Answer:
The length of the shadow is 48.28 feet.
Step-by-step explanation:
The flagpole at its shadow form a 46, 44, 90 triangle.
Let AB be the flagpole. AC is the shadow.
Let's use the sine law to calculate AC.
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall that
tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)
so cos²(<em>θ</em>) cancels with the cos²(<em>θ</em>) in the tan²(<em>θ</em>) term:
(sin²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>))
Recall the double angle identity for cosine,
cos(2<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
so the 1 in the denominator also vanishes:
(sin²(<em>θ</em>) - 1) / (2 cos²(<em>θ</em>))
Recall the Pythagorean identity,
cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1
which means
sin²(<em>θ</em>) - 1 = -cos²(<em>θ</em>):
-cos²(<em>θ</em>) / (2 cos²(<em>θ</em>))
Cancel the cos²(<em>θ</em>) terms to end up with
(tan²(<em>θ</em>) cos²(<em>θ</em>) - 1) / (1 + cos(2<em>θ</em>)) = -1/2
Answer:
Option (B)
Step-by-step explanation:
From the graph attached,
There are two functions 'f' and 'g' graphed.
Value of the function 'h' at x = 1,
y = h(1) = 0
Now we know g[h(1)] = g(0) [By substituting the value of h(1) = 0]
Therefore, value of the function 'g' at x = 0,
y = g(0) = -5 [y-intercept at x = 0]
Option (B) will be the correct option.
I think it is a rectangle..........But i'm not sure what are your options
Answer:
1000
Step-by-step explanation:
To find the value of a digit in a number, set all the other digits to zero.
The value of 7 in 7042 is 7000.
The value of 7 in 427 is 007 = 7.
Then the question is "how many times larger is 7000 than 7?" That result is found by dividing 7000 by 7:
7000/7 = 1000
The 7 in 7042 is 1000 times larger than the 7 in 427.
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<em>Another way to consider this</em>
The 7 in 7042 is in the "thousands" place. The 7 in 427 is in the "ones" place. The thousands place is 3 places to the left of the ones place. Each place moved to the left increases the value by a factor of 10, so the value of a digit in the thousands place is 10×10×10 = 1000 times that of the same digit in the ones place.
