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2 years ago

A library has 12,500 fiction books and 19,000 nonfiction books.

Mathematics

1 answer:

valentina_108 [34]2 years ago

7 0

Answer:

1,260 books (or C)

Step-by-step explanation:

1. 2/5 of fiction (12,500) are out, so 5,000 are out

2. 2/5 of non-fiction (19,000) are out, so 7,600 are out

3. Total books checked out are 12,600

4. 1/10 of checked out books are due this week, so 1,260 books (10%)

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Find the distance between 2-4i and d 6+i

liq [111]

Answer:

7.211

Step-by-step explanation:

-For two points in the complex plane, the distance between the points is the modulus of the of the difference of the two complex numbers.

-Point 2-4i has the coordinates (2,-4)

-Point 6+i has the coordinates (6,1)

#We must find the distance between the two coordinates (2,-4) and (6,1):

$=\sqrt{(6-2)^2+(1--4)^2}\\\\=\sqrt{4^2+6^2}\\\\=\sqrt{52}\\\\=7.211$

Hence, the distance between the two points is 7.211

8 0

2 years ago

An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work (in J) needed to pump half of the water out of the

Nitella [24]

Answer:

$W=2452.5 J$

Step-by-step explanation:

The work is define as the integral of the force times distance. So we have:

$W=\int^{a}_{b}Fxdx$

Now, we can write the force in terms of density.

$F=m*g=\rho Vg$

V is the volume (V=2*1*1=2 m³)

So the work will be:

$W=\int^{0.5}_{0} 2*1000*9.81*xdx=\int^{0.5}_{0} 2*1000*9.81*xdx=\int^{0.5}_{0}19620xdx=19620(\frac{x^{2}}{2})|^{0.5}_{0}$

The limit of integration is between 0 and 0.5 because we want to pump half of the water out of the aquarium.

$W=19620(\frac{x^{2}}{2})|^{0.5}_{0}=19620(\frac{0.5^{2}}{2})$

$W=2452.5 J$

I hope it helps you!

8 0

2 years ago

Emelio wants to solve this equation. x 5 = 35 Help him follow the steps to finish solving for x. 1. Multiplication property of e

antiseptic1488 [7]

Answer: 175

Step-by-step explanation

3 0

2 years ago

Read 2 more answers

Section 5.2 Problem 17:

Elina [12.6K]

This DE has characteristic equation

$4r^2 - 12r + 9r = (2r - 3)^2 = 0$

with a repeated root at r = 3/2. Then the characteristic solution is

$y_c = C_1 e^{\frac32 x} + C_2 x e^{\frac32 x}$

which has derivative

${y_c}' = \dfrac{3C_1}2 e^{\frac32 x} + \dfrac{3C_2}2 x e^{\frac32x} + C_2 e^{\frac32 x}$

Use the given initial conditions to solve for the constants:

$y(0) = 3 \implies 3 = C_1$

$y'(0) = \dfrac52 \implies \dfrac52 = \dfrac{3C_1}2 + C_2 \implies C_2 = -2$

and so the particular solution to the IVP is

$\boxed{y(x) = 3 e^{\frac32 x} - 2 x e^{\frac32 x}}$

8 0

1 year ago

Evaluate y = 7x when x = -5

borishaifa [10]

Answer:

-35

Step-by-step explanation:

7 x -5 = -35

hope this helped!! ^^

5 0

2 years ago