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Allisa [31]
1 year ago
9

15. Higher Order Thinking Nancy made a

Mathematics
1 answer:
Andreas93 [3]1 year ago
8 0

The length of the rectangle is 20 inches, and the width of the rectangle is 4 inches if the table runner has an area of 80 square inches. The length and width of the table runner are whole numbers. The length is 5 times greater than the width.

<h3>What is the area of the rectangle?</h3>

It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.

The formula for finding the area of a rectangle is given by:

Area of rectangle = length × width

The area of the table runner = 80 square inches

Let's assume the length of the rectangle is L and the width is W

Then L = 5×W ...(1)

L×W = 80 ...(2)

Put the value of L in the equation (2)

5W(W) = 80

5W² = 80

W² = 16

W = ±4

Width cannot be negative.

W = 4 inches putting this value in the equation (1)

L = 5(4) = 20 inches

Thus, the length of the rectangle is 20 inches, and the width of the rectangle is 4 inches if the table runner has an area of 80 square inches. The length and width of the table runner are whole numbers. The length is 5 times greater than the width.

Learn more about the area here:

brainly.com/question/14383947

#SPJ1

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A mass of 1 g is set in motion from its equilibrium position with an initial velocity of 6in/sec, with no damping and a spring c
yan [13]

a) y(t)=0.0016 sin(94.9t) [m]

b) 0.033 s

c) -0.152 m/s

Step-by-step explanation:

a)

The force acting on the mass-spring system is (restoring force)

F=-ky

where

k = 9 is the spring constant

y is the displacement

Also, from Newton's second law of motion, we know that

F=my''

where

m = 1 g = 0.001 kg is the mass

y'' is the acceleration

Combining the two equations,

my''=-ky

This is a second order differential equation; the solution for y(t) is

y(t)=A sin(\omega t-\phi)

where

A is the amplitude of motion

\omega=\sqrt{\frac{k}{m}}=\sqrt{\frac{9}{0.001}}=94.9 rad/s is the angular frequency

The spring starts its motion from its equilibrium position, this means that y=0 when t=0; therefore, the phase shift must be

\phi=0

So the displacement is

y(t)=A sin(\omega t)

The velocity of the spring is equal to the derivative of the displacement:

v(t)=y'(t)=\omega A cos(\omega t)

We know that at t = 0, the initial velocity is 6 in/s; since 1 in = 2.54 cm = 0.0254 m,

v_0=6(0.0254)=0.152 m/s

And since at t = 0, cos(\omega t)=1

Then we have:

v_0=\omega A

From which we find the amplitude:

A=\frac{v_0}{\omega}=\frac{0.152}{94.9}=0.0016 m

So the solution for the displacement is

y(t)=0.0016 sin(94.9t) [m]

b)

Here we want to find the time t at which the mass returns to equilibrium, so the time t at which

y=0

This means that

sin(\omega t)=0

We know already that the first time at which this occurs is

t = 0

Which is the beginning of the motion.

The next occurence of y = 0 is instead when

\omega t = \pi

which means:

t=\frac{\pi}{\omega}=\frac{\pi}{94.9}=0.033 s

c)

As said in part a), the velocity of the mass-spring system at time t is given by the derivative of the displacement, so

v(t)=\omega A cos(\omega t)

where we have

\omega=94.9 rad/s is the angular frequency

A=0.0016 m is the amplitude of motion

t is the time

Here we want to find the velocity of the mass when the time is that calculated in part b):

t = 0.033 s

Substituting into the equation, we find:

v(0.033)=(94.9)(0.0016)cos(94.9\cdot 0.033)=-0.152 m/s

4 0
3 years ago
Annie has two jobs. She gets paid $13.04 per hour for tutoring at City College and $9.75 per hour at a coffee shop. Last week sh
Tanzania [10]

Answer:

ahow much did she earn(in dollars)

6 0
2 years ago
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Will positive numbers always have a higher absolute value than negative numbers?
Reika [66]
-I5I=-5 vs. I-5I= 5

The absolute value will stay the same for both negative and positive. The result will change depending on where you put your absolute value signs.
6 0
3 years ago
The pendulum swings at an arc of 30 cm and its successive swings reduced to 10% of the previous swings. What is the total distan
OleMash [197]

Answer:

S_g=  33.333cm

Step-by-step explanation:

From the question we are told that

Arc of 30 cm

10% reduction after each swing

Generally sum of geometric sequence is given by the equation

    S_g=\frac{a(1-r^n)}{1-r}

Mathematically solving for total distance traveled we have

    S_g=\frac{30(1-(0.10^5)}{1-(0.10)}

    S_g=\frac{30}{0.9}

Therefore the total distance traveled  by the pendulum after 5 swings

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3 years ago
3(3 - 8x) - 1 = -6x - 28
Wewaii [24]

Answer:

x=2

Step-by-step explanation:

3(3 - 8x) - 1 = -6x - 28

Distribute

9 -24x -1 = -6x -28

Combine like terms

8 -24x = -6x -28

Add 24x to each side

8-24x+24x = -6x-28+24x

8 = 18x-28

Add 28 to each side

8+28 = 18x-28+28

36 = 18x

Divide each side by 18

36/18 = 18x/18

2 =x

6 0
3 years ago
Read 2 more answers
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