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3 years ago

Find the volume of this rectangular prism using V=Bh.

Mathematics

1 answer:

Arisa [49]3 years ago

4 0

Answer:

144

Step-by-step explanation:

5(9)=45

v=bh

v=(45)(3.2)

v=144

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Name the figure below in two different ways. B. N

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3 years ago

A boy throws a ball into the air. The equation h=−16t^2+23t+4 models the path of the ball, where h is the height (in feet) of th

lina2011 [118]

Answer:

0.72secs

Step-by-step explanation:

Given the height of the ball in air modeled by the equation:

h=−16t²+23t+4

Required

Total time it spent in the air

To get this we need to calculate its time at the maximum height

At the maximum height,

v = dh/dt = 0

-32t + 23 = 0

-32t = -23

t = 23/32

t = 0.72secs

Hence the total time it spend in the air will be 0.72secs

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3 years ago

Suppose that y = k * (x - 1/3) ^ 2 is a parabola in the xy -plane that passes through the point (2/3, 1) :Find k and the length

Dennis_Churaev [7]

Answer:

k = 9

length of chord = 2/3

Step-by-step explanation:

Equation of parabola: $y=k (x-\frac13)^2$

Part 1

If the curve passes through point $(\frac23 ,1)$ , this means that when $x=\dfrac23$ , $y = 1$

Substitute these values into the equation and solve for $k$ :

$\implies 1=k \left(\dfrac23-\dfrac13\right)^2$

$\implies 1=k \left(\dfrac13 \right)^2$

Apply the exponent rule $\left(\dfrac{a}{b} \right)^c=\dfrac{a^c}{b^c}$ :

$\implies 1=k \left(\dfrac{1^2}{3^2} \right)$

$\implies 1=\dfrac{1}{9}k$

$\implies k=9$

Part 2

The chord of a parabola is a line segment whose endpoints are points on the parabola.

We are told that one end of the chord is at $(\frac23 ,1)$ and that the chord is horizontal. Therefore, the y-coordinate of the other end of the chord will also be 1. Substitute y = 1 into the equation for the parabola and solve for x:

$\implies 1=9 \left(x-\dfrac13 \right)^2$

$\implies \dfrac19 = \left(x-\dfrac13 \right)^2$

$\implies \sqrt{\dfrac19} = x-\dfrac13$

$\implies \pm \dfrac13 = x-\dfrac13$

$\implies x=\dfrac23, x=0$

Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)

To calculate the length of the chord, find the difference between the x-coordinates:

$\implies \dfrac23-0=\dfrac23$

**Please see attached diagram for drawn graph. Chord is in red**

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2 years ago

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-2.54 is equal to -2 27/50

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