Answer:
y=3x-1 and y=3x+1
Step-by-step explanation:
y=mx+b form
m stands for the slope which is rise over run.
b stands for the y intercept. where the line intersects with the y axis.
The horizontal distance between light house and boat is 1588.78 feet approximately.
The figure is given by,
Here, AB = height of the lighthouse bacon light above the water = 139 feet
Now angle ACB = 5 degree
Let the horizontal distance of light house from the boat = BC = x feet
So by trigonometric function we get,
tan 5 = AB/BC
tan 5 = 139/x
x = 139/tan 5 = 1588.78 (approximately)
Hence the horizontal distance between light house and boat is 1588.78 feet approximately.
To know more about Trigonometric Function refer to:
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Answer:
Area of trapezium = 4.4132 R²
Step-by-step explanation:
Given, MNPK is a trapezoid
MN = PK and ∠NMK = 65°
OT = R.
⇒ ∠PKM = 65° and also ∠MNP = ∠KPN = x (say).
Now, sum of interior angles in a quadrilateral of 4 sides = 360°.
⇒ x + x + 65° + 65° = 360°
⇒ x = 115°.
Here, NS is a tangent to the circle and ∠NSO = 90°
consider triangle NOS;
line joining O and N bisects the angle ∠MNP
⇒ ∠ONS =
= 57.5°
Now, tan(57.5°) = 
⇒ 1.5697 = 
⇒ SN = 0.637 R
⇒ NP = 2×SN = 2× 0.637 R = 1.274 R
Now, draw a line parallel to ST from N to line MK
let the intersection point be Q.
⇒ NQ = 2R
Consider triangle NQM,
tan(∠NMQ) = 
⇒ tan65° =
⇒ QM =
QM = 0.9326 R .
⇒ MT = MQ + QT
= 0.9326 R + 0.637 R (as QT = SN)
⇒ MT = 1.5696 R
⇒ MK = 2×MT = 2×1.5696 R = 3.1392 R
Now, area of trapezium is (sum of parallel sides/ 2)×(distance between them).
⇒ A = (
) × (ST)
= (
) × 2 R
= 4.4132 R²
⇒ Area of trapezium = 4.4132 R²
Using the profit concept, it is found that she makes a profit of $4 selling a dozen cookies for six dollars.
<h3>What is a profit?</h3>
The profit is given by the <u>subtraction of the revenue by the total costs</u>.
In this problem:
- For the dozen cookies, she earned a revenue of 6 dollars.
- In all, the total cost of the 12 cookies was of 0.5 + 0.7 + 0.4 + 0.4 = 2 dollars.
6 - 2 = 4, hence she makes a profit of $4.
More can be learned about the profit concept at brainly.com/question/4001746
Answer:
The maximum value of the equation is 1 less than the maximum value of the graph
Step-by-step explanation:
We have the equation
.
We can know that this graph will have a maximum value as this is a negative parabola.
In order to find the maximum value, we can use the equation 
In our given equation:
a=-1
b=4
c=-8
Now we can plug in these values to the equation

Now we can plug the x value where the maximum occurs to find the max value of the equation

This means that the maximum of this equation is -4.
The maximum of the graph is shown to be -3
This means that the maximum value of the equation is 1 less than the maximum value of the graph