Answer:
Correct answer is 54.82 ft.
Step-by-step explanation:
First of all, let us label the diagram and do the construction as per the attached answer image.
Let us consider
:

Let side AB = d ft and let side BC = x ft
We need to find AB to find the shortest distance across the river.
Using trigonometric identity of tangent:


Now, let us have a look at another right angled triangle ABD:
Let us consider
:

side AB = d ft and side BD = x+75 ft
Using trigonometric identity of tangent:


Correct answer is 54.82 ft.
Answer:
rise 4, run -2. the gradiant is 2
Step-by-step explanation:
(X1,Y1)___(X2,Y2)
| | | |
(-2,2)_____(0,6)
X1-X2, Y1-Y2.
-2-0= -2= (-2,_)
2-6= 4= (_,4)
(-2,4)
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Answer:
The answer is 48 units³
Step-by-step explanation:
If we simply draw out the region on the x-y plane enclosed between these lines we realize that,if we evaluate the integral the limits all in all cannot be constants since one side of the triangular region is slanted whose equation is given by y=x. So the one of the limit of one of the integrals in the double integral we need to evaluate must be a variable. We choose x part of the integral to have a variable limit, we could well have chosen y's limits as non constant, but it wouldn't make any difference. So the double integral we need to evaluate is given by,

Please note that the order of integration is very important here.We cannot evaluate an integral with variable limit last, we have to evaluate it first.after performing the elementary x integral we get,

After performing the elementary y integral we obtain the desired volume as below,

Answer:
The rate is 1.75 feet/seconds or 105 feet/minute.
Step-by-step explanation:
Given that,
Li walks at a constant rate of 7 feet in 4 seconds
To find the constant of proportionality, divide 7 feet by 4 seconds.
So,

1.75 ft/s is the constant of proportionality
We know that, 1 minute = 60 seconds
k = 105 feet/minute
So, the rate is 1.75 feet/seconds or 105 feet/minute.