Two angles that add up to 90 degrees
In average, when x increases by 1, f(x) also increases by the same value of 1 between x=2 and x=6 :)
Multiply the exponents
3 * -2 = -6
It would be 2^-6
Format: a^-b = 1/a^b
1/2^6 = 1/64
The solution is 1/64
Answer:
(a) 27°
(b) 17.9m
Step-by-step explanation:
According to the attachment
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let AB be the ladder
BC be the distance between the ladder and wall
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(a) We have to find ∠A by trigonometry formula
![\sf \sin A = \frac{perpendicular}{hypotenuse}](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Csin%20A%20%20%3D%20%20%5Cfrac%7Bperpendicular%7D%7Bhypotenuse%7D%20)
Here angle A is facing BC so it is perpendicular
and AB is the longest side so it is hypotenuse
![\sf \implies \sin A = \frac{BC}{AB} \\ \\ \\ \sf \implies \sin A = \frac{9}{20} \\ \\ \\ \sf \implies \sin A = 0.45 \\ \\ \\ \sf \implies \sin A = \sin27{ \degree} \\ \\ \\ \sf \purple {A = 27{ \degree}}](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Cimplies%20%5Csin%20A%20%3D%20%20%5Cfrac%7BBC%7D%7BAB%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%20%5Cimplies%20%20%5Csin%20A%20%3D%20%20%20%5Cfrac%7B9%7D%7B20%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%5Cimplies%20%20%5Csin%20A%20%3D%200.45%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%20%5Cimplies%20%20%5Csin%20A%20%3D%20%20%5Csin27%7B%20%5Cdegree%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%5Cpurple%20%7BA%20%3D%2027%7B%20%5Cdegree%7D%7D)
(b)
AC is the distance from the upper end of the ladder to ground
we will find it by Pythagoras theorem
![\sf {hypotenuse}^{2} = {perpendicular}^{2} + {base}^{2} \\ \\ \\ \sf \implies {AB}^{2} = {BC}^{2} + {AC}^{2} \\ \\ \\ \sf \implies {20}^{2} = {9}^{2} + {AC}^{2} \\ \\ \\ \sf \implies 400 = 81 + {AC}^{2} \\ \\ \\ \sf \implies 400 - 81 = {AC}^{2} \\ \\ \\ \sf \implies 319 = {AC}^{2} \\ \\ \\ \sf \implies \sqrt{319} = AC \\ \\ \\ \sf \blue{\implies 17.86 = AC}](https://tex.z-dn.net/?f=%20%5Csf%20%7Bhypotenuse%7D%5E%7B2%7D%20%20%3D%20%20%7Bperpendicular%7D%5E%7B2%7D%20%20%2B%20%20%20%7Bbase%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%20%5Cimplies%20%20%7BAB%7D%5E%7B2%7D%20%20%3D%20%20%7BBC%7D%5E%7B2%7D%20%20%2B%20%20%7BAC%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%5Cimplies%20%20%7B20%7D%5E%7B2%7D%20%20%3D%20%20%7B9%7D%5E%7B2%7D%20%20%2B%20%20%7BAC%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%20%5Cimplies%20400%20%3D%2081%20%2B%20%20%7BAC%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%20%5Cimplies%20400%20-%2081%20%3D%20%20%7BAC%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%5Cimplies%20319%20%3D%20%20%7BAC%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%20%5Cimplies%20%20%20%5Csqrt%7B319%7D%20%20%3D%20AC%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Csf%20%20%20%5Cblue%7B%5Cimplies%2017.86%20%3D%20AC%7D)
So these are basically isolating the variables.
The first equation is 3g + 5 =17.
In order to isolate the variable, we would have to get g by itself, that means 5 would have to go. In order to do this, we would do the opposite. Since it is positive 5 we would add negative 5, in order for it to disappear. This works because a positive 5 and negative 5 cancel each other out. Whatever you do to one side of the equation you have to do to the other, since we subtract 5 on one side we have to subtract 5 on the other. Therefore we would do 17-5.
Now we have 3g=12
We know that 3g is basically 3 multiplied by g. The opposite of multiplication is division.Therefore we would divide by 3 on both sides.
The answer to the first question would be g= 4.
And if you want to check if your answer is correct you plug the value in.
So
3(4) + 5 =17