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3 years ago

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The sum of three numbers is 96. The third number is 6 less than the first. The second number is 3 times the third. What are the

numbers?

1 answer:

11Alexandr11 [23.1K]3 years ago

6 0

Let the first number be x.

Third number = x - 6

Second number = 3(x - 6) = 3x - 18

Sum of the numbers = 96

x + 3x - 18 + x - 6 = 96

5x -24 = 96

5x = 120

x = 24

Thus,

The first number is 24. The second number is 54. The third number is 18.

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denis23 [38]

Answer:

81000 people went to Bonnaroo.

192000 people went to Lollapalooza.

Step-by-step explanation:

Given:

Total number of people attending festivals, $N=273000$

Number of people attending Lollapalooza is 30,000 more than twice the people attending Bonnaroo.

Unknown:

Number of people attending Lollapalooza and Bonnaroo.

Let the number of people attending Bonnaroo be $x$ .

Therefore, the number of people attending Lollapalooza is equal to $30000+2x$

Evaluate:

Sum of people attending Bonnaroo and Lollapalooza is equal to the total number of people attending the festivals. So,

$x+30000+2x=N\\3x+30000=273000\\3x=273000-30000\\3x=243000\\x=\frac{243000}{3}=81000$

Substitute and Solve:

Now, we have, $x=81000$ .

Substitute 81000 for $x$ and solve for the number of people attending both the festivals. This gives,

Number of people attending Bonnaroo = $x=81000$

Number of people attending Lollapalooza = $30000+2x=30000+2(81000)=30000+162000=192000$

Therefore, 81000 people went to Bonnaroo and 192000 people went to Lollapalooza.

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=5%28sin%28t%29%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%2Bycos%28t%29%29%29%3Dcos%28t%29%20%20%28sin%28

Nataliya [291]

Assuming you mean

$5\sin t\dfrac{\mathrm dy}{\mathrm dt}+5y\cos t=\cos t\sin^2t$

This ODE is linear in $y$ , and you can already contract the left hand side as the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[5y\sin t\right]=\cos t\sin^2t$

Integrating both sides with respect to $t$ yields

$5y\sin t=\displaystyle\int\cos t\sin^2t\,\mathrm dt$
$5y\sin t=\dfrac13\sin^3t+C$
$y=\dfrac1{15}\sin^2t+C\csc t$

Given that $y\left(\dfrac\pi2\right)=9$ , we have

$9=\dfrac1{15}\sin^2\dfrac\pi2+C\csc\dfrac\pi2$
$9=\dfrac1{15}+C$
$C=\dfrac{134}{15}$

so that the particular solution over the interval is

$y=\dfrac1{15}\sin^2t+\dfrac{134}{15}\csc t$

6 0

3 years ago

What is the monomial if a square of a monomial is:1 9/16 a12b6

san4es73 [151]

Answer:

$1\dfrac{1}{4}a^6b^3$

Step-by-step explanation:

A square of a monomial is $1\dfrac{9}{16}a^{12}b^6$ that is $\dfrac{25}{16}a^{12}b^{6}$

Use properties of exponents:

$(a^m)^n=a^{mn}\\ \\\dfrac{a^m}{b^m}=\left(\dfrac{a}{b}\right)^m\\ \\a^mb^m=(ab)^m$

Note that

$\dfrac{25}{16}=\dfrac{5^2}{4^2}=\left(\dfrac{5}{4}\right)^2\\ \\a^{12}=a^{6\cdot 2}=(a^6)^2\\ \\b^6=b^{3\cdot 2}=(b^3)^2$

Then

$\dfrac{25}{16}a^{12}b^{6}=\left(\dfrac{5}{4}\right)^2\cdot (a^6)^2\cdot (b^{3})^2=\left(\dfrac{5}{4}a^6b^3\right)^2$

So, the monomial is

$\dfrac{5}{4}a^6b^3=1\dfrac{1}{4}a^6b^3$

5 0

4 years ago

Simplify the expression <br> 3( 2x - 4) -1n<br><br> pls hurry

lions [1.4K]

Answer:

(3)(2x) + 3 (-4) + - 1n

6x + -12 + - n

Answer -n + 6x - 12

3 0

3 years ago

Find the slope of the tangent line to the graph of x= 5y^3-6y ^2 - 3 at (-4,1)

Zigmanuir [339]

Implicit differentiation

take derivitive of both sides

1=15y^2dy/dx-12ydy/dx
1=dy/dx(15y^2-12y)
divide both sides by (15y^2-12y)
1/(15y^2-12y)=dy/dx

sub the point (-4,1)
1/(15(1)^2-12(1))=dy/dx
1/(15-12)=dy/dx
1/3=dy/dx
slope is 1/3

4 0

4 years ago