Answer:
1. Western erodes 2 ft/yr; Dunes builds up at 5 ft/yr
2. Sometime in 2006
3. Solve simultaneous equations
Step-by-step explanation:
1. Erosion patterns
(a) Western Beach
In 15 yr, Western Beach erodes from 100 ft to 70 ft.
The rate of erosion is 30 ft/15 yr = 2 ft/yr.
(b) Dunes Beach
In 15 yr, Dunes Beach builds up from 20 ft to 95 ft.
The rate of buildup is 75 ft/15 yr = 5 ft/yr.
2. Beaches with equal width
From the table, it appears that the beaches will have the same width sometime in year 11 (2006).
3. Best approximation
The graph below also shows that it happens part way through year 11 (2006).
We could get an even better solution by calculating the equations of the two lines and solving the simultaneous equations.
Answer:
The scale factor is
Step-by-step explanation:
Line segmentAB has vertices A(−3, 4) and B(1, −2) .
A dilation, centered at the origin, is applied to AB. The image has vertices
A'(-1,4/3) and B′(1/3, −2/3) .
We know the rule for dilation by scale factor of k, is
This means that;
But we know, A' has coordinates (-1,4/3)
This means that
We could also compare:
4k=4/3
Which gives
k=⅓
Three of the four towns are on the vertices of the triangle ΔCBD, through
which the bearing can calculated.
<h3>Response:</h3>From the given information, we have;
AC = AB = 25 km
∠BAC = 90° (definition of angle between north and east)
ΔABC = An isosceles right triangle (definition)
∠ACD = ∠ABC = 45° (base angles of an isosceles right triangle)
The bearing of <em>D</em> from <em>B</em> is the angle measured from the north of <em>B</em> to the
direction of <em>D.</em>
<em />
Therefore;
Learn more about bearings in mathematics here:
Options:
a. Nikki's proposed placement will light a greater area than Dylan's placement.
b. Dylan's proposed placement will light a greater area than Nikki's placement.
c. Both proposed placements will light the same sized area.
d. Nikki's proposed placement will light more than half the yard.
e. Dylan's proposed placement will light more than half the yard.
f. Dylan's proposed placement will light exactly half of the yard.
g. Nikki's proposed placement will light less than half of the yard.
Answer:
C) Both proposed placements will light the same sized area.
F) Dylan's proposed placement will light exactly half of the yard.
Step-by-step explanation:
The area of a triangle is (base x height) / 2, and both lights illuminate the same base and height = (60 x 38) / 2 = 1,140 sq ft
Both Dylan's and Nikki's proposed placement will lit exactly half of the yard. The yard's total area = 60 x 38 = 2,280 sq ft, which is twice the area lit by the lights.
