Given compound inequality 89 – 9.8t < 10.6 or 89 – 9.8t > 20.4.
Let us solve them one by one.
89 – 9.8t < 10.6
Subtracting 89 from both sides, we get
89-89 – 9.8t < 10.6 - 89
-9.8t < -78.4
Dividing both sides by -9.8, we get
t > 8.
<em>Note: Inequality sign get flip on dividing both side by a negative number.</em>
89 – 9.8t > 20.4
Subtracting 89 from both sides, we get
89-89 – 9.8t < 20.4 - 89
-9.8 t < - 68.6.
Dividing both sides by -9.8, we get
t < 7
<em>Note: Inequality sign get flip on dividing both side by a negative number.</em>
<h3><em> The solution to the inequality 89 – 9.8t < 10.6 is </em>t > 8. </h3><h3> The solution to the inequality 89 – 9.8t > 20.4 is t < 7.</h3>
When the projectile hits the ground:
89 – 9.8t = 0
Subtracting 89 from both sides, we get
89 - 89 – 9.8t = 0 -89.
-9.8t = -89.
Dividing both sides by 9.8, we get
<h3>to the nearest whole second t is about 9 seconds.</h3><h3>Therefore, variable solution set is {t < 7, t > 8, t = 9}.</h3><h3 />
Well, let's first solve each equation:
1.) -4x + 6 - 3x = 12 - 2x - 3x
To start, combine each like-term on each side of the equal sign (The numbers with variables in-common // the numbers alike on the same side of the equal sign):
-7x + 6 = 12 - 5x
Now, we get the two terms with variables attached to them, on the same side, so, we do the opposite of subtraction, which is, addition:
-7x + 6 = 12 - 5x
+5x +5x
_____________
-2x + 6 = 12
Next, you do the opposite of addition, which is, subtraction, and, subtract 6 from both sides:
-2x + 6 = 12
-6 -6
____________
-2x = 6
Finally, divide by -2 on each side, to find out what the value of 'x' is:
-2x = 6
÷-2 ÷-2
________
x = -3
So, the answer is not 'A.'
_________________________________________
Now, we test out the rest of the equations, the exact same way:
2.) 4x + 6 + 3x = 12 + 2x + 3x
Combine your like-terms, on each side of the equal sign:
7x + 6 = 12 + 5x
Now, get both terms, with the variable, 'x,' to the same side, and, to do that, do the opposite of addition, which is, subtraction:
7x + 6 = 12 + 5x
-5x -5x
______________
2x + 6 = 12
Next, subtract 6 from both sides:
2x + 6 = 12
-6 -6
__________
2x = 6
Finally, divide by 2, on both sides:
2x = 6
÷2 ÷2
__________
x = 3
So, the answer is 'B.'
_________________________________________
3.) 4x + 6 - 3x = 12 - 2x - 3x
Again, we combine the like-terms, on both sides of the equal sign:
x + 6 = 12 - 5x
Now, we get both terms with the variable 'x,' to the same side, and, the opposite of subtraction, is addition, so, we're going to add 5x to both sides:
x + 6 = 12 - 5x
+ 5x + 5x
______________
6x + 6 = 12
Now, we subtract 6 from each side, because, the opposite of addition, is subtraction:
6x + 6 = 12
- 6 - 6
_____________
6x = 6
Now, divide by 6, on both sides:
6x = 6
÷ 6 ÷ 6
_____________
x = 1
So, the answer is not 'C.'
_________________________________________
4.) 4x + 6 - 3x = 12x + 2x + 3x
First, we combine the like-terms:
x + 6 = 17x
Next, we get both terms, with the variable, 'x,' to the same side:
x + 6 = 17x
-x -x
_____________
6 = 16x
Now, divide by 16, on both sides:
X = 3/8
So, 'D,' is not the answer.
_______________________
The answer is, 'B.'
I hope this helps!
Part (a)
The radius is r = 42 because OA = 42.
The circumference, aka distance around the circle, is
C = 2*pi*r
C = 2*(22/7)*42
C = 264
We're told that arc AB is 110 mm which is 110/264 = 5/12 of the full distance around the circle.
So we'll apply 5/12 to the full rotation 360 to get (5/12)*360 = 150
<h3>
Answer: 150 degrees</h3>
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Part (b)
Compute the area of the full circle
A = pi*r^2
A = (22/7)*(42)^2
A = 5544
Then take 5/12 of this because we only want 5/12 of the full circle area (to get the area of the shaded pizza slice)
(5/12)*(5544) = 2310
<h3>Answer: 2310 square mm</h3>
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Side note: Both answers are approximate because pi = 22/7 is approximate.
