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OlgaM077 [116]
3 years ago
14

A slide 4.4 m long makes an angle of 33 with the ground. How high is the top of the slide above the ground

Mathematics
1 answer:
svp [43]3 years ago
5 0
Using the information given we will only need the Cosine and Sine equations.  i made a diagram (cant take a picture, in my study hall) labeled the sides of the triangle A, B, and C.  with C as the hypotenuse, A as the Opposite, and B as the adjacent (will not be needed as A is the height). i will be rounding the th nearest thousandth. 
Using Sine (SIN=Opposite/Hypotenuse), we can find A.

SIN(33)=A/4.4

SIN(33)≈.545

.545≈A/4.4

now multiply each side by 4.4 to get rid of the division

(.545*4.4)≈((A/4.4)4.4)

2.396≈A
 

so the answer would be that the slide is about 2.396 M high
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Determine the astm grain size number if 33 grains per square inch are measured at a magnification of 270×
strojnjashka [21]
8.9

The equation for the grain size is expressed as the equality:
Nm(M/100)^2 = 2^(n-1)
where
Nm = number of grains per square inch at magnification M.
M = Magnification
n = ASTM grain size number

Let's solve for n, then substitute the known values and calculate.
Nm(M/100)^2 = 2^(n-1)

log(Nm(M/100)^2) = log(2^(n-1))
log(Nm) + 2*log(M/100) = (n-1) * log(2)
(log(Nm) + 2*log(M/100))/log(2) = n-1
(log(Nm) + 2*log(M/100))/log(2) + 1 = n

(log(33) + 2*log(270/100))/log(2) + 1 = n
(1.51851394 + 2*0.431363764)/0.301029996 + 1 = n
(1.51851394 + 0.862727528)/0.301029996 + 1 = n
2.381241468/0.301029996 + 1 = n
7.910312934 + 1 = n
8.910312934 = n

So the ASTM grain size number is 8.9

If you want to calculate the number of grains per square inch, you'd use the
same formula with M equal to 1. So:
Nm(M/100)^2 = 2^(n-1)
Nm(1/100)^2 = 2^(8.9-1)
Nm(1/10000) = 2^7.9
Nm(1/10000) = 238.8564458
Nm = 2388564.458

Or about 2,400,000 grains per square inch.
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3 years ago
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The erased digits are 1, 0, 0.
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