Answer:
- time = 1second
- maximum height = 16m
Step-by-step explanation:
Given the height of a pumpkin t seconds after it is launched from a catapult modelled by the equation
f(t)=-16t²+32t... (1)
The pumpkin reaches its maximum height when the velocity is zero.
Velocity = {d(f(x)}/dt = -32t+32
Since v = 0m/s (at maximum height)
-32t+32 = 0
-32t = -32
t = -32/-32
t = 1sec
The pumpkin reaches its maximum height after 1second.
Maximum height of the pumpkin is gotten by substituting t = 1sec into equation (1)
f(1) = -16(1)²+32(1)
f(1) = -16+32
f(1) = 16m
The maximum height of the pumpkin is 16m
In 2012, the population of a small town was 3,560. The population is decreasing at a rate of 1.7% per year. How can you rewrite an exponential growth ...
Answer: 25 pounds
Step-by-step explanation:
1 pound = 16 oz
400 oz / 16 oz = 25 pounds
I am not a professional, I am simply using prior knowledge!
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Answer:
D. x = 10, m<TRS = 60°
Step-by-step explanation:
m<QRS = 122° (given)
m<QRT = (7x - 8)° (given)
m<TRS = (6x)° (given)
m<QRT + m<TRS = m<QRS (angle addition postulate)
(7x - 8)° + (6x)° = 122° (substitution)
Solve for x
7x - 8 + 6x = 122
Add like terms
13x - 8 = 122
13x = 122 + 8
13x = 130
x = 130/13
x = 10
✔️m<TRS = (6x)°
Plug in the value of x
m<TRS = (6*10)° = 60°
You can solve this either just plain algebra or with the use of trigonometry.
In this case, we'll just use algebra.
So, if we let M be the the point that partitions the segment into a ratio of 3:2, we have this relation:
KM/ML = 3/2
KM = 1.5 ML
We also have this:
KL = KM + ML
Substituting KM,
KL = (3/2) ML + ML
KL = 2.5 ML
Using the distance formula and the given coordinates of the K and L, we get the length of KL
KL = sqrt ( (5-(-5)^2 + (1-(-4))^2 ) = 5 sqrt(5)
Since,
KL = 2.5 ML
Substituting KL,
ML = (1/2.5) KL = (1/2.5) 5 sqrt(5) = 2 sqrt(5)
Using again the distance formula from M to L and letting (x,y) as the coordinates of the point M
ML = 2 sqrt(5) = sqrt ( (5-x)^2 + (1-y)^2 ) [let this be equation 1]
In order to solve this, we need to find an expression of y in terms of x. We can use the equation of the line KL.
The slope m is:
m = (1-(-4))/(5-(-5) = 0.5
Using the general form of the linear equation:
y = mx +b
We substitue m and the coordinate of K or L. We'll just use K.
-5 = (0.5)(-4) + b
b = -1.5
So equation of the line is
y = 0.5x - 1.5 [let this be equation 2]
Substitute equation 2 to equation 1 and solving for x, we get 2 values of x,
x=1, x=9
Since 9 does not make sense (it does not lie on the line), we choose x=1.
Using the equation of the line, we get y which is -1.
So, we get the coordinates of point M which is (1,-1)