To solve this problem, we must do a method of trial and error to find
for the next highest integer with exactly three factors. We know that the value
of k must be greater than 4, therefore by using trial and error to find for the
correct answer:
Factors of 5:1, 5
Factors of 6:1, 2, 3, 6
Factors of 7:1, 7
Factors of 8:1, 2, 4, 8
Factors of 9:1, 3, 9
Therefore we stop at 9 since this is already our answer. It has exactly
three factors.
The sum of the factors is:
sum of factors = 1 + 3 + 9
<span>sum of factors = 13</span>
About 4.1 seconds. How long was the ball in the air? We are told that t represents time in seconds since the ball was thrown, so it started to be 'in the air' at t = 0 To answer the question, then, we need to know the time when it stopped being in the air. We are told that the ball hit the ground. So that's what happened when it stopped being airborne. We need to relate that event to the mathematics we're working with. What can we say about h , the height of the ball when the ball hits the ground? Answer: The height will be 0 when the ball stops being in the air. Now translate this back to the mathematics: The ball is in the air from t = 0 until the time t when h = 0 . Find the time t that makes h = 0 . That means: solve: − 5 t 2 + 20 t + 2 = 0 We can solve this by solving: 5 t 2 − 20 t − 2 = 0 (Either multiply both sides of the equation by − 1 , or add 5 x 2 − 20 x and − 2 to both sides and then re-write it the other way around) That's a quadratic equation, so try to factor first. But don't spend too much time trying to factor, because not every quadratic is easily factorable and that's OK, because we still have the quadratic formula if we need it. We do need it. t = − ( − 20 ) ± √ ( − 20 ) 2 − 4 ( 5 ) ( − 2 ) 2 ( 5 ) = 20 ± √ 440 10 = 20 ± √ 4 ( 110 ) 10 = 20 ± 2 √ 110 10 = 2 ( 10 ± √ 110 ) 2 ( 5 ) = 10 ± √ 110 5 We can see that 10 < √ 110 < 11 . In fact ( 10 + 1 2 ) 2 = 10 2 + 10 + 1 4 = 110.25 Using 10.25 as an approximation for √ 110 , we get : for the solution t = 10 − √ 110 5 we'll get a negative t . That doesn't make sense. The other solution gives t ≈ 10 + 10.25 5 = 20.5 5 = 4.1 seconds. So the ball was in the air from t = 0 until about t = 4.1 . The elapsed time is the difference, 4.1 seconds.
Answer:
75 ft / none of these (43)
Step-by-step explanation:
formula: (area =1/2bh)
so you take base × height and then take half of that number (divide by 2)
Answer
<em>A</em><em>s</em><em>s</em><em>a</em><em>l</em><em>a</em><em>m</em><em> </em><em>w</em><em>a</em><em>l</em><em>i</em><em>a</em><em>k</em><em>u</em><em>m</em><em> </em>
The distance between both lines is 2.24 units
Step-by-step explanation:
There is no straight method to find the distance between two lines. The distance can be found out by finding a point on one line and then finding the distance of that point from the other line. The y-coordinate of point is obtained by putting any value of x in equation . The x and y combined give us the point.
Given
We have to find the distance of this point from y=2x+5
The formula for finding distance of a point (x,y) from a line is:
A=2
B=-1
C=5
Putting the values in the formula
Rounding off will give: 2.24 units
The distance between both lines is 2.24 units
Keywords: Equations of lines
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