The dependent variable y is missing in the given differential equation. Proceed as in Example 1 and solve the equation by using the substitution u = y'.
y'' + (y' )^2 + 4 = 0

Answer:

[tex]x_n=7(-3)^{n-1}[/tex]

Step-by-step explanation:

First, write some equations so we can figure out the common ratio and the initial term. The standard explicit formula for a geometric sequence is:

[tex]x_n=ar^{n-1}[/tex]

Where xₙ is the nth term, a is the initial value, and r is the common ratio.

We know that the second and fifth terms are -21 and 567, respectively. Thus:

[tex]a_2=-21\\a_5=567[/tex]

Substitute them into the equations:

[tex]x_2=ar^{(2)-1}\\-21=ar[/tex]

And:

[tex]a^5=ar^{(5)-1}\\567=ar^4[/tex]

To find a and r, divide both sides by a in the first equation:

[tex]r=-\frac{21}{a}[/tex]

And substitute this into the second equation:

[tex]567=a(\frac{-21}{a} )^4[/tex]

Simplify:

[tex]567=a(\frac{(-21)^4}{a^4})[/tex]

The as cancel out. (-21)^4 is 194481:

[tex]\frac{567}{1}=\frac{194481}{a^3}[/tex]

Cross multiply:

[tex]194481=567a^3\\a^3=194481/567=343[/tex]

Take the cube root of both sides:

[tex]a=\sqrt[3]{343} =7[/tex]

Therefore, the initial value is 7.

And the common ratio is (going back to the equation previously):

[tex]r=-21/a\\r=-21/(7)\\r=-3[/tex]

Thus, the common ratio is -3.

Therefore, the equation is:

[tex]x_n=7(-3)^{n-1}[/tex]

Answer:

4.7 =x

Step-by-step explanation:

PQS = PQR + RQS

119 = 72+ 10x

Subtract 72 from each side

119 - 72 = 72+10x -72

47 = 10x

Divide by 10

47/10 = 10x/10

4.7 =x

Answer:  82 sq. units .

Step-by-step explanation:

Let A (9, −1), B (−1, 7), C(−5, 2), D(5, −6) are the vertices of rectangle.

Then we plot them on graph ( as provided in attachment)

Length = AB [tex]=\sqrt{(9+1)^2+(-1-7)^2}[/tex] units  [By distance formula : [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]]

[tex]=\sqrt{(10)^2+(-8)^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}[/tex] units

Width = BC = [tex]\sqrt{(-1+5)^2+(7-2)^2}[/tex] units

[tex]=\sqrt{4^2+5^2}\\\\=\sqrt{16+25}\\\\=\sqrt{41}[/tex]

Area = length x width

= [tex]2\sqrt{41}\times\sqrt{41}=2\times41= 82\text{ sq. units}[/tex]

Hence, the  area of the rectangle is 82 sq. units .

Answer:

12,950

Step-by-step explanation:

drama: 23%

other: 27%

comedy: 20%

23% + 27% + 20% = 70%

70% of 18,500 =

= 0.7 * 18,500

= 12,950

Answer:

Step-by-step explanation:

12x - 2 + 20x - 10 = 180

32x - 12 = 180

32x = 192

x = 6

12*6 - 2

72 - 2 = 70

the solution is b

Look it up then u get the answer

Answer:

hey mate!

kindly see attached picture

hope it helped you:)

Answer:

[tex] \dfrac{df^{1}(16)}{dx} = \pm \dfrac{1}{10} [/tex]

Step-by-step explanation:

[tex] f(x) = x^2 + 4x - 5 [/tex]

First we find the inverse function.

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

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

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

[tex] y^2 + 4y = x + 5 [/tex]

[tex] y^2 + 4y + 4 = x + 5 + 4 [/tex]

[tex] (y + 2)^2 = x + 9 [/tex]

[tex] y + 2 = \pm\sqrt{x + 9} [/tex]

[tex] y = -2 \pm\sqrt{x + 9} [/tex]

[tex]f^{-1}(x) = -2 \pm\sqrt{x + 9}[/tex]

[tex]f^{-1}(x) = -2 \pm (x + 9)^{\frac{1}{2}}[/tex]

Now we find the derivative of the inverse function.

[tex]\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2}(x + 9)^{-\frac{1}{2}}[/tex]

[tex]\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2\sqrt{x + 9}}[/tex]

Now we evaluate the derivative of the inverse function at x = 16.

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{16 + 9}}[/tex]

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{25}}[/tex]

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2 \times 5 }[/tex]

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{10}[/tex]

Answer:

[tex]\Huge \boxed{x=-1}[/tex]

Step-by-step explanation:

[tex]x^2+2x=-1[/tex]

Adding 1 to both sides of the equation.

