A tree that is 10 feet tall casts a 20 foot shadow. What is the length of the shadow of a nearby 30 foot tall tree

Answer:

$69.21

Step-by-step explanation:

Since the box has a square base the length and breadth of the box will be equal. Let it be [tex]x[/tex]

Let h be the height of the box

V = Volume of the box = [tex]620\ \text{cm}^3[/tex]

[tex]x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}[/tex]

Now surface area of the box with an open top is given

[tex]s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}[/tex]

Differentiating with respect to x we get

[tex]\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}[/tex]

Equating with zero

[tex]0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74[/tex]

Double derivative of the function

[tex]\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0[/tex]

So, x at 10.74 is the minimum value of the function.

[tex]h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37[/tex]

So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.

The total area of the sides is [tex]4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2[/tex]

The area of the base is [tex]x^2=10.74^2=115.35\ \text{cm}^2[/tex]

Cost of the base is $0.40 per square cm

Cost of the side is  $0.10 per square cm

Minimum cost would be

[tex]230.7\times 0.1+0.4\times 115.34=\$69.21[/tex]

The minimum cost of the box is 69.21 dollars.

Answer:

Unitary cost (per pound)= $0.682

Step-by-step explanation:

Giving the following information:

Total cost= $3.75

Total pounds= 5.5 pounds

To calculate the unitary cost of each pound, we need to use the following formula:

Unitary cost= total cost / total pounds

Unitary cost per pound= 3.75 / 5.5

Unitary cost per pound= $0.682

Answer:

quadratial

Step-by-step explanation:

Answer:

= -56.22

Step-by-step explanation:

have a great day

pls mark as brainliest!

hope this helped!

Answer:

-56.22

just calculated it (:

Answer:

Step-by-step explanation:

x^2 +12x-28=0

x^2+(14-2)x-28=0

x^2+14x-2x-28=0

X(X+14)-2(X+14)=0

(X+14)(X-2) is the factor of this quadratic equation.

417

Step-by-step explanation:

I hope this helps :)

Answer:

1,232 ft/min (feet per minute)

Step-by-step explanation:

14 miles = 73,920 feet

1 hour = 60 minutes

73, 920 / 60 = 1,232 feet/minute

Answer:

6/53

Step-by-step explanation:

Answer: x=60

Step-by-step explanation:

x+22+x+6+x−28=180

Step 1: Simplify both sides of the equation.

x+22+x+6+x−28=180

x+22+x+6+x+−28=180

(x+x+x)+(22+6+−28)=180(Combine Like Terms)  22+6=28 and then 28-28=0

3x=180  

3x=180

Step 2: Divide both sides by 3.

3x/3 = 180/3

x=60

hope this was helpful.

Answer:

Between 2.25 and 2.5

Step-by-step explanation:

The square root of 6 is 2.4494.... which is closer to 2.5

Answer:

10

Step-by-step explanation:

you do the one plus the nine which gives you 11 then subtract 2 which gets you 9 then add 4 which gets you 13 then minus 3 which gets you 10.

Answer:

x=11, y=1 or (11, 1)

Step-by-step explanation:

I used substitution to solve this. Basically wherever there's an x, I would fill it in as 12-y.

2(12-y)+3y=29

24+2y+3y=29

24+5y=29

subtract 24 from both sides

5y=5

divide by 5

y=1

Now substitute y back in to get x.

x=12-1

x=11

You can also graph this into desmos, and wherever they intercept, that's your answer.  I hope this helps!

Answer:

13. 1/4x

14. -2/4x or -1/2x

15 1/3x or 2/6x

16. Zero

Step-by-step explanation:

13. goes up once and goes to the side 4 times

14. goes down twice and goes to the side 4 times

15. goes up one time and three to the side

16. zero slope, the line is horizontal

Answer:

13. 1/4

14. -1/2

15 1/3

16. Zero

Step-by-step explanation:

Answer:

The density is 8.5 g/cm³

Step-by-step explanation:

The density formula is density = mass/volume

When we plug our numbers into the formula, we get:

Density = 2210 / 260

We can then solve and get our answer 8.5 g/cm³

It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 . The density is 8.5 g/cm³.

Suppose that a finite amount of substance is there having its properties as:

The mass of substance = m kg

The density of substance = d kg/m³

The volume of that substance = v m³

Then, they are related as:

[tex]d = \dfrac{m}{v}[/tex]

It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 .

density = mass/volume

When we substitute our numbers into the formula, we get:

Density = 2210 / 260

Density = 8.5 g/cm³

It is given a piece of metal has a mass of 2210g the volume of the metal is 260cm ^3 . The density is 8.5 g/cm³

Learn more about mass, volume and density relation here:

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Answer:

23

Step-by-step explanation:

cuz it starts with 13 as a1

Answer:

The number is 2

Step-by-step explanation:

To attempt this question, we need to represent the number with (x).

