Answer:
the object is in the air on the time interval (0.24 sec, 6.51 sec)
Step-by-step explanation:
The object is 'in the air' for all t such that h> 0. We need to find the roots of h = -16t^2 + 108t - 25 = 0. From the graph we see that both t values are positive. Once we find them, we subtract the smaller t from the larger t, which results in the length of time the object is in the air.
Use the quadratic formula to find the roots of h(t). The coefficients of t are {-16, 108, -25}, and so the discriminant b^2 - 4ac is
108² - 4(-16)(-25) = 11664 - 1600 = 10064, whose square root is 100.32.
Then the quadratic formula x = (-b ± √[b² - 4ac)/(2a) becomes
-108 ± 100.32 108 ± 100.32
t = ---------------------- = --------------------- = 3.375 ± 3.135
2(-16) 32
or t = 6.51 or t = 0.24 (both times expressed in seconds).
So, again, the object is in the air on the time interval (0.24 sec, 6.51 sec)
<span>12 cm
The solution to this problem requires the Pythagorean theorem which is
a^2 + b^2 = c^2
where
a,b = legs of the right triangle
c = hypotenuse of right triangle
Let's substitute the known values into the equation and solve
a^2 + b^2 = c^2
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 144
b = 12
So the length of the 2nd leg is 12 cm.</span>
Answer:
B: 24
(Sorry if this is wrong i tried my best)
Answer:
Width 2 4 6 8
Area 10 20 30 40
Step-by-step explanation:
Area of a rectangle = length × width
Calculate width when length = 5 inches
When length = 5 inches and width = 2 inches
Area of a rectangle = length × width
A = 5 × 2
= 10 square inches
When length = 5 inches and width = 4 inches
Area of a rectangle = length × width
A = 5 × 4
= 20 square inches
When length = 5 inches and width = 6 inches
Area of a rectangle = length × width
A = 5 × 6
= 30 square inches
When length = 5 inches and width = 8 inches
Area of a rectangle = length × width
A = 5 × 8
= 40 square inches
Given the same length and different width
Width 2 4 6 8
Area 10 20 30 40
The symbols make it hard to solve, but it's still doable.
m = melon
c = coconut
f = flamingo
s = shirt
m - c + 1 = 4
f + f = c
m + s = 15 - 3
8 - m = m
Using the last equation, we can solve for a value of m.
Add m to both sides.
8 = 2m
Divide both sides by 2.
m = 4
The value of m is 4, and so we have one variable done.
m + s = 15 - 3
Replace value of m with 4.
4 + s = 15 - 3
Simplify right side.
4 + s = 12
Subtract 4 from both sides.
s = 8
The value of s is 8, and so we have two variables done.
m - c + 1 = 4
Replace value of m.
4 - c + 1 = 4
Combine like terms.
5 - c = 4
Subtract 5 from both sides.
-c = -1
Multiply all terms by -1.
c = 1
The value of c = 1.
We can now solve the final equation.
f + f = c
Replace value of c.
f + f = 1
Combine like terms.
2f = 1
Divide both sides by 2.
f = 0.5
We have all four variables solved for.
<h3>M, or melon, is equal to 4.</h3><h3>S, or shirt, is equal to 8.</h3><h3>C, or coconut, is equal to 1.</h3><h3>F, or flamingo, is equal to 0.5</h3>
