Answer:
Graph G
Step-by-step explanation:
The graphs are attached
Given that the oil-well contractor drills a shaft 7 meters deeper into the ground every 2 hours, hence the rate at which the shaft drills = 7 meter / 2 hours = 3.5 meters per hour
Since the drill goes into the ground, hence the rate is negative that is -3.5 meters per secong
The slope (rate of change) of a line (m) is given by:
a) For graph F, the line passes through the point (0,0) and (10, -20). Hence:
b) For graph G, the line passes through the point (0,0) and (10, -70). Hence:
c) For graph H, the line passes through the point (0,0) and (10, -35). Hence:
d) For graph J, the line passes through the point (0,-3.5) and (10, -3.5). Hence:
Answer:
9 inches
Step-by-step explanation:
Do the question algebraically, represented by this equation:
let x be the shorter piece
x + (x + 8) = 26 (longer piece is 8 units longer)
Remove brackets
x + x + 8 = 26 Combine like terms
2x + 8 = 26 Start isolating "x"
2x + 8 - 8 = 26 - 8 Subtract 8 from both sides
2x = 18
2x/2 = 18/2 Divide both sides by 2
x = 9 shorter piece
The shorter piece would be 9 inches.
If you needed the longer piece too:
longer piece = x + 8
x + 8
= 9 + 8
= 17
The longer piece would be 17 inches.
Check your answer:
Longer + Shorter = 26 Substitute the lengths
17 + 9 = 26 Add
26 = 26 same number
LS = RS left side equals right side
The answer is correct.
BC is 10 units and AC is 
units
Step-by-step explanation:
Let us revise the sine rule
In ΔABC:
- AB is opposite to ∠C
- BC is opposite to ∠A
- AC is opposite to ∠B
Let us use this rule to solve the problem
In ΔABC:
∵ m∠A = 45°
∵ m∠C = 30°
- The sum of measures of the interior angles of a triangle is 180°
∵ m∠A + m∠B + m∠C = 180
∴ 45 + m∠B + 30 = 180
- Add the like terms
∴ m∠B + 75 = 180
- Subtract 75 from both sides
∴ m∠B = 105°
∵ 
∵ AB = 
- Substitute AB and the 3 angles in the rule above
∴ 
- By using cross multiplication
∴ (BC) × sin(30) = × sin(45)
∵ sin(30) = 0.5 and sin(45) = 
∴ 0.5 (BC) = 5
- Divide both sides by 0.5
∴ BC = 10 units
∵ 
- Substitute AB and the 3 angles in the rule above
∴ 
- By using cross multiplication
∴ (AC) × sin(30) = × sin(105)
∵ sin(105) = 
∴ 0.5 (AC) = 
- Divide both sides by 0.5
∴ AC = units
BC is 10 units and AC is units
Learn more:
You can learn more about the sine rule in brainly.com/question/12985572
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Answer:
- g(2.95) ≈ -1.8; g(3.05) ≈ -0.2
- A) tangents are increasing in slope, so the tangent is below the curve, and estimates are too small.
Step-by-step explanation:
(a) The linear approximation of g(x) at x=b will be ...
g(x) ≈ g'(b)(x -b) +g(b)
Using the given relations, this is ...
g'(3) = 3² +7 = 16
g(x) ≈ 16(x -3) -1
Then the points of interest are ...
g(2.95) ≈ 16(2.95 -3) -1 = -1.8
g(3.05) ≈ 16(3.05 -3) -1 = -0.2
__
(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)
0.2 is a decimal between 0.25 and 0.125