Let the number be x

Five more than the number is:

5 + x

Seven-halves means 1/2 × 7 = 7/2

Mathematically, the question is saying:

5 + x = 7/2 × x

5 + x = 7x/2

Cross multiply;

2(5 + x) = 7x

10 + 2x = 7x

We collect like terms;

10 = 7x - 2x

10 = 5x

x = 10/5

x = 2

The number represented by x is 2

We want to convert the given sentence into an equation, and then solve it. We will see that the number is 2.

We start with the sentence:

"Five more than a number is equal to seven-halves of the number"

if we define x as the number, we can write:

5 + x = (7/2)*x

Now we can solve this equation for x, we will get:

5 + x = (7/2)*x

5 = (7/2)*x - x = (7/2 - 1)*x

5 = (7/2 - 2/2)*x = (5/2)*x

(2/5)*5 = x

2 = x

So the number is 2.

If you want to learn more about linear equations, you can read:

https://brainly.com/question/4074386

Answer:

45 Degrees

Step-by-step explanation:

Compare to its other side

Answer:

12m by 3m

Step-by-step explanation:

lol please mark brainliest

Answer:

no puedo alludar te perdón

Answer:

$1

Step-by-step explanation:

i hope i read it right

Answer:

1

Step-by-step explanation:

cuz half of 2 is 1

Answer:

Being proportional between two entities, refers to the 'Constant of Proportionality' that would be fixed between them which establishes a relationship between them when multiplied or divided.

If we considered it on a graph, the 'Constant Of Proportionality' may take any real values between the coordinate pairs x and y [x,y]. As even 0 is a real number, it will surely be a constant of proportionality when multiplied since its product would result in itself (0). Hence, both x and y turns 0.

As the coordinates of the origin are always (0,0), the graph  (Or the slope) would surely pass through the origin.

Example :

If we consider a graph such that x=y.

And if we multiply or divide any real number (a) between them.

ax=ay

As a is a variable, and can take the value of 0, the graph can pass through the origin as x and y nullify becoming the coordinates of the origin.

Answer:

Step-by-step explanation:

The domain would only include positive integers.

Answer: Blue, orange, purple and red

Step-by-step explanation:

Answer:

The blue, pink, orange, purple, and red.

Answer: The answer would be -5w-1

Step-by-step explanation:

Answer:

xcgvb                     vgjbnnnnnnnnnn vbjn bvh

Step-by-step explanation:

Answer:

A) 7 and 8

Step-by-step explanation:

root of 7 is 2.64575..... then when u multiply by 3

3*2.64575=7.93725

Answer:

[tex]m=\frac{-14}{11}[/tex]

General Formula and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Point (9, -5)

Point (-2, 9)

Step 2: Find slope m

Since S is closed, you can use the divergence theorem, which says

[tex]\displaystyle\iint_S \vec F(x,y,z) \cdot \mathrm d\vec S=\iiint_R \mathrm{div}\vec F(x,y,z)\,\mathrm dV[/tex]

where R is the interior of the surface S.

We have

div F (x, y, z) = ∂/∂x (0) + ∂/∂y (y) + ∂/∂z (-z) = 1 - 1 = 0

so the flux would be 0.

In this exercise we have to calculate the flux by the divergent theorem:

The flux would be ZERO

Since S is closed, you can use the divergence theorem, which says:

[tex]\int\limits\int\limits_s {F(x,y,z} \, ds= \int\limits \int\limits\int\limits_R {divF(x, y, z)} \, dv[/tex]

where R is the interior of the surface S. We have:

[tex]\nabla F (x, y, z) = 1-1= 0[/tex]

so the flux would be ZERO.

See more about vectorial calculus at : brainly.com/question/6960786

Answer:

(x, y) Right-arrow (x – 3, y + 4)

(the top one)

applying the appropriate transactional rule When the coordinates are added to or subtracted from, the values of x and y change.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given four transformations of coordinates (x, y)

Mathematical transformations describe how 2D figures move around a plane or coordinate system.

thus for (x, y ) => (x - 3), (y + 4)

From the given rule:

x is decreased by 3 and y is increased by 4 or in other words, we can say the graph moves downward by 3 units and to the right by 4 unit

for (x, y ) => (x + 3), (y - 4)

From the given rule:

x is increased by 3 and y is decreased by 4 or in other words, we can say the graph moves upward by 3 units and to the left by 4 units.

for (x, y ) => (x + 4), (y - 3)

From the given rule:

x is increased by 4 and y is decreased by 3 or in other words, we can say the graph moves upward by 4 units and to the left by 3 units.

Therefore, using the correct rule of the transaction The value of x and y will increase or decrease by adding or subtracting from the coordinates.

Learn more about coordinates here:

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Answer:

3x = 0

Step-by-step explanation:

Given,

y = 10

now,

5x+2y = 20

or, 5x+2×10=20

or, 5x = 20-20

or, 5x = 0

or, x = 0/5

or, x = 0

Again,

3x = 3×0 =0