The graph below plots a function f(x):graph of line segment going through ordered pairs 0,150 and 3, 0
If x represents time, the average rate of change of the function f(x) in the first three seconds is ___.
Answer for Blank 1:
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(0,150) and (3,0)
We can easily solve for the slope.
m = (y2 - y1) / (x2 - x1)
m = (0 - 150) / (3 - 0) = -50
Therefore, the average rate of change of the function in the three seconds is -50.
Answer:
-50
Step-by-step explanation:
The rate of change formula = f(b) - f(a) / b - a
f(b) = the end number (so basically 0 becuase the line ends on the point (3, 0))
f(a) = the start number (so basically 150 becuase the line starts on the point (0, 150)
b = the end time (so basically 3 becuase the line ends on the point (3, 0))
a = the start time (so basically 0 becuase the line starts on the point (0, 150)
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sorry if that is confusing... moving on...
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You would apply these numbers = 0 - 150 / 3 - 0 = -150 / 3 = -50
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This is your rate of change
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I hope this helped :)
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Answers
Answer:
16.65 ft
Step-by-step explanation:
You want the length of the shortest ladder that will reach a building over an 8 ft high fence that is 4 ft from the building.
Similar triangles
As in the attached diagram, we can define the length of segment AX from the fence to the ladder base as 'x'. Then the length of the ladder to the top of the fence is found using the Pythagorean theorem to be ...
BX = √(x² +8²)
The remaining length of the ladder is the hypotenuse of a triangle similar to ∆BAX. The scale factor is DA/AX = 4/x, so the length of the remaining ladder is ...
CB = (4/x)BX = (4/x)√(x² +8²)
Ladder length
The total ladder length is the sum of its parts:
CX = CB +BX
CX = (4/x)√(x² +8²) +√(x² +8²)
CX = (1 +4/x)√(x² +8²)
Minimum length
The minimum length will be that associated with the value of x that makes the derivative of CX be zero. The second attachment shows the derivative of the total length function in terms of generic distances DA=d and BA=h. For this problem, where (d, h) = (4, 8), the derivative is ...
CX' = (1+4/x)x/√(x² +8²) -(4/x²)√(x² +8²)
Expressing this over a common denominator, we have ...
CX' = (x³ -4·8²)/(x²√(x²+8²))
This is zero when ...
x³ -4·8² = 0 ⇒ x = 4∛4 ≈ 6.3496
Total length
Using this value in the ladder length formula above, we find the length of the ladder to be ...
CX = (1 +4/6.3496)√(6.3496² +8²) ≈ 16.64775
The length of the shortest ladder is about 16.65 feet.
Answers
What will the height be at t = 1 second
PLEASE HELP,,STUCK :(
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The water ballon will hit the ground after 1.66447 seconds.
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2)
The height will be 12 feet if t = 1 second.
Final answer:
To find when the balloon hits the ground, set the height function equal to zero and solve using the quadratic formula. The balloon will hit the ground after approximately 1.924 seconds. To find the height at t = 1 second, substitute t = 1 into the height function to get a height of 12 feet.
Explanation:
To find when the water balloon hits the ground, we need to set the height function, h(t), equal to zero and solve for t. In this case, the height function is given by h(t) = -16t^2 + 25t + 3.
Setting h(t) equal to zero, we get:
-16t^2 + 25t + 3 = 0
Using the quadratic formula, t = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = -16, b = 25, and c = 3, we can determine the value of t.
After substituting the values into the quadratic formula and solving for t, we find two values: t ≈ 0.051 seconds and t ≈ 1.924 seconds. Since we are looking for when the balloon hits the ground, we can ignore the first solution and conclude that the balloon will hit the ground after approximately 1.924 seconds.
To find the height at t = 1 second, we can substitute t = 1 into the height function. This gives us:
h(1) = -16(1)^2 + 25(1) + 3 = -16 + 25 + 3 = 12 feet.
Learn more about Quadratic Formula here:
#SPJ11
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5x5z=25z
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It seems that multiplication tables were invented by Pythogore .
Later in the middle ages , a abacus has been invented by a guy who where living near my house : Gerbert d'Aurillac who became pape (Sylvestre 2 ,945-1003).
Answers
Answer:126 grams
Step-by-step explanation: