Robert was using a bucket that holds 243.5 ounces (oz) of water when full. The bucket loses 0.3 oz of water per second. After 20 seconds, Robert noticed the leak and plugged the leak. How much water, in ounces, remained in the bucket?

-Note from user: Hello! Could you please help me? I want to learn how to do this in the future so it would be appreciated if u add an explanation to your answer, thanks and please respond before 11:59)

Answer:

[tex]y(x) = 0[/tex]

Step-by-step explanation:

Let P(1) = 0, the differential equation becomes:

y" + 3y' + 2y = 0

Also let y' = my and y'' = m²y

Substitute

m²y+3my+2y = 0

(m²+3m+2)y = 0

The auxiliary equation is expressed as:

m²+3m+2 = 0

Factorize

m²+2m+m+2 = 0

m(m+2)+1(m+2) = 0

(m+1)(m+2) = 0

m+1 = 0 and m+2 = 0

m₁ = -1 and m₂ = -2

Since the value of m is real and distinct, the solution to the differential equation will be expressed as:

[tex]y = C_1e^{m_1x}+C_2e^{m_2x}\\[/tex]

[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\[/tex]

Given the initial condition y(0) = 0

[tex]y(0) = C_1e^{-0}+C_2e^{-2(0)}\\0 = C_1+C_2\\C_1+C_2 = 0 ................. 1[/tex]

If y'(0) = 0

[tex]y'(x) = -C_1e^{-x}-2C_2e^{-2x}\\y'(0) = -C_1e^{-0}-2C_2e^{-2(0)}\\0 = -C_1-2C_2\\C_1-2C_2 = 0...................... 2[/tex]

Solve eqn 1 and 2 simultaneously

From 1:

C₁ = -C₂ .......... 3

Substitute equation 3 into 2:

-C₂-2C₂ = 0

-3C₂ = 0

C₂ = 0

Substitute the constant into the differential equation.

[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\\\y(x) = 0[/tex]

Answer:

B, C, and E

Step-by-step explanation:

B because 0.75*10=7.5. C because 4*0.75=3. And E because 0.75 is how much each snickers bar is is that is the unit price

Answer:

[tex]4x^2-5x+8=0[/tex]

Step-by-step explanation:

[tex]4x^2-3x+9=2x+1[/tex]

We need to get the equation in standard form:

[tex]ax^2+bx+c=0[/tex]

Subtract [tex]2x[/tex] from both sides of the equation:

[tex]4x^2-5x+9=1[/tex]

Subtract [tex]1[/tex] from both sides of the equation:

[tex]4x^2-5x+8=0[/tex]

Answer:

x =  -14

Step-by-step explanation:

Hi there !

36 = - 3(x + 2)

36 = - 3x - 6

3x = - 36 - 6

3x = - 42

x = - 42/3

x = - 14

Good luck !

Answer:

10³                                        

no need to thank me, it was easy

Answer: 23

Step-by-step explanation:

Answer:

4^4×6^2

Step-by-step explanation:

There are four 4's and two 6's

So in exponential form it is 4^4×6^2

Answer:

(0,-7) and (3.5,0) are where your dots will go

Step-by-step explanation:

Answer:

-63k - 45

Step-by-step explanation:

combine like terms

Answer:

-5 degrees (the first one )

Step-by-step explanation:

Divide -10 by 2 to get the number of degrees in F were lowered in one hour like so:

-10 / 2

= -5

Therefore, the temperature dropped 5 degrees in one hour.

Answer:

the answer is 337

Step-by-step explanation:

-236+573=337

Answer:

Tyler and llan scored 24 points.

Explanation:

Another way to state this problem is what is 48% of 50.

"Percent" or "%" means "out of 100" or "per 100", Therefore 48% can be written as

48

100

.

When dealing with percents the word "of" means "times" or "to multiply".

Finally, lets call the number we are looking for "n".

