Answer:
5. y = 2x + 4
6. y = (-1/2)x - 2
Step-by-step explanation:
5. We want to find the slope-intercept form of this, which is y = mx + b, where m is the slope and b is the y-intercept.
Slope is change in y divided by change in x. Here, let's take two random points: (-2, 0) and (0, 4). Then we have:
m = (4 - 0) / (0 - (-2)) = 4 / 2 = 2
The slope is thus 2.
The y-intercept is where the line crosses the y-axis. We see it does so at the point (0, 4), so b = 4.
Our equation is thus: y = 2x + 4.
6. Again, let's find the slope. Pick any two points: (-4, 0) and (0, -2). The slope will be:
m = (-2 - 0) / (0 - (-4)) = -2 / 4 = -1/2
Now, look at the point (0, -2); that's where the line crosses the y-axis, so the y-intercept is b = -2.
Thus, the equation is: y = (-1/2)x - 2.
Answer:
69.01 m
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Tan = Opposite/Adjacent
The tangent function is useful for problems like this. Let the height of the spire be represented by h. The distance (d) across the plaza from the first surveyor satisfies the relation ...
tan(50°) = (h -1.65)/d
Rearranging to solve for d, we have ...
d = (h -1.65)/tan(50°)
The distance across the plaza from the second surveyor satisfies the relation ...
tan(30°) = (101.65 -h)/d
Rearranging this, we have ...
d = (101.65 -h)/tan(30°)
Equating these expressions for d, we can solve for h.
(h -1.65)/tan(50°) = (101.65 -h)/tan(30°)
h(1/tan(50°) +1/tan(30°)) = 101.65/tan(30°) +1.65/tan(50°)
We can divide by the coefficient of h and simplify to get ...
h = (101.65·tan(50°) +1.65·tan(30°))/(tan(30°) +tan(50°))
h ≈ 69.0148 ≈ 69.01 . . . . meters
The tip of the spire is 69.01 m above the plaza.
Angle A is 10 degrees because you need to subtract 43 by 35 and u get 8 then u subtract 18 by 8.
Glad could help