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3 years ago

Help plzzz...also give steps

Mathematics

2 answers:

erica [24]3 years ago

4 0

The answer is 392 sorry if it’s wrong

geniusboy [140]3 years ago

3 0

Answer:

392π

Step-by-step explanation:

Equation is 1/3(piR^2)*h

Radius is 7, 7 squared is 49.

1/3(49π)(24)

392π

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Devaughn is 15 years older than Sydney. the sum of their ages is 113. what is sydneys age?

NISA [10]

Answer:

Step-by-step explanation:

devaughn= x+15

sydney= x

set an equation adding both their ages

x+x+15=113

2x+15=113

subtract 15 from both sides

2x=98

x=49

sydney is 49

4 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

Please help me (Will give brainliest)

Volgvan

This is very similar to the last question:-

0.51No = No e^_0.0001t

t = ln 0.51 / 0.0001

= 6733 years

6 0

3 years ago

Mark as brainly answerereeere asap

aliya0001 [1]

Answer : 84m^2=A
Photo Shows Solving Steps.

Hope this helps!

~ Penny

5 0

3 years ago

Read 2 more answers

1. The perimeter of a piece of paper is 18 cm.

OlgaM077 [116]

Answer:

a) length = 3 and width = 6

Area of the rectangle = 3 × 6 = 18 cm²

b) length = 7 and width = 2

Area of the rectangle = 7 × 2 = 14 cm²

c) length = 5 and width = 4

Area of the rectangle = 5× 4 = 20 cm²

Step-by-step explanation:

Given perimeter of the paper = 18 cm

we know that the paper has a rectangle shape

The perimeter of the rectangle = 18 cm

2( l + w ) = 18

we choose length = 3 and width = 6

The perimeter of the rectangle = 2( 3+6) = 18 cm

Area of the rectangle = 3 × 6 = 18 cm²

we choose length = 7 and width = 2

The perimeter of the rectangle = 2( 7+2) = 18 cm

Area of the rectangle = 7 × 2 = 14 cm²

we choose length = 5 and width = 4

The perimeter of the rectangle = 2( 5+4) = 18 cm

Area of the rectangle = 5× 4 = 20 cm²

3 0

2 years ago