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3 years ago

A building lot in a city is shaped as a 30°-60°-90° triangle, like the figure shown.

Mathematics

2 answers:

Julli [10]3 years ago

4 0

Check the picture below.

In-s [12.5K]3 years ago

4 0

A) You can find the length of the side of the lot opposite the 60° angle <span> (which we will call "x") as below:
</span>
Tan(α)=Opposite/Adjacent

α=60°
Opposite=41 feet
Adjacent=x

When you substitute these values into Tan(α)=Opposite/Adjacent, you obtain:

Tan(60°)=x/41
(41)Tan(60°)=x
x=41√3
x=71.01 feet

B) Now, you can <span>find the length of the hypotenuse:
</span>
Cos(α)=Adjacent/Hypotenuse

α=60°
Adjacent=41 feet
Hypotenuse=y

When you substitute these values into Cos(α)=Adjacent/Hypotenuse, you obtain:

Cos(60°)=41/y
yCos(60°)=41
y=41/Cos(60°)
y=82 feet

You might be interested in

Explain how to evaluate f(g(0)).

alekssr [168]

Answer as a fraction: 17/6

Answer in decimal form: 2.8333 (approximate)

==================================================

Work Shown:

Let's use the two black points to determine the equation of the red f(x) line.

Use the slope formula to get...

m = slope

m = (y2-y1)/(x2-x1)

m = (4-0.5)/(2-(-1))

m = (4-0.5)/(2+1)

m = 3.5/3

m = 35/30

m = (5*7)/(5*6)

m = 7/6

Now use the point slope form

y - y1 = m(x - x1)

y - 0.5 = (7/6)(x - (-1))

y - 0.5 = (7/6)(x + 1)

y - 0.5 = (7/6)x + 7/6

y = (7/6)x + 7/6 + 0.5

y = (7/6)x + 7/6 + 1/2

y = (7/6)x + 7/6 + 3/6

y = (7/6)x + 10/6

y = (7/6)x + 5/3

So,

f(x) = (7/6)x + 5/3

We'll use this later.

---------------------

We ultimately want to compute f(g(0))

Let's find g(0) first.

g(0) = 1 since the point (0,1) is on the g(x) graph

We then go from f(g(0)) to f(1). We replace g(0) with 1 since they are the same value.

We now use the f(x) function we computed earlier

f(x) = (7/6)x + 5/3

f(1) = (7/6)(1) + 5/3

f(1) = 7/6 + 5/3

f(1) = 7/6 + 10/6

f(1) = 17/6

f(1) = 2.8333 (approximate)

This ultimately means,

f(g(0)) = 17/6 as a fraction

f(g(0)) = 2.8333 as a decimal approximation

8 0

2 years ago

Mr. Kohl has a breaker containing n milliliters of solution to distribute to the students in his chemistry class. If he gives ea

77julia77 [94]

Answer:

There were 26 students in his class and the teacher had 83 ml of the solution.

Step-by-step explanation:

Mr. Kohl has a "x" amount of solution, if he divides it by the number of students "n" he'll give each student 3 milliliters and have a left over of 5 milliliters. If the amount of solution Mr. Kohl had was "x + 21" then he'd be able to give each student 4 milliliters of the solution. From these informations we have:

x = 3*n + 5

(x + 21)/n = 4

x + 21 = 4*n

x = 4*n - 21

Now that we have two equations and two variables we can solve the system of equations, as seen bellow:

3*n + 5 = 4*n - 21

3*n - 4*n = -21 - 5

-n = -26

n = 26

x = 4*26 - 21 = 83 ml

There were 26 students in his class and the teacher had 83 ml of the solution.

3 0

2 years ago

Kianna lives in a town where the streets are laid out in a grid. She uses a coordinate plane to draw a map of the town, with her

Dmitrij [34]

Answer:

1. The coordinates of Jo’s house are (-4,-2).

2. Kianna walks 8 blocks west, and 2 blocks south.

3. The coordinates of Elena’s house are (4,-2).

4. Kianna is incorrect.

Step-by-step explanation:

1. Since Jo’s house is reflected across both axes, we must reflect the coordinates two times. So we can reflect the coordinates of Kianna’s house across the x-axis first, which would give you the coordinates (4,-2). Then we reflect (4,-2) across the y axis, giving us the coordinates (-4,-2). So Jo’s house has the coordinates (-4,-2).

3. Since Elena’s house is only a reflection of Jo’s house across the x-axis only, we can reflect Kianna’s house’s coordinates (4,2). When we reflect (4.2) over the x-axis, that gives us the coordinates (4,-2). So therefore Elena’s house has the coordinates (4,-2).

4. Kianna is incorrect, if Elena’s house was a reflection of her house across the y-axis, the coordinates would be (-4,2).

(A reflection can be thought of as folding or "flipping" an object over the line of reflection. The original object is called the pre-image, and the reflection is called the image.)

Hope this helps.

7 0

2 years ago

Read 2 more answers

Solve for w. 0.05w = 15

steposvetlana [31]

In order to find the value first multiply both sides by 100 to simplify the equation:
0.05w*100=15*100
5w=1500
Next, divide both sides of the equation by 5:
5w/5=1500/5
w=300
The final solution is w=300!

Hope i could help.
have a great day

4 0

3 years ago

Read 2 more answers

The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB in slope-intercept form that contains poi

ale4655 [162]

Answer:

<h3>The answer is option D</h3>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

y = 2x + 4

comparing with the above equation for a line

The slope / m = 2

Since the lines are parallel their slope are also the same

Slope of parallel line = 2

So we have

The equation of the line using point

( 3 , -2) and slope 2 is

y + 2 = 2( x - 3)

y + 2 = 2x - 6

y = 2x - 6 - 2

We have the final answer as

Hope this helps you

7 0

3 years ago