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ICE Princess25 [194]

3 years ago

13

Patti's Pet Palace has a 90-gallon fish tank. When it needs to be cleaned, it can be drained at a rate of 2 gallons per minute.

Assuming the tank was full, and x represents the number of minutes the tank has been draining, which of the following equations represents the amount of water in the tank after x minutes?
y = 2x + 90

y = 90x - 2

y = 90 - 2x

y = 2x - 90

2 answers:

shtirl [24]3 years ago

8 0

Your answer is <span>y = 90 - 2x
</span>
Hope this helps.

dangina [55]3 years ago

6 0

Y = 90 - 2x

This should be the correct answer

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Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$

Thus, the required solution is

$y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.$

6 0

3 years ago

I need help on my warm up!! pls thx!

xxMikexx [17]

Step-by-step explanation:

$\tt{30.16 = 17.56 + 5x}$

Swap the sides of the equation :

⤑ $\tt{17.56 + 5x = 30.16}$

We want to remove the 17.56 first.

Since the original equation is 17.56 , we are going to use the opposite operation and subtract 17.56 from both sides :

⤑ $\tt{5x + 17.56 - 17.56 = 30.16 - 17.56}$

Simplify. 17.56 - 17.56 = 0 on the left. 30.16 - 17.36 = 12.6 on the right.

⤑ $\tt{5x = 12.6}$

Then, we need to think about how to remove the coefficient 5. Since the opposite of multiplication is division , I am going to divide both sides by 5.

⤑ $\tt{ \frac{5x}{5} = \frac{12.6}{5}}$

Simplify. 5/5 = 1 on the left and 12.6/5 = 2.52 on the right. So, Our answer is x = 2.52.

$\pink{ \boxed{ \boxed { \tt{Our \: final \: answer : \underline{ \underline{ \bold{ \tt{x = 2.52}}}}}}}}$

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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7 0

3 years ago

Identify the horizontal

jonny [76]

Answer:

y=0

Step-by-step explanation:

Hello!

To solve this problem and find the asymptote you must find the value of x, for which F (x) (or y) becomes infinite, for this we solve the equation for X

$y=\frac{3}{5X} \\X=\frac{3}{5y}$

As you can see if Y takes a value of zero, then X would tend to be an infinitely large value so we conclude the horizontal asymptote is y = 0, I also attached the graph!

8 0

3 years ago

What is the measure of ∠C in the figure below

sertanlavr [38]

Answer:

C. 56°

Step-by-step explanation:

An isosceles triangle has two sides that are equal. ∆ABC has two equal sides. Thus, the angles opposite the two sides of an isosceles triangle are also congruent to each other.

<C and <A are congruent to each other.

m<A = 56°, therefore,

m<C = 56°

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3 years ago

5. What is the solution of |3x-3|_<18?

Mrrafil [7]

Answer : D

WORK...
$|3x-3| \leq 18
$

PART 1:
$3x-3 \leq 18
 add 3 on both sides... 3x \leq 21 divide by 3 on both sides... x \leq 7$

PART 2:
$3x-3 \geq -18 add 3 on both sides... 3x \geq -15
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plug both answers together..
$-5 \leq x \leq 7$

8 0

3 years ago