Newton's Law of Cooling
Tf=Ts+(Ti-Ts)e^(-kt) where Tf is temp at time t, Ts is temp of surroundings, Ti is temp of object/fluid. So we need to find k first.
200=68+(210-68)e^(-10k)
132=142e^(-10k)
132/142=e^(-10k)
ln(132/142)=-10k
k=-ln(132/142)/10
k≈0.0073 so
T(t)=68+142e^(-0.0073t) so how long until it reaches 180°?
180=68+142e^(-0.0073t)
112=142e^(-0.0073t)
112/142=e^(-0.0073t)
ln(112/142)=-0.0073t
t= -ln(112/142)/(0.0073)
t≈32.51 minutes
Answer:
Y = 170, Z = 64.
Step-by-step explanation:
Since y is the external angle to x, which you got right, it is in fact, 180-10, = 170 degrees. And since z is the external to our unknown angle, that means it is equal to the sum of the other two angles in the triangle. That means z is 54 + 10, which is 64.
Answer:
A) ERROR
B) ∠C = 26°
Step-by-step explanation:
Houston, We have a problem!!! too much information
If we had a legit triangle, the law of sines would hold
19/sin138 = 8/sin20
28.395 = 23.390
as this is NOT an equality, the triangle does not exist as described.
IF it did, we'd get different results depending on which set we used
∠F = 180 - 138 - 20 = 22°
Law of sines
19/sin138 = DE/sin22 ⇒ DE = 19sin22/sin138 = <u>10.63697...</u>
or
8/sin20 = DE/sin22 ⇒ DE = 8sin22/sin20 = <u>8.762211...</u>
If we attempt to use Law of cosines
DE² = 19² + 8² - 2(19)(8)cos22 = <u>11.9639...</u>
so really none is correct because we attempt to use trig calculations to a non-triangle.
12) AC² = 15² + 19² - 2(15)(19)cos120
AC = 29.51270...
29.51270 / sin120 = 15/sinC
C = arcsin(15sin120/29.51270) = 26.1142... <u>26°</u>
62400 is what percent of 156000
<span>= 62400 / 156000 </span>
<span>= 0.4 </span>
<span>Converting decimal to a percentage: </span>
<span>0.4 * 100 = 40%</span>
Well, $920 multiplied by .15 would equal 138 and
since 138 divided by 138 would equal 920. 15% of his income aka $138 would go towards his taxes.
Hope this helped!
have a great day! (:
