma estándar para determinar los datos requeridos de cada caso. La ecuación estándar de la elipse tiene el siguiente problema:

(x - h)² / a² + (y - k)² / b² = 1

Donde:

(h, k) - Centro de la elipse.a, b - Longitudes de los semiejes.

a) 81 · x² + 144 · y² = 11664

x² / 144 + y² / 81 = 1

x² / 12² + y² / 9² = 1

Longitud del semieje mayor: 12

Longitud del semieje menor: 9

c = √(12² - 9²)

c ≈ 7.937

Coordenadas de los focos: F₁ (x, y) = (- 7.937, 0), F₂ (x, y) = (7.937, 0)

Vértices: V₁ (x, y) = (- 12, 0), V₂ (x, y) = (12, 0)

Longitud del lado recto

144 · y² = 11664 - 81 · x²

y² = (11664 - 81 · x²) / 144

y = ± (1 / 12) · √(11664 - 81 · x²)

y = ± (1 / 12) · √(11664 - 81 · 7.937²)

y = ± 6.750

La longitud del lado recto es 13.5.

b) 36 · x² + 25 · y² = 3600

x² / 10² + y² / 12² = 1

Longitud del semieje mayor: 12

Longitud del semieje menor: 10

c = √(12² - 10²)

c ≈ 6.633

Coordenadas de los focos: F₁ (x, y) = (0, - 6.637), F₂ (x, y) = (0, 6.637)

Vértices: V₁ (x, y) = (0, - 12), V₂ (x, y) = (0, 12)

Longitud del lado recto

36 · x² = 3600 - 25 · y²

x² = 100 - (25 / 36) · y²

x = √[100 - (25 / 36) · y²]

x = √[100 - (25 / 36) · 6.637²]

x = ± 8.331

La longitud del lado recto es 16.662.

Para aprender más sobre secciones cónicas: https://brainly.com/question/16156916

#SPJ1

Aperson invest 10,000 shillings for 40 months compounded monthly. Find the accumulated amount If the rate is 5% per annum.

Answers

monthly interest rate is : [tex]\sqrt[12]{1.05}[/tex]

So in forty month there will be : 10 000 * ( [tex]\sqrt[12]{1.05}[/tex] )^40 ≈11 776,06

What are the solutions of the equation 9x4 - 2x2 - 7 = 0? Use u substitution to solve.

Answers

9x^4 - 2x^2 - 7 = 0
(x + 1)(x - 1)(9x^2 + 7) = 0
Therefore, x = -1 , OR x = 1.

9x^2 + 7 has no real solutions.

Hope it helps : )

What are the domain and range of g(x)=√x+4?
OD: [4, ∞) and R: [0, ∞)
OD: (-4, ∞) and R: (-∞, 0)
OD: [-4, ) and R: [0, ∞)
OD: (4,) and R: (-∞, 0)

Answers

Answer:

Domain [-4 , +∞)

Range [0 , +∞)

Step-by-step explanation:

the function g such that g(x)=√(x+4) ,is defined

for the values of x that verify :

x + 4 ≥ 0

⇔ x ≥ -4

Then

The domain of g is [-4 , +∞)

………………………………………………

Let x ∈ [-4 , +∞)

then x ≥ -4

then x + 4 ≥ 0

then g(x) = √(x+4) ≥ 0

Therefore, we can affirm that the range of g is [0 , +∞)

Fill in the missing term in the pair of equivalent ratios. *
5:30 15:
Your answer
The state low temperatures for five states are as follows: -42

Answers

I’m sure the missing term is 90

On a piece of graph paper, plot the following points: A (3, 1), B (1, 5), C (9, 9), and D (11, 5). These coordinates will be the vertices of a quadrilateral. How would you use the distance formula and the slope formula to prove that this figure is actually a rectangle?

Answers

The given coordinates are actually a rectangle

How to determine the quadrilateral type?

The coordinates are given as:

A (3, 1), B (1, 5), C (9, 9), and D (11, 5).

Calculate the distance between the coordinates using:

[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(3 -1)^2 +(1-5)^2} =\sqrt {20[/tex]

[tex]BC = \sqrt{(1 -9)^2 +(5-9)^2} =\sqrt {80[/tex]

[tex]CD = \sqrt{(9 -11)^2 +(9-5)^2} =\sqrt {20[/tex]

[tex]DA = \sqrt{(11 -3)^2 +(5-1)^2} =\sqrt {80[/tex]

The above shows that the opposite sides are congruent

Next, we calculate the slopes using:

m = (y2- y1)/(x2- x1)

So, we have:

AB = (1- 5)/(3-1) = -2

BC = (5- 9)/(1-9) = 1/2

CD = (9- 5)/(9-11) = -2

DA = (5- 1)/(11-3) = 1/2

The slopes of adjacent sides are opposite reciprocals.

