Answer:
- The smaller one is x = 3
- and the larger one is x = 6
Step-by-step explanation:
A "critical number" is a function argument where the function has zero or undefined slope. A polynomial function never has undefined slope, so we're looking for the x-values where f'(x) = 0.
A graphing calculator easily shows the points that have zero slope. They are found at x = 3 and x = 6.
_____
Setting the derivative to zero is another way to find the points with zero slope:
f'(x) = 6x^2 -54x +108 = 6(x^2 -9x +18) = 6(x-3)(x-6)
The derivative will be zero where the factors are zero, at x=3 and x=6.
The critical numbers are x=3 and x=6.
∛(-45) = ∛((-1) × 45) = ∛(-1) × ∛45 = -∛45
Similarly,
∛(-101) = - ∛101
Now,
• 3³ = 27 and 4³ = 64, and 27 < 46 < 64, so ∛27 < ∛45 < ∛64, which places ∛45 between 3 and 4
• 5³ = 125, so ∛101 would similarly fall between 4 and 5
So to summarize, we have
3 < ∛45 < 4 < ∛101 < 5
so that
-5 < ∛(-45) < -4 < ∛(-101) < -3
so the integer between these numbers is -4.
Answer:
A) 315/1005
Explanation:
Total choices: 120 + 255 + 35 + 60 + 200 + 110 + 75 + 150 = 1005
Favorable choices: 255 + 60 = 315
probability:
favorable choices/total choices
315/1005
21/67
Answer:
45,000 is the starting salary with zero sales
.05 is the amount multiplied by the number of sales that is added to her salary
For each sale we add .05 to her salary
Step-by-step explanation:
y = 45,000 +.05x
Rewriting as
y = .05x +45,000
This is in slope intercept form ( y=mx+b) where m is the slope and b is the y intercept
.05 is the slope and 45,000 is the y intercept
45,000 is the starting salary with zero sales
.05 is the amount multiplied by the number of sales that is added to her salary
For each sale we add .05 to her salary
Angle <QAB is =15° because the opposite angles of an isosceles triangle are equal.
The length of the straight line AB = 80cm
<h3>Calculation of angle of a triangle</h3>
The angle at a point = 360°
Angle AQB= 360 - 210° = 150
But the angle that makes up a triangle= 180°
180-150= 30°
But <QAB = <QBA because triangle AQB is an isosceles triangle.
30/2 = 15°
To calculate the length of the straight line the following is carried out using the sine laws.
a/ sina, = b sinb
a= 8cm, sin a { sin 15)
b= ? , sin B = 150
make b the subject formula;
8/sin15= b/sin 150
b= 8 × sin 150/sin 15
b= 80cm
Learn more about isosceles triangle here:
brainly.com/question/25812711
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