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3 years ago

Can uh help me in this

Mathematics

1 answer:

iren2701 [21]3 years ago

4 0

Answer:

Step-by-step explanation:

b) a² - 1 + b(b - 2a) = a² -1 + b*b - b*2a {distributive property}

=a² - 1 + b² - 2ab

= (a² - 2ab + b² ) - 1

= (a - b)² - 1² {use identity x²-y²= (x+ y)(x -y)}

= (a - b + 1)(a -b +1)

b) 15 +8y + y² - 2x - x² = (y² + 8y + 15) - x² - 2x

= (y² + 5y + 3y + 15) - x(x + 2)

= [ y(y + 5) + 3(y +5)] - x(x + 2)

= [(y + 5)(y+3) ] - x(x +2)

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I thought of the number that is between 104 and 140. The number is divisible by 6 and 15. What is my number?

Katena32 [7]

Answer:

120

Step-by-step explanation:

Lets find the numbers multiples of 6 that are in the range from 104-140:

108, 114, 120, 126, 132, 138

Now out of these lets find which is divisible by 15

$\frac{108}{15}=7.2\\\\\frac{114}{15}=7.6\\\\\frac{120}{15}=8\\\\\frac{126}{15}=8.4\\\\\frac{132}{15}=8.8\\\\\frac{138}{15}=9.2$

120 Is the only solution in this set which is also equally divisible by 15, making it the answer.

7 0

1 year ago

If (1)=0, what are all the roots of the function f(x)=x3+3x2-x-3?use the remainder theorem

Anon25 [30]

If $f(1)=0$ , then by the remainder theorem $\dfrac{f(x)}{x-1}$ has a remainder of 0, which means $f(x)$ is divisible by $x-1$ . In fact,

$x^3+3x^2-x-3=x^2(x+3)-(x+3)=(x^2-1)(x+3)=(x-1)(x+1)(x+3)$

So we know 1 is a root, and the other two roots are -1 and -3.

6 0

3 years ago

A tank contains 240 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu

Novosadov [1.4K]

Answer:

$A(t)=240-220e^{-\frac{t}{40}}$

Step-by-step explanation:

A tank contains 240 liters of fluid in which 20 grams of salt is dissolved.

Volume of the tank = 240 liters
Initial Amount of Salt in the tank, A(0)=20 grams

Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min

$R_{in}=$ (concentration of salt in inflow)(input rate of fluid)

$R_{in}=(1\frac{gram}{liter})( 6\frac{Liter}{min})=6\frac{gram}{min}$

$R_{out}=$ (concentration of salt in outflow)(output rate of fluid)

$R_{out}=(\frac{A(t)}{240})( 6\frac{Liter}{min})\\R_{out}=\frac{A}{40}$

Rate of change of the amount of salt in the tank:

$\dfrac{dA}{dt}=R_{in}-R_{out}$

$\dfrac{dA}{dt}=6-\dfrac{A}{40}$

We then solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{40}=6\\$The integrating factor: e^{\int \frac{1}{40}dt} =e^{\frac{t}{40}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{40}}+\dfrac{A}{40}e^{\frac{t}{40}}=6e^{\frac{t}{40}}\\(Ae^{\frac{t}{40}})'=6e^{\frac{t}{40}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{40}})'=\int 6e^{\frac{t}{40}} dt\\Ae^{\frac{t}{40}}=6*40e^{\frac{t}{40}}+C, $(C a constant of integration)\\Ae^{\frac{t}{40}}=240e^{\frac{t}{40}}+C\\$Divide all through by e^{\frac{t}{40}}\\A(t)=240+Ce^{-\frac{t}{40}}$

Recall that when t=0, A(t)=20 (our initial condition)

$20=240+Ce^{-\frac{0}{40}}\\20-240=C\\C=-220\\$Therefore, the number A(t) of grams of salt in the tank at time t\\A(t)=240-220e^{-\frac{t}{40}}$

3 0

3 years ago

The sum of the interior angles of a regular pentangon

natima [27]

Answer:

540

Step-by-step explanation:

ARCHITECTURE The Pentagon in Washington, D.C. is shaped like a regular pentagon. Find the sum of the measures of the interior angles of the largest pentagon-shaped section of the Pentagon building. = 180(3) or 540 Simplify. The sum of the measures of the interior angles is 540.

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2 years ago

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Find the volume in cubic yards - PLSS HELPP AND HURRY PLS

Agata [3.3K]

Answer:

2408.55 cubic yards

Step-by-step explanation:

use pi times radius squared times height, then divide by 3

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2 years ago

Can uh help me in this ​

Can uh help me in this