Sandra throws an object straight up into the air with an initial velocity of 38 ft/s from a platform that is 30 ft above the gro
2 answers:
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<h2>Answer:</h2>
<em> The side of the triangle is either 38.63ft or 10.35ft</em>
<h2>Step-by-step explanation:</h2>This problem can be translated as an image as shown in the Figure below. We know that:
- The side of the square is 10 ft.
- One of the vertices of an equilateral triangle is on the vertex of a square.
- Two other vertices are on the not adjacent sides of the same square.
Let's call:
Since the given triangle is equilateral, each side measures the same length. So:
x: The side of the equilateral triangle (Triangle 1)
y: A side of another triangle called Triangle 2.
That length is the hypotenuse of other triangle called Triangle 2. Therefore, by Pythagorean theorem:
We have another triangle, called Triangle 3, and given that the side of the square is 10ft, then it is true that:
Therefore, for Triangle 3, we have that by Pythagorean theorem:
Matching equations (1) and (2):
Using quadratic formula:
Finding x from (1):
<em>Finally, the side of the triangle is either 38.63ft or 10.35ft</em>
<u>Question</u>:
The ratio of students to teachers at a school is 19 : 1. How many students are there in each total number of people?
A: 100 people
b. 280 people
c.440 people
d.760 people
<u>Answer</u>:
A )95 students and 5 teachers
B)266 students and 14 teachers
C)418 students and 22 teachers
D)722 students and 38 teachers
<u>Step-by-step explanation:</u>
<u><em>A: 100 people</em></u>
Ratio = 19 : 1
The sum of the ratio is 19 + 1 = 20
Scale factor =
scale factor = 5
The number students is = 95
The number of teachers is = 5
<em><u>b. 280 people </u></em>
Ratio = 19 : 1
The sum of the ratio is 19 + 1 = 20
Scale factor =
scale factor = 14
The number students is = 266
The number of teachers is = 14
<em><u>c.440 people</u></em>
Ratio = 19 : 1
The sum of the ratio is 19 + 1 = 20
Scale factor =
scale factor = 22
The number students is = 418
The number of teachers is = 22
<em><u>d.760 people</u></em>
Ratio = 19 : 1
The sum of the ratio is 19 + 1 = 20
Scale factor =
scale factor = 38
The number students is = 722
The number of teachers is = 38