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3 years ago

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A rock is thrown upward from a bridge into a river below. The function f(t) = −16???? 2 + 41t + 130 determines the height of the

rock above the surface of the water (in feet) in terms of the number of seconds t since the rock was thrown.

1 answer:

Butoxors [25]3 years ago

7 0

Answer:

The bridge's height above the water is 130 feets.

Step-by-step explanation:

A rock is thrown upward from a bridge into a river below :

$h(t)=-16t^2+41t+130$

Here t is time in seconds

It is required to find the bridge's height above the water. When it reaches the height of the rock above the surface of the water, then :

h(t) = 0

$f(0)=-16t^2+41t+130\\\\f(0)=-16(0)^2+41(0))+130\\\\f(0)=130\ ft$

So, the bridge's height above the water is 130 feets.

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You need 660 mL of a 40% alcohol solution. On hand, you have 35% alcohol mixture. You also have a 95% alcohol mixture. How much

ozzi

Answer:

A. 605 mL of the 35% solution

B. 55 mL of the 95% solution

Step-by-step explanation:

It is given that, you need 660 mL of a 40% alcohol solution. On hand, you have 35% alcohol mixture. You also have a 95% alcohol mixture.

Let x and y be the amount of 35% alcohol solution and 95% alcohol solution (in mL) respectively.

So,

Amount equation: $x+y=660$ ...(1)

Alcohol equation : $0.35x+0.95y=0.40(660)\Rightarrow 0.35x+0.95y=264$ ...(2)

On solving (1) and (2), we get

$0.35(660-y)+0.95y=264$

$231-0.35y+0.95y=264$

$0.6y=264-231$

$y=\dfrac{33}{0.6}$

$y=55$

Now, substitute y=55 in (1).

$x+55=660$

$x=660-55$

$x=605$

Therefore, we need 605 mL of the 35% solution and 55 mL of the 95% solution.

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3 years ago

What expression shows the relationship between the value of any term and n, its position in the sequence for the given sequence?

Nookie1986 [14]

Answer:

B) 2n + 1

Step-by-step explanation:

Each term increases by 2 units so the common difference is 2. Then plug in 1 into the equations that have a slope of 2 and see if you get 3 out. You do for 2n + 1.

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4 years ago

Let A(t)A(t) be the area of a circle with radius r(t)r(t), at time tt in min. Suppose the radius is changing at the rate of drdt

torisob [31]

Answer:

At a point when r = 6 ft

The rate of change of Area with time is given as

(dA/dt) = 36π = 113.1 ft²/min

Step-by-step explanation:

Area of a circle, A = πr²

A = πr²

(dA/dt) = (dA/dr) × (dr/dt)

(dA/dr) = 2πr, (dr/dt) = 3

(dA/dt) = 2πr × 3 = 6πr

At a point when r = 6 ft

(dA/dt) = 6πr = 6π × 6 = 36π = 113.1 ft²/min

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3 years ago

The ground-state wave function for a particle confined to a one-dimensional box of length L is Ψ=(2/L)^1/2 Sin(πx/L). Suppose th

Hitman42 [59]

Answer:

(a) 4.98x10⁻⁵

(b) 7.89x10⁻⁶

(c) 1.89x10⁻⁴

(d) 0.5

(e) 2.9x10⁻²

Step-by-step explanation:

The probability (P) to find the particle is given by:

$P=\int_{x_{1}}^{x_{2}}(\Psi\cdot \Psi) dx = \int_{x_{1}}^{x_{2}} ((2/L)^{1/2} Sin(\pi x/L))^{2}dx$

$P = \int_{x_{1}}^{x_{2}} (2/L) Sin^{2}(\pi x/L)dx$ (1)

The solution of the intregral of equation (1) is:

$P=\frac{2}{L} [\frac{X}{2} - \frac{Sin(2\pi x/L)}{4\pi /L}]|_{x_{1}}^{x_{2}}$

(a) The probability to find the particle between x = 4.95 nm and 5.05 nm is:

$P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{4.95}^{5.05} = 4.98 \cdot 10^{-5}$

(b) The probability to find the particle between x = 1.95 nm and 2.05 nm is:

$P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{1.95}^{2.05} = 7.89 \cdot 10^{-6}$

(c) The probability to find the particle between x = 9.90 nm and 10.00 nm is:

$P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{9.90}^{10.00} = 1.89 \cdot 10^{-4}$

(d) The probability to find the particle in the right half of the box, that is to say, between x = 0 nm and 50 nm is:

$P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{0}^{50.00} = 0.5$

(e) The probability to find the particle in the central third of the box, that is to say, between x = 0 nm and 100/6 nm is:

$P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{0}^{16.7} = 2.9 \cdot 10^{-2}$

I hope it helps you!

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4 years ago

PLEASE HELP ASAP!!

QveST [7]

Answer:

The radius of the circle is 3.5 inches.

Step-by-step explanation:

The radius is half the diameter:R= 1/2 d

Substitute the value of d (7 inches) in the formula to find r:

r= 1/2 x 7 in

r= 3.5 in

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3 years ago

Read 2 more answers