The functions y=x2+cx2 are all solutions of equation: xy′+2y=4x2, (x>0). Find the constant c which produces a solution which also satisfies the initial condition y(10)=2.

Answer:

B

Step-by-step explanation:

Given

[tex]\frac{1}{(t-2)^2}[/tex] = 6 + [tex]\frac{1}{(t-2)}[/tex] ( multiply through by (t - 2)²

1 = 6(t - 2)² + t - 2 ← distribute parenthesis and simplify

1 = 6(t² - 4t + 4) + t - 2

1 = 6t² - 24t + 24 + t - 2

1 = 6t² - 23t + 22 ( subtract 1 from both sides )

6t² - 23t + 21 = 0 ← in standard form

(2t - 3)(3t - 7) = 0 → in factored form

Equate each factor to zero and solve for t

2t - 3 = 0 ⇒ 2t = 3 ⇒ t = [tex]\frac{3}{2}[/tex] ← p

3t - 7 = 0 ⇒ 3t = 7 ⇒ t = [tex]\frac{7}{3}[/tex]  ← q

Thus

p × q = [tex]\frac{3}{2}[/tex] × [tex]\frac{7}{3}[/tex] = [tex]\frac{21}{6}[/tex] = [tex]\frac{7}{2}[/tex] → B

Answer:

8.66 x 10^3

Step-by-step explanation:

8.66 * 1000 (10^3) = 8660

Answer:

2 in

Step-by-step explanation:

Answer:

2 - 2n

Step-by-step explanation

We can use n for the number.

2 - 2(n)

2- 2n

Answer:

2(n-1)

Step-by-step explanation:

Let n be the number

=>2-2n

=>2(n-1)

Answer:

TRUE

Step-by-step explanation:

if the adjacent angles are equal, then they are right angles.

Answer:

p= (9.1 x 10^-31)(2.18 x 10^6)   p = 1.9 x 10^-22kg*m/s

Step-by-step explanation:

for i said so

The momentum of electron is [tex]1.9\times 10^{26}[/tex] kg m per second.

Given, mass of electron is [tex]9.1\times 10^{-31}[/tex] kg.

And its velocity is [tex]2.18 \times 10^6[/tex] m per s.

We have to calculate its momentum.

We know that momentum is numerically equal to the product of mass and velocity of a particle and denoted by p.

So, [tex]p=mv[/tex]

[tex]p= 9.1\times10^{-31}\times2.18\times10^{6}[/tex]

[tex]p=19.838\times10^{25}[/tex]

[tex]p=1.9\times10^{26}[/tex]

Hence the momentum of electron is [tex]1.9\times 10^{26}[/tex] kg m per second.

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Answer:

x=4

Step-by-step explanation:

18 = 3(3x − 6)

Divide each side by 3

18/3 = 3( 3x-6)/3

6 = 3x-6

Add 6 to each side

6+6 = 3x-6+6

12 = 3x

Divide by 3

12/3 = 3x/3

4 =x

Answer: 4 = x

Step-by-step explanation: To solve this equation, we start by

distributing the 3 through the parenthses on the right side.

3(3x) is 9x and 3(-6) is -18.

So our equation now reads 18 = 9x - 18.

Our next step is to get the x term by itself on the right side.

So we add 18 to both sides to get 36 = 9x.

Now divide both sides by 9 to get 4 = x.

Answer:

9.3

Step-by-step explanation:

Step 1: Calculate. We calculate the square root of 87 to be: √87 = 9.32737905308882.

Step 2: Reduce. 9.32.

Step 3: Round. Round 9.32 so you only have one digit after the decimal point to get the answer: 9.3.

Details are missing;

A board of 15 balloons. 4 are purple, 3 red, 4 blue, 2 yellow and 2 green

Answer:

the probability that both the balloons you break are purple = 2/35

Step-by-step explanation:

Since there are 15 balloons and 4 are purple. It means that probability of the first balloon being purple is;

4/15

Now, if the first balloon is purple, it means we have 3 purple left out of the remaining 14. Thus probability of the second being purple = 3/14

Thus;

the probability that both the balloons you break are purple = 4/15 × 3/14 = 2/35

Answer:

The equation is;

T = 87.4 ± 1.5

Maximum value of T = 88.9 °F

Minimum value of T = 85.9 °F

Step-by-step explanation:

We are given the stated temperature as 87.4 °F

Now, we are told that this stated temperature differs from the actual temperature by no more than 1.5 degrees Fahrenheit.

Thus, if the actual temperature is T, it means that T should either be 1.5 more than 87.4 or 1.5 less than 87.4.

Thus the equation is;

87.4 ± 1.5 = T

So maximum value of T = 87.4 + 1.5 = 88.9 °F

While minimum value of T = 87.4 - 1.5 = 85.9 °F

Answer:

left 7 and up 13

Step-by-step explanation:

The translation path of Point A (3, -8) to A'(-4,-5) exists 3 units down and 7 units to the left.

A translation in mathematics does not turn, but rather moves a shape left, right, up, or down. Congruent translations are those in which the translated shapes (or the image) seem to be the same size as the source ones. Just one or more directions have they shifted.

Each point in a figure is moved by the same amount and in the same direction during a translation, a type of transformation.

With a sort of transformation called translation, every point in a figure is moved the same distance in the same direction.

The translation path of Point A (3, -8) to A'(-4,-5) exists 3 units down and 7 units to the left.

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1

GIVE ME BRAINLIEST MY GUY PLZ

1 problem

Because there are 13 problem and if she completed 12 of them yesterday .Only 1 will be left for today.

