<h3>
Answer: Choice C</h3>
Explanation:
The commutative law of multiplication says that A*B = B*A, for any real numbers A,B. The order of multiplication doesn't matter.
That's why 15*3 is the same as 3*15.
This is because having 15 groups of 3 leads to 3+3+3+...+3 = 45 (imagine adding 15 copies of '3' together), and having 3 groups of 15 gets us 15+15+15 = 45 as well.
Or you could picture a rectangular table that has 15 rows and 3 columns. It has 45 inner cells. If the table had 3 rows and 15 columns, then we'd still have 45 inner cells.
35% = 98
100% = 280
35% of the number is 98 so 100% of the number is 280, you do this by multiplying 100% by 98 and then dividing the number by 35%.
Hello.
1. Understand that this requires inverse trigonometry.
2. For A, we can use sin^-1 if we want (we could use cos^-1 or tan^-1 as well because all sides are given)
Definition of sin^-1 with how it is derived
sin(theta) = O/H <—> sin^-1(O/H)
Angle A: (When calculating an angle, ensure that your calculation is in degree mode instead of radian mode.) 2ND, then QUIT on TI
sin^-1(7/25) = 16.26020471°
(round as needed)
Angle &: (also in degree mode)
All angles of a triangle add to 180°.
1. 180° - (angle B + Angle A) = Angle &
2. 180° - (90° + 16.26020471°) = 73.73979529°
(round as needed)
To quickly check: 16° + 90° + 73° = 180°, as expected for a triangle
From the picture you provided,
The angle values make sense because that triangle represents a 30-60-90 degree triangle. (Also, a good trick is to know that the smallest angle of a triangle will always have the smallest side value, and the largest angle has the largest side value.)
Unless we have an equilateral triangle!
Good luck to you!
Step-by-step explanation:
In this case we have:
Δx = 3/n
b − a = 3
a = 1
b = 4
So the integral is:
∫₁⁴ √x dx
To evaluate the integral, we write the radical as an exponent.
∫₁⁴ x^½ dx
= ⅔ x^³/₂ + C |₁⁴
= (⅔ 4^³/₂ + C) − (⅔ 1^³/₂ + C)
= ⅔ (8) + C − ⅔ − C
= 14/3
If ∫₁⁴ f(x) dx = e⁴ − e, then:
∫₁⁴ (2f(x) − 1) dx
= 2 ∫₁⁴ f(x) dx − ∫₁⁴ dx
= 2 (e⁴ − e) − (x + C) |₁⁴
= 2e⁴ − 2e − 3
∫ sec²(x/k) dx
k ∫ 1/k sec²(x/k) dx
k tan(x/k) + C
Evaluating between x=0 and x=π/2:
k tan(π/(2k)) + C − (k tan(0) + C)
k tan(π/(2k))
Setting this equal to k:
k tan(π/(2k)) = k
tan(π/(2k)) = 1
π/(2k) = π/4
1/(2k) = 1/4
2k = 4
k = 2
