Answer: Δx = 0.5
Step-by-step explanation:
We have the interval:
[−3, −1]
and we partition it into 4 equal intervals.
first, the range of our interval is equal to the difference between the extremes, this is:
-1 - (-3) = -1 + 3 = 2
Then, if we divide it into 4, we have 4 segments with a range of:
2/4 = 0.5
Then the subinterval delta is 0.5, and the 4 intervals are:
[−3, -2.5], [−2.5, −2], [−2, −1.5], [−1.5, −1]
Answer:
six and eight hundred fourty-seven thousandths
Step-by-step explanation:
6 + 0.8 + 0.04 + 0.007 is called extended form, six and eight hundred fourty-seven thousandths is called word form.
Length of deck is 40 feet
<h3><u><em>Solution:</em></u></h3>
Sam wants the deck to have an overall perimeter of 60 feet
Perimeter of rectangular deck = 60 feet
Let "L" be the length of rectangle and "W" be the width of rectangle
Given that plans for a rectangular deck call for the width to be 10 feet less than the length
Width = length - 10
W = L - 10 ------ eqn 1
<em><u>The perimeter of rectangle is given as:</u></em>
perimeter of rectangle = 2(length + width)
Substituting the known values we get,
60 = 2(L + L - 10)
60 = 2(2L - 10)
60 = 4L - 20
80 = 4L
L = 20
Thus the length of deck is 20 feet
Answer:
see below
Step-by-step explanation:
<h3>Given</h3>
- Distance is 142.2 m, correct to 1 decimal place
- Time is 7 seconds, correct to nearest second
<h3>To find:</h3>
- Upper bound for the speed
<h3>Solution </h3>
<em>Upper bound for the speed = upper bound for distance/lower bound for time</em>
- Upper bound for distance = 142.25 m (added 0.1/5 = 0.05)
- Lower bound for time = 6.5 seconds (subtracted 1/2 = 0.5)
<u>Then, the speed is:</u>
- 142.25/6.5 = 21.88 m/s
- 21.88 = 21.9 m/s correct to 1 decimal place
- 21.88 = 22 m/s correct to nearest m/s
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• 1 + cot² x = csc²x and csc x = 
• sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Consider the left side
sin²Θ( 1 + cot²Θ )
= sin²Θ × csc²Θ
= sin²Θ × 1 / sin²Θ = 1 = right side ⇔ verified
-----------------------------------------------------------------
Consider the left side
cos²Θ - sin²Θ
= cos²Θ - (1 - cos²Θ)
= cos²Θ - 1 + cos²Θ
= 2cos²Θ - 1 = right side ⇒ verified
