Answer:
Exterior angles are the ones on the outside and same side means they sit on the same side of the bisector so your answer is 1 and 8
Step-by-step explanation:
801= 8.01×10^2
0.0801= 8.01×10^-2
8,010,000= 8.01×10^6
.00000801=8.01×10^-6
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
A because complementary angles means 2 angles that add together to equal 90 degrees and it's possible for both angles to be 45.
<h2>
Greetings!</h2>
Answer:
Option 4
Step-by-step explanation:
Firstly, we need to make the two x's or the two y numbers the same. Lets multiply the second equation by 2:
(2x + 3y = 5 ) * 2 =
4x + 6y = 10
Now, subtract the second equation from the first one:
(4x - y = -11) - (4x + 6y = 10)
4x - 4x = 0
-y - 6y = -7y
-11 - 10 = -21
-7y = -21
Divide both sides by -7:
y = 3
Plug 3 into the first equation as y:
4x - 3 = -11
4x = -11 + 3
4x = -8
x = -2
So x = -2 and y = 3. We need to find one of the options that equals this.
<h3>Option 1)</h3>
-4x - 9y = -21
-10y = -30
40x - 90y = -210
-90y = -270
40x - 0 = 40x
-90y - - 90y = -90 + 90 = 0y
-210 - -270 = -210 + 270 = 60
40x = 60
x = 1.5
We already know this isn't equivalent because the x value is not the x value of the given equation.
<h3>Option 2) </h3>
4x + 3y = 5
2y = -6
_______
8x + 6y = 10
6y = -18
8x - 0 = 8x
6y - 6y = 0
10 - -18 = 10 + 18 = 28
8x = 28
x = 3.5
So we know this isn't equivalent because again, the x value isn't the same as the given equation.
<h3>Option 3</h3>
7x - 3y = -11
9x = -6
-----------
63x - 27y = -99
63x = -42
----------------
63x - 63x = 0
-27y - 0 = -27y
-99 - - 42 = -99 + 42 = -57
-27y = -57
-9y = -19
9y = 19
y = 19/9
So we know this one isn't equivalent as the y value isn't the same as the given equation.
<h3>Option 4</h3>
12x - 3y = -33
14x = -28
x = -28/14 = -2
12(-2) - 3y = -33
-24 - 3y = -33
-3y = -33 + 24
-3y = -9
y = 9/3
y = 3
So x = -2 and y = -3 which is the same as the first equation.
<h2>Hope this helps!</h2>
