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ollegr [7]
2 years ago
10

Group of baseball fans can see home plate from a 40 meter tall building outside the stadium. The angle of vision has a tangent o

f
9
4
. What is the horizontal distance, in meters, to home plate?
Mathematics
1 answer:
dimulka [17.4K]2 years ago
5 0

Answer:

17.78 meters

Step-by-step explanation:

Let

x ----> the horizontal distance, in meters, to home plate

\theta ----> the angle of vision

we know that

tan(\theta)=\frac{40}{x} ----> by TOA (opposite side divided by the adjacent side)

we have

tan(\theta)=\frac{9}{4}

substitute

\frac{9}{4}=\frac{40}{x}

solve for x

x=40(4)/9\\x=17.78\ m

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Samara is adjusting a satellite because she finds it is not focusing the income radio waves perfectly. The shape of her satellit
gogolik [260]

Answer:

\boxed{\text{(6, 3)}}

Step-by-step explanation:

The conic form of the equation for a sideways parabola is

(y - k)² = 4p(x - h)

The focus is at (h + p, k)

The equation of Samara's parabola is

(y - 3)² = 8(x - 4)

h = 4

p = 8/4 = 2

k = 3

h + p = 6

So, the focus point of the satellite dish is at

\boxed{\textbf{(6, 3)}}

8 0
1 year ago
5. the price of an ipod dropped from $299.99 to $180.55. what was the percent decrease in price? (round to nearest hundredth per
max2010maxim [7]
If you would like to know what was the percent decrease in price, you can calculate this using the following steps:

x% of $299.99 is $180.55
x% * 299.99 = 180.55
x/100 * 299.99 = 180.55
x = 180.55 * 100 / 299.99
x = 60.19%

100% - 60.19% = 39.81%

The correct result would be 39.81%.
3 0
2 years ago
A dormitory has 40 students---12 sophomores, 8 juniors, and 20 seniors. Which of the following is equal to the number of ways to
Maurinko [17]

Answer:

The number of ways is equal to 12!8!20!

Step-by-step explanation:

The multiplication principle states that If a first experiment can happen in n1 ways, then a second experiment can happen in n2 ways ... and finally a i-experiment can happen in ni ways therefore the total ways in which the whole experiment can occur are

n1 x n2 x ... x ni

Also, given n-elements in which we want to put them in a row, the total ways to do this are n! that is n-factorial.

For example : We want to put 4 different objects in a row.

The total ways to do this are 4!=4.3.2.1=24 ways.

Using the multiplication principle and the n-factorial number :

The number of ways to put all 40 in a row for a picture, with all 12 sophomores on the left,all 8 juniors in the middle, and all 20 seniors on the right are : The total ways to put all 12 sophomores in a row multiply by the ways to put the 8 juniors in a row and finally multiply by the total ways to put all 20 senior in a row ⇒ 12!8!20!

4 0
2 years ago
The New Haven High School cheerleaders got a t-shirt gun. The cheerleaders stand
nevsk [136]

Answer: the gun was held 4ft high i.e H = 4ft

Step-by-step explanation:

To determine how high the gun was held when it was fired H;

Before firing the t-shirt up, the gun and the t-shirt are both at the same height.

Therefore,

H = h(0) i.e h(t) at t = 0

h(t) = -16t^2 + 64t + 4

H = h(0) = -16(0)^2 + 64(0) + 4

H = 4ft

7 0
2 years ago
In the diagram below, BC is an altitude of ABD. To the nearest whole unit, what is the length of CD?
dem82 [27]
First we need to calculate the 2 angles that make up Angle B at the top of the triangle.
 Using that angle we can find the length of CD.


 See the attached picture:

7 0
2 years ago
Read 2 more answers
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