Find tan (22.5)
Answer: #-1 + sqrt2#
Explanation:
Call tan (22.5) = tan t --> tan 2t = tan 45 = 1
Use trig identity: # tan 2t = (2tan t)/(1 - tan^2 t)# (1)
#tan 2t = 1 = (2tan t)/(1 - tan^2 t)# -->
--> #tan^2 t + 2(tan t) - 1 = 0#
Solve this quadratic equation for tan t.
#D = d^2 = b^2 - 4ac = 4 + 4 = 8# --> #d = +- 2sqrt2#
There are 2 real roots:
tan t = -b/2a +- d/2a = -2/1 + 2sqrt2/2 = - 1 +- sqrt2
Answer:
#tan t = tan (22.5) = - 1 +- sqrt2#
Since tan 22.5 is positive, then take the positive answer:
tan (22.5) = - 1 + sqrt2
Answer: 89.6 kg of water
Step-by-step explanation:
Find the total volume of the tank:
(80cm)*(35cm)*(40cm) = 112,000 cm^3
4/5 of this would be 89,600 cm^3
Water has a mass of 1 gram/cm^3
(1 gram/cm^3)*(89,600 cm^3) = 89,600 g of water
(89,600 g)*(1 kg/1,000 g) = 89.6 kg of water
Probability =
(number or amount of possible successes)(total number or amount of possible outcomes)
Area of any circle is (pi) x (radius squared)
Area of the whole board = (pi) x (13 squared) = 169 pi square inches
Area of the shaded region = (pi) x (5 squared) = 25 pi square inches
Probability = (success area) / (total possible area) = 25pi/169pi = <u>0.15 </u>(rounded)
Notice that if you do it my way ... keep 'pi' in the fraction ... you don't even
need to know what the value of 'pi' is, because there's one in the top and
bottom of the fraction, and they cancel.
Where are the answer choices ?
B.
<span>$5852.86
Working;
</span><span>A = P(1 + r)^t
A=5000(1+</span>
)^5
A=<span>5852.86</span>