Answer:

6

Step-by-step explanation:

C=9.2v + 21.2

76.4 = 9.2v + 21.2

76.4 - 21.2 = 9.2v

55.2 = 9.2v

v= 55.2 / 9.2 = 6

Answer:

B) 12.56

Step-by-step explanation:

The formula for circumference of a circle is 2πr.

Substitute r for 2 and it becomes 4π.

4π ≈ 12.56

Answer: is 12.56

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

Answer: Opposite of -53 = -(53) = 53

Step-by-step explanation: An opposite number of n is the exact same number as n on the other side of the number line. the opposite of n is n.

Answer:

106.68 cm

Step-by-step explanation:

Change ft to inches

3.5 ft * 12 inches / 1 ft = 42 inches

Change inches to cm

42 inches * 2.54 cm/ inch =106.68 cm

Answer:

106.68cm

Step-by-step explanation:

divide by feet untill you get inches

Answer:

one half of a plus six times b divided by seven

Step-by-step explanation:

Answer:

Georgette did not complete the factorization; 9 is a composite number.

Step-by-step explanation:

9 can be broken down to 3x3

So it the prime factorization of 72 should be 2x2x2x3x3

Georgette’s error is Georgette should have expressed 8 as 4 × 4, not 2 × 4.

The correct option is D.

The correct prime factorization of 72 is 2³ × 3², which means it can be expressed as the product of prime numbers raised to their respective exponents.

Analyzing the factor tree provided by Georgette, we can see that she made an error when branching from 72 to 8 and 9.

The prime factorization of 8 should be 2³, not 2 × 4, and the prime factorization of 9 should be 3², not 2 × 2.

Therefore, Georgette's error is that she have expressed 8 as 2³ × 1 or 4 × 2, not as 2 × 4.

The correct factor tree for 72 would be:

    72

  /  \

2   36

    / \

   2   18

       / \

      2   9

          / \

         3   3

So, the prime factorization of 72 is 2³ × 3².

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Answer:- 136.9

Step-by-step explanation:

3median=2mean+mode

3(137)=2(137.05)+mode

411=274.1+mode

411-274.1=mode

mode=136.9

Answer: 6 OR 6/1

3         8             24            6

-    x     -    =        _     =       -     OR 6

4          1              4              1

Step-by-step explanation: Hope this helps!  ~Pooch ♥

Answer:

[tex]CD = 15[/tex]

Step-by-step explanation:

Given

[tex]BC = x + 4[/tex]

[tex]CD = 5x[/tex]

[tex]BD = 5x + 7[/tex]

Required

Determine CD

Since Point C is on segment BD, then we have

[tex]BD = BC + CD[/tex]

Substitute x + 4 for BC; 5x for CD and 5x + 7 for BD

[tex]5x + 7 = x + 4 + 5x[/tex]

Collect Like Terms

[tex]5x - 5x - x = 4 - 7[/tex]

[tex]- x = -3[/tex]

Multiply both sides by -1

[tex]x = 3[/tex]

Substitute 3 for x in [tex]CD = 5x[/tex]

[tex]CD = 5(3)[/tex]

[tex]CD = 15[/tex]

Hence, the length of CD is 15 units

Answer:

Step-by-step explanation:

Given

Required

Determine CD

Since Point C is on segment BD, then we have

Substitute x + 4 for BC; 5x for CD and 5x + 7 for BD

Collect Like Terms

Multiply both sides by -1

Substitute 3 for x in  

Hence, the length of CD is 15 units

Step-by-step explanation:

8000647 dollars

Step-by-step explanation:

broggxtxycycuvuh8y7rtwh4w5iwutettixgdbf

Answer: 10 hours

Step-by-step explanation: so if you do 10 times 2.00 it equals 20 dollars or you can divide 20 and 2

Answer:

60-x

Step-by-step explanation:

a number = x

Answer:

With $30, Peter can afford 5 hours

Step-by-step explanation:

Given

Insurance Charge = $7.5

Charges = $4.5 per hour

Required

Determine the number of hours $30 can afford

First, we need to determine the equation.

Total Charges = Charges per hour + Insurance Charge

Substitute values for Charges per hour and Insurance Charge

Total Charges = 4.5 per hour + 7.5

Let the number of hours be n;

So,

Total Charges = 4.5n + 7.5

To calculate Peter's; substitute 30 for total charges

[tex]30 = 4.5n + 7.5[/tex]

Subtract 7.5 from both sides

[tex]4.5n = 30 - 7.5[/tex]

[tex]4.5n = 22.5[/tex]

Divide both sides by 4.5

[tex]n = \frac{22.5}{4.5}[/tex]

[tex]n = 5[/tex]

Hence;

With $30, Peter can afford 5 hours

Answer:

If a = b and b = c, then a = c

Step-by-step explanation:

The transitive property of equality tells us that if we have two things that are equal to each other and the second thing is equal to a third thing, then the first thing is also equal to the third thing.

Answer:

If a = b and b = c, then a = c

Step-by-step explanation:

i got it right on a test

Answer:

  14 cm

Step-by-step explanation:

The applicable formula is ...

  s = rθ

  s = (7 cm)(2) = 14 cm

Answer:

MO = 17

Step-by-step explanation:

First, you need to define what if the unknown x.

segment MN and NO are equal to MO.

thus, your equation for the combination is x +8

Now set the values equal to each other

x + 8 = 3x - 10 (subtract x from both sides)

8 = 2x - 10 ( get your x value alone, add 10 to both sides)

18 = 2x (simplfy)

x = 9

Now plug x value into MO

3 (9) - 10 = 17

Check with opposing equation:

9 + 8 = 17 √