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tiny-mole [99]
3 years ago
14

The area of the Mojave desert is 25000 square miles a sqale drawing of the desert has an area of 10suare inches. What is the sca

le of the map
Mathematics
1 answer:
Tpy6a [65]3 years ago
5 0

Answer:

1 in : 50 mi . . . or . . . 1 : 3,168,000

Step-by-step explanation:

Dividing the areas by 10, you get 1 square inch corresponding to 2500 square miles. Those areas are equivalent to 1 inch square and 50 miles square. Hence the scale factor is 1 inch : 50 miles.

Sometimes map scales are expressed as a dimensionless ratio. The number of inches in 50 miles is

... (50 mi)×(5280 ft/mi)×(12 in/ft) = 3,168,000 in

so, the map scale can be expressed as 1 : 3,168,000.

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Giovanni justifies whether the expression –4x – 8 is equivalent to Negative 2 (x + 1) minus 2 (x + 3) by letting x = 3 in both e
Vladimir [108]

Answer:

When x = 3, the solutions to the expressions are–20 and –20

Step-by-step explanation:

–4(3) – 8   Multiply

-12 - 8       Subtract

-20

-2(3 + 1) - 2(3 + 3)     Simplify in the parentheses

-2(4) - 2(6)                 Multiply

-8 - 12                        Subtract

-20

               

6 0
3 years ago
Read 2 more answers
An object is heated to 100°. It is left to cool in a room that
stepladder [879]

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling for this one.  It involves natural logs and being able to solve equations that require natural logs.  The formula is as follows:

T(t)=T_{1}+(T_{0}-T_{1})e^{kt} where

T(t) is the temp at time t

T₁ is the enviornmental temp

T₀ is the initial temp

k is the cooling constant which is different for everything, and

t is the time (here, it's in minutes)

If we are looking first for the temp after 20 minutes, we have to solve for the k value.  That's what we will do first, given the info that we have:

T(t) = 80

T₁ = 30

T₀ = 100

t = 5

k = ?

Filling in to solve for k:

80=30+(100-30)e^{5k} which simplifies to

50=70e^{5k} Divide both sides by 70 to get

\frac{50}{70}=e^{5k} and take the natural log of both sides:

ln(\frac{5}{7})=ln(e^{5k})

Since you're learning logs, I'm assuming that you know that a natural log and Euler's number, e, "undo" each other (just like taking the square root of something squared).  That gives us:

-.3364722366=5k

Divide both sides by 5 to get that

k = -.0672944473

Now that we have a value for k, we can sub that in to solve for T(20):

T(20)=30+(100-30)e^{-.0672944473(20)} which simplifies to

T(20)=30+70e^{-1.345888946}

On your calculator, raise e to that power and multiply that number by 70:

T(20)= 30 + 70(.260308205) and

T(20) = 30 + 18.22157435 so

T(20) = 48.2°

Now we can use that k value to find out when (time) the temp of the object cools to 35°:

T(t) = 35

T₁ = 30

T₀ = 100

k = -.0672944473

t = ?

35=30+100-30)e^{-.0672944473t} which simplifies to

5=70e^{-.0672944473t}

Now divide both sides by 70 and take the natural log of both sides:

ln(\frac{5}{70})=ln(e^{-.0672944473t}) which simplifies to

-2.63905733 = -.0672944473t

Divide to get

t = 39.2 minutes

3 0
3 years ago
Describe how to transform the graph of f(x) = x2 to obtain the graph of the related function g(x).
olga55 [171]

9514 1404 393

Answer:

  1. left 1 unit
  2. down 2 units

Step-by-step explanation:

The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.

1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)

__

2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)

6 0
3 years ago
Which ratio is smaller 8 to 2 or 10 to 1
GalinKa [24]

Simplify the ratio 8 to 2 to be 4 to 1

Now compare 4 to 1 and 10 to 1

4 is smaller than 10 so the ratio 8 to 2 is smaller.

5 0
3 years ago
If a tree 41.8 feet tall casts a shadow that is 27 feet long, find the height of a tree casting a shadow that is 18.3 feet long
Neko [114]

Answer:

28.3 feet

Step-by-step explanation:

Given a tree 41.8 feet tall casts a shadow that is 27 feet long

So the Tangent of the angle of the sahdow remains the same for the both trees.

We know that  Tanx=\frac{height of the tree}{length of the shadow}

\frac{height of the tree1}{length of the shadow1} = \frac{height of the tree2}{length of the shadow2}

\frac{41.8}{27} =\frac{x}{18.3}

x=\frac{41.8}{27}\times18.3 =28.3

Therefore the height of the tree is 28.3 feet

6 0
3 years ago
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