<h3>
Answer: 73</h3>
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Work Shown:
Check out the diagram below. Note the pair of alternate interior angles that are congruent (each 37 degrees). Then focus on triangle ABC. With the reference angle being at A, this means we use the tangent function because BC = x is the opposite side and AB = 97 is the adjacent side.
tan(angle) = opposite/adjacent
tan(A) = BC/AB
tan(37) = x/97
97*tan(37) = x
x = 97*tan(37)
x = 73.094742859971
For the last step, you'll need a calculator that can handle trig functions. Make sure the calculator is in degree mode. The result here is approximate. This rounds to 73 when rounding to the nearest whole number.
(22 x sin(65))/sin(53) =24.96604654 rounded of to nearest tenth = 25
So X = 25
Answer:
Hence the function which has the smallest minimum is: h(x)
Step-by-step explanation:
We are given function f(x) as:
- f(x) = −4 sin(x − 0.5) + 11
We know that the minimum value attained by the sine function is -1 and the maximum value attained by sine function is 1.
so the function f(x) receives the minimum value when sine function attains the maximum value since the term of sine function is subtracted.
Hence, the minimum value of f(x) is: 11-4=7 ( when sine function is equal to 1)
- Also we are given a table of values for function h(x) as:
x y
−2 14
−1 9
0 6
1 5
2 6
3 9
4 14
Hence, the minimum value attained by h(x) is 5. ( when x=1)
- Also we are given function g(x) ; a quadratic function passing through (2,7),(3,6) and (4,7)
so, the equation will be:
Hence on putting these coordinates we will get:
a=1,b=3 and c=7.
Hence the function g(x) is given as:
So,the minimum value attained by g(x) could be seen from the graph is at the point (3,6).
Hence, the minimum value attained by g(x) is 6.
Hence the function which has the smallest minimum is h(x)
Total mold spores at end of 9.30 am is 26901.
Step-by-step explanation:
Number of molds = 14000
Rate = 9.7% per hour
Number of hours = 12 am to 9.30 am = 9
hours
Growth of mold = 14000 * 9.7% * 9
= 12901
Total mold spores at end of 9.30 am = 14000 + 12901
= 26901
Hence, the expected number of mold spores at 9.30 am is 26901.