This means that the sides are perpendicular

Hence, the given coordinates are actually a rectangle

Answers

An appropriate numerical summary is descriptive statistics.

What is a numerical summary?

It should be noted that a numerical summary means a number used to describe specific characteristics of a data set.

In this case, descriptive statistics can be used. This is used to describe the data set.

Learn more about numerical summary on:

brainly.com/question/13846750

#SPJ1

which integer is closest to the third root of -23

Answers

Answer:

The number 23 is prime. Therefore, the cube root of 23 = ∛23 = 2.8439.

Step-by-step explanation:

Express v=
(2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0)

Answers

The expression of v = (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0) is [tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]

Linear Combinations

To express v= (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0), it will be written as:

[tex](2,1,5)=x(1,2,1)+y(1,0,2)+z(1,1,0)[/tex]

This will yield the following equations:

x + y + z = 2........(1)

2x + z = 1..........(2)

x + 2y = 5........(3)

The solution to the system of equations above is:

x = 1, y = 2, z = -1

Therefore, the linear combination is:

[tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]

Learn more on linear combinations here:https://brainly.com/question/17407318

#SPJ1

;
Use the expression in the accompanying discussion of sample size to find the size of each sample if you want to estimate the
difference between proportions of men and women who own smartphones. Assume that you want 99% confidence that your
error is no more than 0.035.
Click the icon to view the discussion of sample size.
The sample should include men and
(Type whole numbers.)
women.

Answers

The sample should include 2702 men and 2702 women.

Given that you want to be 99% sure your error doesn't exceed 0.035.

A sample is a group of people selected from a larger population to provide data to researchers. The number of members of the population included in the sample is called the sample size.

The significance level is the probability that the test statistic is in the critical range if the null hypothesis is actually true. The confidence interval is 99% or 0.99.

The level of significance α = 1-0.99 = 0.01

the margin of error, ME = 0.035

The Z-critical value at the 99% confidence level or at the significance level of 0.01 is 2.575 (from standard normal tables).

We will now use the formula:[tex]n=\frac{Z^2_{critical}}{2(ME)^2}[/tex].

Substitute the values in the above formula, we get

n = (2.575) ² / (2 × (0.035) ²)

n = 6.630625 / (2 × 0.001225)

n = 6.630625 / 0.00245

n = 2701.966

Therefore, the sample should include 2702 males and 2702 females with a 99% certainty that the error does not exceed 0.035

Learn more about significance level from here brainly.com/question/4599596

#SPJ1

If sin(theta)=0.7 what is tan(theta)?

Answers

The value of tan theta from the given. expression is 7/√51

Trigonometry identity

Trigonometry identity are expressions written in terms of sine, cosine and tangents.

Given the following trigonometry values as shown:

sin(theta)=0.7

Convert the decimal to fractions

sin(theta)= 7/10

According to SOH CAH TOA;

sin theta = opp/hyp

Determine the adjacent

adj = √hyp²-opp²

Substitute the values;

adj = √10²-7²

adj = √100-49

adj = √51

Determine the value of tan theta

tan(theta) = opp/adj

Substitute

tan(theta) = 7/√51

Hence the value of tan theta from the given. expression is 7/√51

Learn more on trig identity here: https://brainly.com/question/20094605

#SPJ1

Money savers bank offers a savings account that earns 6% interest compounded continuously. If Manuel deposits $2200, how much will he have in the account after three years?

Answers

Answer:

2633.88

Step-by-step explanation:

Pe^rt

2200*e^.06*3

Sarah had three times as many quarters as nickels. She had $3.20 in all. How many quarters did she have?

A. 12
B. 15
C. 4

Answers

Answer:

A. 12

Step-by-step explanation:

If she had 12 quarters, then she would have to have 4 nickels according to the problem.

12 * .25 = $3 (money in quarters)

4 * .05 = $.2 ( money in nickels)

Adding those 2 together, we get $3.2.

She have 12 quarters

what is unitary method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

There are two situation in Unitary method:

There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

If she had 12 quarters, then

12 * .25 = $3 ( quarters)

4 * .05 = $.2 ( in nickels)

Hence, she have 12 quarters.

Learn more about unitary method here:

https://brainly.com/question/22056199

#SPJ2

During an unusual storm, the temperature fell 8° C, rose 5° C, fell 4° C,
and then rose 6° C. If the temperature was 32° C at the outset of the storm,
what was it after the storm was over?

