<h3>
Answer: 100 meters</h3>
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Explanation:
If you draw out the diagram, then you'll find that a 45-45-90 triangle forms. The nice thing about this type of triangle is that the two legs are always the same length. The horizontal leg is 100 meters, so the vertical leg must also be 100 meters.
Side note: this type of triangle is an isosceles right triangle.
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You could use the tangent rule to get the same thing
tan(angle) = opposite/adjacent
tan(45) = 100/x
1 = 100/x
1*x = 100
x = 100
In this case, the opposite leg is the vertical leg since it is furthest from the angle of elevation.
Answer:
Maximum rate of change at the point (-1,2) = √17
Direction is the direction of the gradient
Step-by-step explanation:
The gradient of a function (scalar or vectorial ) is a vector in the direction of maximum rate of change then
f( x,y ) = x*2y + 2y
grad = δ/δx i + δ/δy j + δ/δz k
grad f(x,y) = [ δ/δx i , δ/δy] = [ 2y , x+2 ]
at the point ( -1 , 2 )
grad f(x,y) = [4 , 1]
| grad f(x,y) | = √ (4)² + (1)² = √17
Answer:
4. 2(3k+4y-14).
5. 76+34.9.
6.10t-8
Step-by-step explanation:
4.since it's 6k+8y-14 all of the numbers can be divided by 2 then the you just put a 2 in front of everything and then(3k+4y-14).
5. (22+11.5x)+(54+23.4x).
=(22+54)+(11.5x+23.4x).
=76+34.9x.
=34.9x+76.
6.(9t-3)+(-5+t).
=(9t+t)+(-3-5).
=10t-8.
Answer:
a) 0.1108
(b) 0.0173
Step-by-step explanation:
We are given that 20% of all stock investors are retired people. A random sample of 25 stock investors is taken.
Firstly, the binomial probability is given by;
where, n = number of trails(samples) taken = 25
r = number of successes
p = probability of success and success in our question is % of
retired people i.e. 20%.
Let X = Number of people retired
(a) Probability that exactly seven are retired people = P(X = 7)
P(X = 7) =
= = 0.1108
(b) Probability that 10 or more are retired people = P(X >= 10)
P(X >= 10) = 1 - P(X <= 9)
Now, using binomial probability table, we find that P(X <= 9) is 0.98266 at n = 25, p = 0.2 and x= 9
So, P(X >= 10) = 1 - 0.98266 = 0.0173.
Answer:
2,016.67 sq. cm
Step-by-step explanation:
Given the approximate ratio of the sides of a rectangle as 3:4:5.
Total ratio = 3+4+5 = 12
Area of the rectangle = 1/2*base *height
get the base;
base = 3/12 * 220
Base = 55cm
Get the height
Height = 4/12 * 220
Height = 880/12
Height = 73.3cm
Area = 1/2 * 55 * 73.3
Area = 2,016.67 sq. cm
