In a school of 2100 students, the ratio of teachers to students is 1:14. Some teachers join the school and the ratio changes to
2:21. Find the number of teachers who joined the school.
1 answer:
Answer:
50 Teachers
Step-by-step explanation:
To solve this problem, we first need to find the number of teachers <em>before </em>the new teachers were added. To do so, I created Model 1. On the bottom of the ratios, we have students. On the top, is teachers. The X is the number of teachers we are trying to find. Following the model, I multiplied 2,100 x 1 (2,100) and divided it by 14 to get 150 teachers. Then, I set up a similar model with the new student-teacher ratio (Model 2). From there, I multiplied 2,100 x 2 (4,200) and divided it by 21 to get 200 teachers. Now I have the original number of teachers and the new number of teachers. Subtract the new by the original to find the teachers added and you get the answer of 50 teachers added.
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We have to find the potential solutions to from least to greatest.
Using the properties of ln function.
Therefore, we get
taking antilog on both the sides, we get
So,
Therefore, the potential solutions to 2 ln x = 4 ln 2 from least to greatest is -4 and 4.
1) The slope of the point (0,0) and (2,1) is 1/2.
2) The slope of the point (0,-1) and (2,-5) is -2.
3) The slope of the point (0,7) and (2,4) is -3/2.
4) The points (-1,3) and (-1,-3) has No slope.
5) The slope of the point (1,-3) and (-1,-3) is zero.
<u>Step-by-step explanation:</u>
There are five set of points given in the question.
You need to find out the slope of the line formed by the points.
The formula used to find the slope of a line is given by,
Slope =
1) The given points are (0,0) and (2,1)
(x1,y1) ⇒ (0,0)
(x2,y2) ⇒ (2,1)
Slope =
⇒ 1/2 is the slope.
2) The given points are (0,-1) and (2,-5)
(x1,y1) ⇒ (0,-1)
(x2,y2) ⇒ (2,-5)
Slope =
⇒
⇒ -2 is the slope.
3) The given points are (0,7) and (2,4)
(x1,y1) ⇒ (0,7)
(x2,y2) ⇒ (2,4)
Slope =
⇒ -3/2 is the slope.
4) The given points are (-1,3) and (-1,-3)
(x1,y1) ⇒ (-1,3)
(x2,y2) ⇒ (-1,-3)
Slope =
⇒ -6/0 (No slope)
If the denominator of a fraction is zero, the expression is not a legal fraction because it's overall value is undefined.
∴ There is no slope.
5) The given points are (1,-3) and (-1,-3)
(x1,y1) ⇒ (1,-3)
(x2,y2) ⇒ (-1,-3)
Slope =
⇒ 0/-2
∴ The slope is zero.
Note that (5π)/6 radians = 150°. Therefore the given angle is in quadrant 2.
Refer to the figure shown below.
Reference angles are measured relative to the horizontal axis.
Therefore the reference angle in each quadrant is π/6 radians or 30°.
Denote the reference angle as θ'.
Then, in quadrant 1,
cos θ' = √3/2, sin θ' = 1/2, tan θ' = √3.
Because we are in quadrant 2,
sin θ' = π/6;
sin(5π/6) is positive, but cos (5π/6) and tan (5π/6) are negative.
Answer:
5π/6 is in quadrant 2.
The reference angle, θ' = π/6.
sin(5π/6) is positive, cosine and tangent are negative.
Refer to the figure shown below.
Reference angles are measured relative to the horizontal axis.
Therefore the reference angle in each quadrant is π/6 radians or 30°.
Denote the reference angle as θ'.
Then, in quadrant 1,
cos θ' = √3/2, sin θ' = 1/2, tan θ' = √3.
Because we are in quadrant 2,
sin θ' = π/6;
sin(5π/6) is positive, but cos (5π/6) and tan (5π/6) are negative.
Answer:
5π/6 is in quadrant 2.
The reference angle, θ' = π/6.
sin(5π/6) is positive, cosine and tangent are negative.