The equations of the asymptotes of the given hyperbola are; y = ±(40/9)x
<h3>How to Interpret the equation of a hyperbola?</h3>
We are given;
Vertex at (0,−40)
Focus at (0, 41).
Thus, the equation of the asymptote of the given hyperbola is;
y = ±(40/(√41 - (-40))
y = ±(40/(√81)
y = ±40/9
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Set up a proprtion and cross multiply.
18/7.5=22/4x+1
7.5×22=18 (4x+1)
165=72x+18
147=72x
x=2.04
This would just be $153 multiplied by 2. Because 6•2=12 so you just double the amount he was paid for the 6 days. 153 •2=306. Answer is $306
Answer:
the other two angles are 70° and 20°
Step-by-step explanation:
Applying the sine ratio and the law of sines, the value of h in the diagram is: B. 3.2 yards.
<h3>What is the Sine Ratio?</h3>
Sine ratio for solving a right triangle is: sin ∅ = opp/hyp.
Let's find AT in triangle BAT using the given Law of Sines:
m∠BTA = 180 - (180 - 57) - 46 = 11°
AB = 1 yd
m∠ABT = 46°
Using the law of sines, we have:
sin(m∠ABT)/AT = sin(m∠BTA)/AB
Plug in the values
sin(46)/AT = sin(11)/1
AT = sin(46) × 1 / sin(11)
AT = 3.8 yards
Find h using the sine ratio:
∅ = 57°
Opposite = h
Hypotenuse = AT = 3.8 yards
Substitute
sin 57 = h/3.8
h = sin 57 × 3.8
h ≈ 3.2 yards.
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