Putting this altogether we can write this equation and solve for n

while keeping the equation balanced:

n=48,100 × 50

n = 24,001,00

n= 24

Step-by-step explanation:

Answer:

I took the test

Step-by-step explanation: Linear pair postulate

m<abc + m<cbd =180°

subtraction property of equality

m<abc -90°

All expression and phrase are filled below.

Here,

We have to filled all expression and phrase.

What is right angled triangle?

A right-angled triangle is a triangle, which has one of its interior angles equal to 90 degree.

Now,

Given that;

⇒ m∠CBD = 90 degree  ….(i)    

We have to prove triangle ABC is right angled triangle.

We can see that the line extends down and perpendicular to the line segment BC at point B.

We can also see that ∠ABC and ∠CBD are supplementary angle.

Hence, We prove as;

         Statement                                                Reason

1) m∠CBD = 90 degree                                        ( Given )

2) ∠ABC and ∠CBD are supplementary.  ( Because ABD is a line and  

                                                                ∠ABC and ∠CBD are linear

                                                                pair)                                                

3). ∠ABC+∠CBD = 180 degree                ( Definition of supplementary)

4) ∠ABC+ 90 = 180 degree                      (  m∠CBD = 90 degree )

5) ∠ABC + 90 - 90 = 180° - 90°            ( subtraction property of equality)

∠ABC = 180° – 90°    (from (i))

∠ABC = 90 degree

6) ∠ABC is a right angle.                     ( Definition of right angle)

7) Δ ABC is a right triangle.                  ( Definition of right triangle)

Therefore, according to definition of right angled triangle,

The triangle ABC is a right angled triangle.

To learn more about right angled triangle visit:

https://brainly.com/question/1248322

#SPJ2

Answer:

Divisible by 3 and 9

Step-by-step explanation:

Answer

multiples of 3 and 9

Step-by-step explanation:

3*12=36

9*3=27

9*4=36

Answer:

D and E

Step-by-step explanation:

It is acute because all angles are under 90 degrees. This means that it cannot be F, obtuse. It cannot be A because A scalene triangle is a triangle in which all three sides have different lengths. It cannot be B either because it has 3 sides of equal angles. It cannot be right because non of the angles are 90 degrees. It is equilateral.

Hope this helps.

Answer:

2.02857142857

Step-by-step explanation:

Answer

20 students will take biology, 10 take Integrated Science and 10 take both

Step-by-step explanation:

With Venn diagrams it's best you work from the inside out. With that in mind we know 10 students take both Biology and Integrated Science. In Biology there are 30 total students including the ones that also take both sciences. So we subtract the ones that take both and get 20 students taking only biology. After that there's 30 students total, subtract that from 40, the total number of students and you get 10, the amount of students who take Integrated Science

Answer:

-2

Step-by-step explanation:

x-1(-7)=5

x+7=5

-7 bot sides

-2

Answer:

0

Step-by-step explanation:

5(x+3) replace x with -3

5(-3+3)

5(0)

0

Answer:

3y^2+2y

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

roughly 3%

Step-by-step explanation:

Answer:

about 34.9%

Step-by-step explanation:

I could be wrong on this, but by multiplying his profit per month by 12, and his electricity cost by 12, then you get his yearly profit and cost of electricity. Then, you divide the profit by electricity and wa la you get 34.9%.

PLZ mark me brainliest!!!! :)))))

Answer:

1.25

Thanks,

SunshineMadison101

Answer:

y - 1 = (-2/3)(x + 9)

Step-by-step explanation:

Here you are given a point on a line and the slope of the line.  You'll need to apply the "point-slope" formula

y - k = m(x - h) (Memorize this)

Then m = slope = -2/3, h = -9 and k = 1.

Making the appropriate substitutions, we get:

y - 1 = (-2/3)(x + 9)

Answer:X=14,/ integers are-14,16,18,20

Step-by-step explanation:

Answer: 5b-8

Step-by-step explanation: