# Find reason and statements

Missing reason/statements:

• R1, R2, R3 - Given
• S4. ∠1 ≅ ∠3
• R4. Transitive property
• R5. Definition of congruence
• S6. m∠1 = 120°
• R6. Substitution

## Related Questions

you drink a beverage with 120 mg of caffeine. Each hour, the amount m of caffine in a persons system decreases by 12%. About how much caffeine will be in your system after 3 hours? Round your answer to the nearest milligram

Step-by-step explanation: multiply 120 x 0.12 and you get 14.4, since it’s 3 hours multiply 14.4 3 times and u get 43.2

Evaluate ∫C ysin(z)ds, where C is the circular helix given by the equations x = cos(t), y = sin(t), z = t, 0 ≤ t ≤ 2π. SOLUTION The formula for a line integral in space gives the following. ∫y sin(z)ds = sin2(t) dt = (sin(t))2√ (cos(t))2 + (sin(t))2 + 1dt = 1 2 (1 - cos(2t))dt = √2 2 =

The line integral is

We have

so the integral reduces to

The line integral ∫C ysin(z) ds over the circular helix C, parametrized by x = cos(t), y = sin(t), z = t for 0 ≤ t ≤ 2π, evaluates to π√2.

To evaluate the line integral ∫C ysin(z) ds over the circular helix C given by x = cos(t), y = sin(t), z = t for 0 ≤ t ≤ 2π, we follow these steps:

1. Parameterize the curve: C is already parameterized as x = cos(t), y = sin(t), z = t.

2. Find the differential ds: ds = √(dx² + dy² + dz²) = √(sin²(t) + cos²(t) + 1)dt = √(1 + 1)dt = √2 dt.

3. Evaluate the integral: ∫C ysin(z) ds = ∫[0, 2π] sin(t) * sin(t) * √2 dt = ∫[0, 2π] sin²(t) * √2 dt.

Now, we'll integrate sin²(t) * √2 with respect to t:

∫ sin²(t) * √2 dt = (1/2) * ∫ (1 - cos(2t)) * √2 dt.

Using the power rule for integration, we get:

(1/2) * [(t - (1/2) * sin(2t)) * √2] | [0, 2π].

Plugging in the limits:

(1/2) * [(2π - (1/2) * sin(4π) - (0 - (1/2) * sin(0))) * √2].

Since sin(4π) = sin(0) = 0:

(1/2) * [(2π - 0 - 0) * √2] = π√2.

So, ∫C ysin(z) ds = π√2.

For more such questions on Line Integral :

brainly.com/question/28525062

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10 and 11.Is this relation a function?у
3
6
7 6 5 4
5
3
2
.
1
.
-2 -1
-1
1 2 3 4
g
6 7
8x
8
-2
-3
Yes, this is a function. It does pass the vertical line test.
No, this is not a function. It does NOT pass the vertical line test.
11
What is the independent variable of the following statement?
Luke
goes to the store to buy some candy, The more money he has, the more candy he will buy.
The amount of candy he buys
The amount of money he has
The store he goes to
The type of money he has

10.Yes
11.Number 3

I hope this helps
Yes it’s a function and A the amount of candy

Pls help im a get my but beat if i don't get my grades up. so plz help me

38 units

Step-by-step explanation:

Counting the fully filled as well as more than half filled as 1 unit, but ignoring the less than half field,

Since, there are no half filled,

Area= Number of fully filled+ Number of more than half filled

=38 units

A 30-ft. ladder makes an angle of 60 degrees with the horizontal when it reaches a given spot on a wall. What angle will a 35-ft. ladder make the horizontal if it reaches the sample spot?

The angle will a 35-ft. ladder make the horizontal if it reaches the sample spot is .

Given that,

A 30-ft. ladder makes an angle of 60 degrees with the horizontal.

We have to find,

The angle will a 35ft.ladder make the horizontal if it reaches the sample spot.

According to the question,

A 30-ft. ladder makes an angle of 60 degrees with the horizontal when it reaches a given spot on a wall.

h = 30sin60

Then, the angle will a 35-ft. ladder make the horizontal if it reaches the sample spot.

Hence, The angle will a 35-ft. ladder make the horizontal if it reaches the sample spot is

brainly.com/question/19515865

So first you must find the height at which the "spot" is where the ladder touches the wall...

sin60=h/30

h=30sin60

Now we can find the angle that the 35 ft ladder make when it touches the same spot.

sinα=h/35  and using h we found earlier...

sinα=(30sin60)/35

α=arcsin[(30sin60)/35]

α≈47.93  (α≈47º55'42")

Write the expression multiply 0.035 times of a power of 10 so that the product is greater than one by less than 100

Step-by-step explanation:

Given the number: 0.035 which has three decimal place

• Case 1:  if we multiply  by 10

=> we have: 0.035*10 = 0.35

Hence, the product 0.35 which is smaller than 1 (we do not accept)

• Case 2:  if we multiply  by 1000

=> we have: 0.035*1000 = 35

Hence, the product 35 which is greater than 1 and less than 100

• Case 3:  if we multiply  by 100

=> we have: 0.035*100= 3.5

Hence, the product 3.5 which is greater than 1 and less than 100

• Case 4:  if we multiply  by 10000

=> we have: 0.035*10000= 350

Hence, the product 350 which is greater than 100 (we do not accept)

Therefore, we have two expression: