The function:f ( x ) = x * 0.965^twhere x is the initial amount and t is the number of the years80 = x * 0.965^380 = x * 0.89632x = 80 : 0.89632 ≈ 89Answer:The initial amount of animals was 89.
Answer:
The student will have 130 dollars in the bank at the end of week 11.
Step-by-step explanation:
Pattern:
The pattern given by this graphic is that:
For each passing week, the student will have $10 more in the bank than at the end of the previous week. So, following this pattern:
At the end of 6 weeks, he will have $80.
At the end of 7 weeks, he will have $90.
At the end of 8 weeks, he will have $100.
At the end of 9 weeks, he will have $110.
At the end of 10 weeks, he will have $120.
At the end of 11 weeks, he will have $130.
The student will have 130 dollars in the bank at the end of week 11.
Isolate the variable by dividing each side by factors that don't contain the variable. p=q/2r
78 minutes...............................................
Answer:
12.1 cm
Step-by-step explanation:
Using the law of sines, we can find angle C. Then from the sum of angles, we can find angle B. The law of sines again will tell us the length AC.
sin(C)/c = sin(A)/a
C = arcsin((c/a)sin(A)) = arcsin(8.2/13.5·sin(81°)) ≈ 36.86°
Then angle B is ...
B = 180° -A -C = 180° -81° -36.86° = 62.14°
and side b is ...
b/sin(B) = a/sin(A)
b = a·sin(B)/sin(A) = 13.5·sin(62.14°)/sin(81°) ≈ 12.0835
The length of AC is about 12.1 cm.
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<em>Comment on the solution</em>
The problem can also be solved using the law of cosines. The equation is ...
13.5² = 8.2² +b² -2·8.2·b·cos(81°)
This is a quadratic in b. Its solution can be found using the quadratic formula or by completing the square.
b = 8.2·cos(81°) +√(13.5² -8.2² +(8.2·cos(81°))²)
b = 8.2·cos(81°) +√(13.5² -(8.2·sin(81°))²) . . . . . simplified a bit
