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Anton [14]
2 years ago
7

a 12-ft ladder leans against a building so that the angle between the ground and the ladder is 74°. how high does the ladder rea

ch on the building? (round your answer to the nearest foot.)
Mathematics
1 answer:
WINSTONCH [101]2 years ago
8 0

Answer:

12 feet

Step-by-step explanation:

Sometimes, a simple drawing is a great way to start! In the attached drawing, the red line represents the ladder, the brown represents the ground, and the black represents the building!

We want to find the side of the triangle from where the ladder meets the building to where the building meets the ground. This can be found using trigonometric identities, namely sine:

sin\theta=\frac{opposite}{hypotenuse}

Plug in known values:

sin(74^o)=\frac{x}{12}

Rearrange to isolate the variable:

x=12sin(74^o)

Simplify!

x=11.535140... ft

Round to the nearest foot:

x=12ft

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Answer:

It shows for each gallon consumed, we multiply by 30 to get the amount of miles

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Step-by-step explanation:

10 gallons and 300 miles are related in such a way that you divide the number if miles by number of gallons.

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It shows for each gallon consumed, we multiply by 30 to get the amount of Miles.

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3 years ago
The half-life of Radium-226 is 1590 years. If a sample contains 200 mg, how many mg will remain after 1000 years?
adell [148]

Answer: 129.33 g

Step-by-step explanation:

$$Let $p=A \cdot e^{n t}$ \\$(p=$ present amount, $A=$ initial amount, $n=$ decay rate, $t=$ time)

\begin{aligned}&\Rightarrow \text { Given } p=\frac{A}{2} \ a t  \ t=1590 \\&\Rightarrow \frac{1}{2}=e^{1590n} \Rightarrow n=\frac{\ln (1 / 2)}{1590}=-0.00043594162\end{aligned}

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2 years ago
Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Li
vladimir2022 [97]
As the question states, let r be the number of hours worked at the restaurant, and y be the number of hours of yard work. 
We know that she can only work a maximum of 15 hours per work total, and that at she must work at least 5 hours in the restaurant. 
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r + y ≤ 15
r ≥ 5
We also know that she wants to earn at least 120 dollars, earning $8/hr in the restaurant and $12/hr in the yard:
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What is the maximum of hours Lia can work in the restaurant and still make at leas 120 hours? 
Lia's parents won't let her work more than 15 hours, so we know that the answer won't be higher than 15.
If she worked all 15 hours in the restaurant, she would make 8*15 = 120.
The maximum number of hours she can work in the restaurant is therefore 15 hours

What is the maximum amount of money Lia can earn in a week? 
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2 interrogative

3 verb

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5 declarative

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