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Step-by-step explanation:
x is just a stand-in for an unknown/variable number, so we could use phrases like "a number," "a value," "an unknown," etc. Here, I'll use "a number." We can verbally refer to the result of subtraction as "the difference" as well, so we can write x - 6 in English as "The difference of a number and 6."
Part A
4x10 – 64x2
= 4x2 * x8 – 4x2 * 16
= 4x2 * (x8 – 16) by distributive property
Part B
x8 is (x4)2 and 16 = 42 so a difference of squares is seen in the parentheses. The pattern a2 – b2 = (a + b)(a – b) can be used.
4x2 * (x8 – 16)
= 4x2 * (x4 + 4) * (x4 – 4)
x4 = (x2)2 and 4 = 22 so there is another difference of squares in the last factor. Use the pattern again.
= 4x2 * (x4 + 4) * (x2 + 2) * (x2 – 2)
<span>We know Sin theta is given by Perpendicular/ hypotenuse.
Hence in this case the angle given is 30 degree and hypotenuse is given as 10 foot.
Hence Sin 30= P/ 10
1/2= P/10
Hence on solving value of P is 5.
Now we have to compute the theta value for Perpendicular as 5 and now the height of ramp is increased to 15 foot, hence hypotenuse is now 15 foot.
Hence Sin theta= 5/15
On taking inverse of Sin Theta we will get the theta value as 19.47.
Hence the angle of ramp should is 19.47 degrees.</span>