Answers

{[(32-8)+5]-4}+6= 21 after the storm was over =31 C

solve (6b^2+5)+(8b-20)

Answers

The sum of the given expression is 6b^2+8b-15

Sum of expression

Given the following expression

(6b^2+5)+(8b-20)

We are to take the sum. On expansion;

6b^2+5 + 8b-20

Collect the like terms

6b^2+8b +5 - 20

6b^2+8b-15

Hence the sum of the given expression is 6b^2+8b-15

Learn more on sum of expression here: https://brainly.com/question/723406

#SPJ1

Find the area of the triangle
A
47°
b
32 ft
C
19 ft

Answers

Answer:

222 [ft²].

Step-by-step explanation:

1. the required area can be calculated according to the formula:

A=0.5*b*c*sin(A);

2. after substitution of b=32; c=19 and sin(A)≈0.7313537:

A=0.5*32*19*0.7313537=222.3315248 [ft²].

The answer is A ……………

Carlos spent 1\dfrac141
4
1

1, start fraction, 1, divided by, 4, end fraction hours doing his math homework. He spent 1\dfrac141
4
1

1, start fraction, 1, divided by, 4, end fraction as much time practicing piano.
How many hours did Carlos spend practicing piano?

write as a fraction

Answers

The time Carlos spend practicing his multiplication facts in fraction is 5/16 hours.

Fraction

A fraction is a value which has a numerator (upper or top value) divided by a denominator (lower or bottom value).

Time Carlos spent doing his math homework = 1 1/4 hours

Time spent practicing his multiplication facts = 1/4 of 1 1/4 hours

= 1/4 × 1 1/4

= 1/4 × 5/4

= (1 × 5) / (4 × 4)

= 5/16 hours

Therefore, the time Carlos spend practicing his multiplication facts is 5/16 hours.

Complete question:

Carlos spent 1 1/4 hours doing his math home work. He spent 1/4 of this time practicing his multiplication facts.

How many hours did Carlos spend practicing his multiplication facts?

Learn more about fraction:

https://brainly.com/question/11562149

#SPJ1

What is the area of a poster that is 1 1/2 feet by 2 1/2 feet?

Answers

The area of the poster is 28.75 feet square.

How to determine the area

Note that the area of a rectangle is given as;

Area = length × width

Length = 11. 5 feet

Width = 2. 5 feet

Area = 11. 5 × 2. 5

Area = 28. 75 feet square

Thus, the area of the poster is 28.75 feet square.

Learn more about area of a rectangle here:

https://brainly.com/question/14137384

#SPJ1

F(x) = | sin 3x | -3 find the maximum and minimum value

Answers

Answer:

-2 and -3

Step-by-step explanation:

The minimum of |sin 3x| is 0 and the max is 1 (since the sine function ranges from -1 to 1)

Therefore, the maximum is 1 - 3 = -2 and the minimum is 0 - 3 = -3.

How much will you have saved after 6 years by contributing $1,200 at the end of each year if you expect to earn 11% on the investment?

Answers

Savings after 6 years would be $ 1992.

What are savings?

Savings is the money that remains after expenses and other commitments have been subtracted from income.

Savings are the sum of money that would otherwise be lying about, not being risked on investments or used for consumption.

Savings and investing can be compared because the latter includes putting money at risk in an effort to try to increase wealth.

Indicators of household debt or a negative net worth include negative savings.

According to the question,

Amount contributed(P)= $1200

Rate(R)= 11%

Time(T)= 6 years

Interest(SI)=P*R*T/100

= 1200*11*6/100

= 792

Savings after 6 years = P+ SI

= 1200 + 792

= $ 1992

Learn more about savings here:

https://brainly.com/question/738615

#SPJ1

What type of motion transforms the letter “p” into a “b”?

Answers

The type of motion which transforms the letter “p” into a “b” is; Reflection.

What type of motion transforms the letter “p” into a “b”?

It follows that the task content demands that the type of motion which maps p to b be identified. On this note, it follows that the type of motion in discuss is Reflection. More particularly, a reflection over the horizontal axis most definitely causes this transformation.

Therefore, the motion which transforms the letter “p” into a “b” is; Reflection.

Answers

The probability of winning this game is 0.003

How to solve for the probability of winning

Let us name p to be the probability of winning the game.

We have the expected value to be 100

100 = probability of winning + 1-p x loss

win = 100000 - 200

We then input in the formula

100 = p*99800 +(1-p) x -200

100 = 99800p - 200 + 200p

Collect like terms

100 + 200 = 99800 + 200p

300 = 100000p

Divide through by 100000

This give the

Probability of winning = 0.003

The probability of winning the game is very low hence I would not play.

The factors that would influence the decision are:

The cost of playingThe expected value

Complete question

A game has an expected value to you of ?$100. It costs ?$200 to? play, but if you win you receive? $100,000 (including your ?$200 ?bet), for a net gain of ?$99,800. What is the probability of? winning