Answer:
346380
Step-by-step explanation:
hope you gwt an a
Answer:
2 cm
Step-by-step explanation:
h = 14 cm
Curved surface area of a right circular cylinder = 88 cm²
2πrh = 88
Diameter = 2 * r = 2 * 1 = 2 cm
#1)
A) b = 10.57
B) a = 22.66
#2)
A) a = 1.35 (across from the 15° angle)
∠C = 50.07° (the angle at the top of the triangle)
∠B = 114.93°
B) ∠A = 83°
b = 10.77 (across from angle B)
a = 15.11 (across from angle A)
Explanation
#1)
A) Since b is across from the 25° angle and we have the hypotenuse, we have the information for the sine ratio (opposite/hypotenuse):
sin 25 = b/25
Multiply both sides by 25:
25*sin 25 = (b/25)*25
25*sin 25 = b
10.57 = b
B) We will first use the cosine ratio. Side a is the side adjacent to the angle and we have the hypotenuse, and the cosine ratio is adjacent/hypotenuse:
cos 25 = a/25
Multiply both sides by 25:
25*cos 25 = (a/25)*25
25*cos 25 = a
22.66 = a
Now we will use the Pythagorean theorem. We know from part a that side b = 10.57, and the figure has a hypotenuse of 25:
a²+(10.57)² = 25²
a² + 111.7249 = 625
Subtract 111.7249 from both sides:
a²+111.7249-111.7249=625-111.7249
a² = 513.2751
Take the square root of both sides:
√a² = √513.2751
a = 22.66
#2)
A) Let A be the 15° angle, B be the angle to the right and C be the angle at the top of the triangle. This means side a is across from angle A, side B is across from angle B, and side c is across from angle C.
Using the law of cosines,
a²=3²+4²-2(3)(4)cos(15)
a²=9+16-24cos(15)
a²=25-24cos(15)
a²=1.8178
Take the square root of both sides:
√a² = √1.8178
a = 1.3483≈1.35
Now we can use the Law of Sines to find angle C:
sin 15/1.35 = sin C/4
Cross multiply:
4*sin 15 = 1.35* sin C
Divide both sides by 1.35:
(4*sin 15)/1.35 = (1.35*sin C)/1.35
(4*sin 15)/1.35 = sin C
Take the inverse sine of both sides:
sin⁻¹((4*sin 15)/1.35) = sin⁻¹(sin C)
sin⁻¹((4*sin 15)/1.35) = C
50.07 = C
To find angle B, add angle A and angle C together and subtract from 180:
B=180-(50.07+15) = 180-65.07 = 114.93
B) To find angle A, add angle B and angle C together and subtract from 180:
180-(52+45) = 180-97 = 83
Now use the Law of Sines to find side b (across from angle B):
sin 52/12 = sin 45/b
Cross multiply:
b*sin 52 = 12*sin 45
Divide both sides by sin 52:
(b*sin 52)/(sin 52) = (12*sin 45)/(sin 52)
b = 10.77
Find side a using the Law of Sines:
sin 83/a = sin 52/12
Cross multiply:
12*sin 83 = a*sin 52
Divide both sides by sin 52:
(12*sin 83)/(sin 52) = (a*sin 52)/(sin 52)
15.11 = a
Answer:
The correct answer is 1. I just finished the quiz.
Step-by-step explanation:
Answer is D) 5 mc, 15 t&f
you have two unknown variables, thus you need two equations
definitions:
a = quantity of multiple choice questions
b = quantity of true and false questions
100 points = a*11 points/question + b*3 points/question
20 questions = a +b
using 2nd equation, find equation for 'a':
a = 20 - b
substitute this equation for 'a' into 1st equation:
100 = 11a + 3b
100 = 11(20 - b) + 3b
100 = 220 - 11b + 3b
100 - 220 = -8b
-120 = -8b
-120/-8 = b
15 = b
resolve 2nd equation now knowing value of 'b':
a = 20 - b
a = 20 - 15
a = 5
verify solution is correct by substituting values into first equation
11a + 3b = 100
11(5) + 3(15) = 100
55 + 45 = 100
100 = 100 [OK]
verify solution is correct by substituting values into second equation
a + b = 20
5 + 15 = 20
20 = 20 [OK]