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3 years ago

Find the area of the figure. (Sides meet at right angles.)

Mathematics

1 answer:

Anna71 [15]3 years ago

5 0

Given:

A figure.

To find:

The area of the figure.

Solution:

Draw a line and divide the figure it two parts as shown in the below figure.

From the figure it is clear that the line divides the given figure it two rectangles with dimensions 3 yd by 4 yd and 4 yd by 7 yd.

Area of a rectangle is

$Area=Length\times width$

Using this formula, the areas of both rectangles are

$A_1=3\times 4$

$A_1=12$

And,

$A_2=7\times 4$

$A_2=28$

Now, the area of combined figure is

$A=A_1+A_2$

$A=12+28$

$A=40$

Therefore, the area of given figure is 40 sq yd.

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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

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

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3 years ago

How many solutions are there for 4x>8

Anni [7]

Answer:

$\Huge \boxed{X>2}$

Step-by-step explanation:

$\large \textnormal{To solve this problem, first you have to isolate it on one side of the equation.}$

First, divide by 4 from both sides.

$\displaystyle \frac{4x}{4}=\frac{8}{4}$

Solve.

$\displaystyle 8\div4=\boxed{2}$

Therefore, the solutions of 4x>8 is 2.

In conclusion, the correct answer is x=2.

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4 0

4 years ago

Read 2 more answers

A survey was conducted by an independent price checking company to check an advertiser's claim that it had lower prices than its

Mama L [17]

Answer:

a) critical values ≈ -3.182 and 3.182 shows that there is difference in average prices

b) H0 : μd = 0

Ha : μd ≠ 0

Step-by-step explanation:

<u>a) Determine if there is any significant difference in the average prices </u>

using ∝ = 0.05

and μ( advertiser ) - μ ( competitor ) = μd

test statistic ( t ) = -3.011

df = 3

hence the critical values ( two tailed test ) = -3.182 and 3.182. this shows that there is sufficient evidence to show that there is difference in the average prices

<u>b) state the hypothesis</u>

H0 : μd = 0 ( null )

Alternate hypothesis : Ha : μd ≠ 0

5 0

3 years ago

Eliminating by multiplying <br> X+3y=1<br> -5x+4y=-24

gavmur [86]

Answer:

y = -1 x = 4

Step-by-step explanation:

(X+3y=1) 5 Multiply this equation by 5 to cancel out the x

-5x+4y=-24

-5x + 4y= -24

+ 5x + 15y = 5 Add both equations together

19y = -19 Divide both sides by 19

y = -1

Plug -1 for y into one of the equations

x + 3(-1) = 1 Multiply 3(-1)

x - 3 = 1

+ 3 + 3 Add 3 to both sides

x = 4

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3 years ago

A restaurant can seat 100 people. It has booths that seat 4 people and tables that seat 6 people. So far 5of the booths are full

Pachacha [2.7K]

How many booths and tables are there altogether?

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3 years ago