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cluponka [151]
3 years ago
11

Lisa is repairing fences on a piece of ranch land. She needs to arrive at point A from point B in the diagram. But the land ther

e is low and sometimes floods. Before she decides to risk it, she wants to know how much distance she’ll save if she goes straight from B to A instead of taking the dry path from B to C to A. Angle BCA is a right angle. AC = BC + 21 feet, and AB = BC + 24 feet. a triangle diagram representing Lisa's path If Lisa travels straight from B to A, she’ll walk feet, which will save her feet compared with traveling the longer, drier path.

Mathematics
2 answers:
mihalych1998 [28]3 years ago
4 0

Answer:

Step-by-step explanation:

In this problem, you need to apply the Pythagorean theorem because you know this is a right triangle. The path from B to C to A is a right angle.

AB^{2}=BC^{2}+AC^{2}

The only unknown is going to be BC, you can arrange again this

BC^{2}=AC^{2} - AB^{2}

and change the values

BC^{2} =(BC + 21feet)^{2} - (BC + 24feet) ^{2}

BC^{2} =(BC^{2} +2*21feet*BC+21^{2}feet) +( BC^{2} +2*24feet*BC +24^{2}feet)

BC^{2}=6BC+476-441\\BC^{2}=6BC+135\\BC^{2}-6BC-135=0

and apply Bhaskara rule

BC=15

Now you can come back and know all the lengths

AC=BC+21feet\\AC=36feet\\AB=BC+24feet\\AB=39feet\\BC=15feet

IgorLugansk [536]3 years ago
3 0
Correction from my spelling,

If she walks from A to C to B*

If you have any question upon my solution, please ask !

Hope this helps you :)

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What is the exact perimeter of kite ? Show your work.
Afina-wow [57]

Answer:

<u>The perimeter of the kite is 29 units.</u>

Step-by-step explanation:

1. Let's use the Pythagorean Theorem to find the perimeter of the kite:

With the information given, we have four right triangles with a new point A, intersecting UW and VX. Those triangles are:

Δ UVA

Δ VWA

Δ UXA

Δ XWA

As we can see in the figure, length of UV and VW is the same and the length of UX and WX is also the same.

2. Let's find the value of UV and VW

UV is the hypotenuse of Δ UVA and it sides are 3 and 4 units length. So, we can calculate the length of UV this way:

Length of UV ² = UA ² + VA ²

Replacing with the real values:

Length of UV ² = 3 ² + 4 ²

Length of UV ² = 9 + 16

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√Length of UV ² = √25

<u>Length of UV  = 5 units ⇒ Length of VW = 5 units</u>

3. Let's find the value of UX and WX

UX is the hypotenuse of Δ UXA and it sides are 3 and 9 units length. So, we can calculate the length of UX this way:

Length of UX ² = UA ² + XA ²

Replacing with the real values:

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Length of UX ² = 9 + 81

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√Length of UV ² = √90

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Perimeter of the kite = UV + VW + WX + UX

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<u>Perimeter of the kite = 29 units</u>

7 0
3 years ago
The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. A) Estimate how lo
VLD [36.1K]

Answer:

A) 63.36 years.

B) 100.42 years.

Step-by-step explanation:

We have been given that the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.

A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.

P(t)=7.1(1.011)^{t}            

7.1 \times 2=7.1(1.011)^{t}  

\frac{7.1 \times 2}{7.1} =(1.011)^{t}

2 =(1.011)^{t}

Now let us solve for t using logarithm.

ln(2) =ln (1.011)^{t}      

ln(2) =t \cdot ln(1.011)

0.6931471805599453 =t \cdot 0.0109399400383344  

t=\frac{0.6931471805599453}{0.0109399400383344}

t=63.3593217267282743049\approx 63.36

Therefore, it will take 63.36 years the population to be double.

B) Now we will find the number of years it will take the population to be triple of its size.

7.1 \times 3=7.1(1.011)^{t}

\frac{7.1 \times 3}{7.1} =(1.011)^{t}  

3 =(1.011)^{t}

Now let us solve for t using logarithm.        

ln(3) =ln (1.011)^{t}

ln(3) =t \cdot ln(1.011)

1.0986122886681097 =t \cdot 0.0109399400383344  

t=\frac{1.0986122886681097}{0.0109399400383344}

t=100.4221490079915311298\approx 100.42

Therefore, it will take 100.42 years the population to triple of its size.


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