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tamaranim1 [39]
3 years ago
13

What is a coordinar plane

Mathematics
1 answer:
Mars2501 [29]3 years ago
8 0
The plane<span> determined by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis, intersecting at a point called the origin. Each point in the </span>coordinate plane<span> can be specified by an ordered pair of numbers.</span>
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What is the surface area of the cube with the given edge length, s?
iren [92.7K]
A cube has 6 sides.
 first calculate the area of 1 side  and then multiply it by 6
 

the area for one side = S^2 ( or SxS)

15^2 = 15 x 15  = 225 square inches 

now multiply that by 6:
225 x 6 = 1350 square inches total

the answer is B.
 

8 0
3 years ago
Read 2 more answers
A mass weighing 16 pounds stretches a spring (8/3) feet. The mass is initially released from rest from a point 2 feet below the
mezya [45]

Answer with Step-by-step explanation:

Let a mass weighing 16 pounds stretches a spring \frac{8}{3} feet.

Mass=m=\frac{W}{g}

Mass=m=\frac{16}{32}

g=32 ft/s^2

Mass,m=\frac{1}{2} Slug

By hook's law

w=kx

16=\frac{8}{3} k

k=\frac{16\times 3}{8}=6 lb/ft

f(t)=10cos(3t)

A damping force is numerically equal to 1/2 the instantaneous velocity

\beta=\frac{1}{2}

Equation of motion :

m\frac{d^2x}{dt^2}=-kx-\beta \frac{dx}{dt}+f(t)

Using this equation

\frac{1}{2}\frac{d^2x}{dt^2}=-6x-\frac{1}{2}\frac{dx}{dt}+10cos(3t)

\frac{1}{2}\frac{d^2x}{dt^2}+\frac{1}{2}\frac{dx}{dt}+6x=10cos(3t)

\frac{d^2x}{dt^2}+\frac{dx}{dt}+12x=20cos(3t)

Auxillary equation

m^2+m+12=0

m=\frac{-1\pm\sqrt{1-4(1)(12)}}{2}

m=\frac{-1\pmi\sqrt{47}}{2}

m_1=\frac{-1+i\sqrt{47}}{2}

m_2=\frac{-1-i\sqrt{47}}{2}

Complementary function

e^{\frac{-t}{2}}(c_1cos\frac{\sqrt{47}}{2}+c_2sin\frac{\sqrt{47}}{2})

To find the particular solution using undetermined coefficient method

x_p(t)=Acos(3t)+Bsin(3t)

x'_p(t)=-3Asin(3t)+3Bcos(3t)

x''_p(t)=-9Acos(3t)-9sin(3t)

This solution satisfied the equation therefore, substitute the values in the differential equation

-9Acos(3t)-9Bsin(3t)-3Asin(3t)+3Bcos(3t)+12(Acos(3t)+Bsin(3t))=20cos(3t)

(3B+3A)cos(3t)+(3B-3A)sin(3t)=20cso(3t)

Comparing on both sides

3B+3A=20

3B-3A=0

Adding both equation then, we get

6B=20

B=\frac{20}{6}=\frac{10}{3}

Substitute the value of B in any equation

3A+10=20

3A=20-10=10

A=\frac{10}{3}

Particular solution, x_p(t)=\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)

Now, the general solution

x(t)=e^{-\frac{t}{2}}(c_1cos(\frac{\sqrt{47}t}{2})+c_2sin(\frac{\sqrt{47}t}{2})+\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)

From initial condition

x(0)=2 ft

x'(0)=0

Substitute the values t=0 and x(0)=2

2=c_1+\frac{10}{3}

2-\frac{10}{3}=c_1

c_1=\frac{-4}{3}

x'(t)=-\frac{1}{2}e^{-\frac{t}{2}}(c_1cos(\frac{\sqrt{47}t}{2})+c_2sin(\frac{\sqrt{47}t}{2})+e^{-\frac{t}{2}}(-c_1\frac{\sqrt{47}}{2}sin(\frac{\sqrt{47}t}{2})+\frac{\sqrt{47}}{2}c_2cos(\frac{\sqrt{47}t}{2})-10sin(3t)+10cos(3t)

Substitute x'(0)=0

0=-\frac{1}{2}\times c_1+10+\frac{\sqrt{47}}{2}c_2

\frac{\sqrt{47}}{2}c_2-\frac{1}{2}\times \frac{-4}{3}+10=0

\frac{\sqrt{47}}{2}c_2=-\frac{2}{3}-10=-\frac{32}{3}

c_2==-\frac{64}{3\sqrt{47}}

Substitute the values then we get

x(t)=e^{-\frac{t}{2}}(-\frac{4}{3}cos(\frac{\sqrt{47}t}{2})-\frac{64}{3\sqrt{47}}sin(\frac{\sqrt{47}t}{2})+\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)

8 0
3 years ago
........................
andreyandreev [35.5K]

First expression: (-7)/(-4)

Divide. Note that two negative numbers divided will result in a positive answer

(-7)/(-4) = 7/4 = 1.75

First expression: Greater than 1.

-----------------------------------------------------------------------------------------------------------------

Second expression: -(3/2)

Simplify: 3/2 = 1.5

-(1.5) = -1.5

Second expression: Less than -1

--------------------------------------------------------------------------------------------------------------

Third expression: (-8/5) x (-5/8)

Note that two negatives = one positive answer when multiplying

8/5 x 5/8 = 40/40 = 1

Third expression: Neither

----------------------------------------------------------------------------------------------------------------

Fourth Expression: (-5)/(-3)

Divide: (-5)/(-3) = 5/3 = ~1.67

Fourth Expression: Greater than 1

----------------------------------------------------------------------------------------------------------------

Fifth Expression: (-9)/6

Divide: (-9)/6 = -1.5

Fifth expression: Less than -1

----------------------------------------------------------------------------------------------------------------

hope this helps

5 0
3 years ago
You deposit $7000 into a bank account that has 6% interest compounded SEMIANNUALLY. Determine the amount of money in the bank af
Vlada [557]

Answer:

$11917.03

Step-by-step explanation:

Use Compound Interest Formula:

A = 7,000 (1 + 0.06/2)^2(9)

Simplify:

A = 7,000(1.03)^18

Solve:

A = $11917.03

4 0
3 years ago
2/3 x 6 need help asap​
Mademuasel [1]

Answer:

4

Step-by-step explanation:

3 0
3 years ago
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