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laiz [17]
1 year ago
10

A building is 5 feet tall. the base of the ladder is 8 feet from the building. how tall must a ladder be to reach the top of the

building? explain your reasoning.show your work. round to the nearest tenth if necessary.
Mathematics
1 answer:
iris [78.8K]1 year ago
5 0

The ladder must be 9.4 ft to reach the top of the building

Here, we want to get the length of the ladder that will reach the top of the building

Firstly, we need a diagrammatic representation

We have this as;

As we can see, we have a right triangle with the hypotenuse being the length of the ladder

We simply will make use of Pythagoras' theorem which states that the square of the hypotenuse is equal to the sum of the squares of the two other sides

Thus, we have;

\begin{gathered} x^2=5^2+8^2 \\ x^2=\text{ 25 + 64} \\ x^2\text{ = 89} \\ x=\text{ }\sqrt[]{89} \\ x\text{ = 9.4 ft} \end{gathered}

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Rewrite the Cartesian equation y=-3 as a polar equation.
andreev551 [17]

r

sin

θ

=

−

3

Explanation:

Imagine we have a point  

P

with Rectangular (also called Cartesian) coordinates  

(

x

,

y

)

and Polar coordinates  

(

r

,

θ

)

.

The following diagram will help us visualise the situation better:

https://keisan.casio.com/exec/system/1223526375

https://keisan.casio.com/exec/system/1223526375

We can see that a right triangle is formed with sides  

x

,  

y

and  

r

, as well as an angle  

θ

.

We have to find the relation between the Cartesian and Polar coordinates, respectively.

By Pythagora's theorem, we get the result

r

2

=

x

2

+

y

2

The only properties we can say about  

θ

are its trigonometric functions:

sin

θ

=

y

/

r

⇒

y

=

r

sin

θ

cos

θ

=

x

/

r

⇒

x

=

r

cos

θ

So we have the following relations:

⎧

⎪

⎨

⎪

⎩

r

2

=

x

2

+

y

2

y

=

r

sin

θ

x

=

r

cos

θ

Now, we can see that saying  

y

=

−

3

in the Rectangular system is equivalent to say

r

sin

θ

=

−

3

Answer link

Jim G.

May 19, 2018

r

=

−

3

sin

θ

Explanation:

to convert from  

cartesian to polar

∙

x

x

=

r

cos

θ

and  

y

=

r

sin

θ

⇒

r

sin

θ

=

−

3

⇒

r

=

−

3

sin

θ

4 0
3 years ago
Val is going to plant n vegetables seeds in one garden and 2n+5 vegetables seeds in another. How many seeds is Val going to plan
mezya [45]
Val will plant:
2n+5+n
seeds. 

This is equal to:
3n+5

So, in total, Val will plant 3n + 5 seeds.
8 0
3 years ago
PLEASE PLEASE PLEASE PLEASE (5'1, 5'2, 5'3, 5'4, 5'5, 5'6, 5'7, 5'8, 5'9, 5'9, 5'10, 5'11, 5'12)
Yakvenalex [24]

Answer:5

5 feet 7 inches

Step-by-step explanation:

first add all of the given together and then divide what you get by the number of terms given

(5'2+5'3+5'4+ 5'5+5'6+ 5'7+ 5'8+5'9+5'9,+5'10+5'11+5'12)/12 = 5'7 11/64 inches

then divide 11 by 64 on a calculator and then round the decimal you get to the nearest tenth which gives you the answer 5 feet 7 inches.

4 0
2 years ago
90 hazelnuts have a mass of 125 g. Hazelnuts have 630 calories per 100 g. work out the number of calories per hazelnut
jenyasd209 [6]

90 hazelnuts = 125g

Therefore, the mass of one hazelnut is this...

90 / 90 = 125 / 90

1 hazelnut = 25/18 grams


630 calories = 100 grams

100 divided by 25/18 = 72

Therefore...

630 / 72 = 1 hazelnut

AND THE ANSWER IS

8.75 calories = 1 hazelnut

8 0
3 years ago
Read 2 more answers
Match wash hypotenuse length with the leg lengths that will create a right triangle
Ugo [173]
Hope this can help you

5 0
3 years ago
Read 2 more answers
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