how fast would 1.5 times the fastest rowing speed be? Before you solve. tell the number of decimal places in your answers
1 answer:
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Answer: y = (5832/25)*(5/18)^x
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Explanation:
Any general exponential function is of the form
y = a*b^x
Plug in (x,y) = (3,5) and we get
y = a*b^x
5 = a*b^3
If you plug in (x,y) = (2,18), then we'll get this other equation
18 = a*b^2
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So we have this system of equations
From here, we divide the two equations straight down. The left hand sides divide to 5/18. The right hand sides divide to (ab^3)/(ab^2) which simplifies to b. The 'a' terms cancel and we subtract the exponents for the b terms.
Overall, we end up with b = 5/18
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Use that value of b to find 'a'
18 = a*b^2
18 = a*(5/18)^2
18 = a*(25/324)
18*(324/25) = a
a = 5832/25
You could use the other equation as well to find 'a'
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Therefore, the equation in y = a*b^x form is y = (5832/25)*(5/18)^x
To verify this, plugging in x = 3 should lead to y = 5. Similarly, plugging in x = 2 should lead to y = 18.
Part A:
From the figure shown.
The measure of line TH = 14' 72" = 14' + 72" / 12 = 14' + 6' = 20'
Given that the measure of line HI = 20'
Thus, triangle THI is an isosceles triangle with line TI as the base.
Part B:
To find the base angles we use the Pythagoras theorem.
Recall that the perpendicuar bisector of an isosceles triangle divides the triangle into two equal right triangles.
Dividing the base into two gives 22.5' / 2 = 11.25'
Thus, the perpendicular bisector divides the isosceles triangle into two equal right triangles with base of 11.25' and hypothenus of 20'.
By pythagoras theorem,
Therefore, the base angles is 55.77 degrees.
From the figure shown.
The measure of line TH = 14' 72" = 14' + 72" / 12 = 14' + 6' = 20'
Given that the measure of line HI = 20'
Thus, triangle THI is an isosceles triangle with line TI as the base.
Part B:
To find the base angles we use the Pythagoras theorem.
Recall that the perpendicuar bisector of an isosceles triangle divides the triangle into two equal right triangles.
Dividing the base into two gives 22.5' / 2 = 11.25'
Thus, the perpendicular bisector divides the isosceles triangle into two equal right triangles with base of 11.25' and hypothenus of 20'.
By pythagoras theorem,
Therefore, the base angles is 55.77 degrees.