[tex]x^2+2x+1=-1+1[/tex]

[tex]x^2 +2x+1=0[/tex]

Factoring the left side of the equation.

[tex]x^2 +1x+1x+1=0[/tex]

[tex]x(x+1)+1(x+1)=0[/tex]

[tex](x+1)(x+1) = 0[/tex]

[tex](x+1)^2 =0[/tex]

Taking the square root of both sides of the equation.

[tex]\sqrt{(x+1)^2} =\sqrt{0}[/tex]

[tex]x+1=0[/tex]

Subtracting 1 from both sides of the equation.

[tex]x+1-1=0-1[/tex]

[tex]x=-1[/tex]

Answer:

x = -1

Step-by-step explanation:

[tex]x^2+2x = -1\\=0\\=x^2+2x+1 \\= (x+1)(x+1)\\=(x+1)^2\\\\0 = \sqrt{(x+1)^2} \\= x+1\\\\x+1=0\\x=-1[/tex]

Answer:

The length and width of the parking lot are [tex]\frac{46}{3}[/tex] meters and [tex]\frac{23}{2}[/tex] meters, respectively.

Step-by-step explanation:

The surface formula ([tex]A[/tex]) for the rectangular parking lot is represented by:

[tex]A = w\cdot l[/tex]

Where:

[tex]w[/tex] - Width of the rectangle, measured in meters.

[tex]l[/tex] - Length of the rectangle, measured in meters.

Since, surface formula is a second-order polynomial, in which each binomial is associated with width and length. If [tex]A = 6\cdot x^{2}-19\cdot x -7[/tex], the factorized form is:

[tex]A = \left(x-\frac{7}{2}\,m \right)\cdot \left(x+\frac{1}{3}\,m \right)[/tex]

Now, let consider that [tex]w = \left(x-\frac{7}{2}\,m \right)[/tex] and [tex]l = \left(x+\frac{1}{3}\,m \right)[/tex], if [tex]x = 15\,m[/tex], the length and width of the parking lot are, respectively:

[tex]w =\left(15\,m-\frac{7}{2}\,m \right)[/tex]

[tex]w = \frac{23}{2}\,m[/tex]

[tex]l =\left(15\,m+\frac{1}{3}\,m \right)[/tex]

[tex]l = \frac{46}{3}\,m[/tex]

The length and width of the parking lot are [tex]\frac{46}{3}[/tex] meters and [tex]\frac{23}{2}[/tex] meters, respectively.

Step-by-step explanation:

6 x 1/7 is Less than 1 since 6 x 1/7 is equal to 6/7 in decimal form is 0.8571429.

4 x 4/9 is greater than 1 since 4 x 4/9 is equal to 1 7/9 in decimal form is 1.777...

8 x 1/8 is equal to 1 since 8 x 1/8 is equal to 1.

7 x 1/5 is greater than 1 since 7 x 1/5 is equal to 1 2/5 in decimal form is 1.4

3 x 1/2 is greater than 1 since 3 x 12 is equal to 1 1/2 in decimal form is 1.5

1 x 3/4 is is less than 1 since 1 x 3/4 is equal to 3/4 in decimal form is 0.75

Answer:

x = -1

Step-by-step explanation:

[tex]Midpoint =(1,2)= (x,y)\\J(3,-3)=(x_1,y_1) \:and\:K(x,7)= (x_2,y_2)\\\\x = \frac{x_1+x_2}{2} \\\\1 = \frac{3+x}{2}\\ \\Cross\:Multiply \\2\times 1 = 3+x\\2 =3+x\\2-3=x\\-1=x\\\\x =-1[/tex]

Answer:

[tex] p = \dfrac{I}{rt} [/tex]

Step-by-step explanation:

I = prt

Switch sides.

prt = I

We are solving for p. We want p alone on the left side. p is being multiplied by r and t, so we divide both sides by r and t.

[tex] \dfrac{prt}{rt} = \dfrac{I}{rt} [/tex]

[tex] p = \dfrac{I}{rt} [/tex]

Answer:

Step-by-step explanation:

-7y = -10x - 8

y = 10/7x + 8/7

Answer:

Then angles [tex]\angle B[/tex] and   [tex]\angle C[/tex] both measure [tex]55^o[/tex]

Step-by-step explanation:

Notice that if sides AB and AC are equal, then the angles opposed to them (that is angle [tex]\angle C[/tex] and angle [tex]\angle B[/tex] respectively) have to be equal since equal sides oppose equal angles in a triangle.

So you also know that the addition of the three angles in a triangle must equal [tex]180^o[/tex], then:

[tex]\angle A + \angle B+\angle C= 180^o\\70^o+\angle B + \angle B = 180^o\\2\,\angle B = 180^o-70^o\\2 \angle B=110^o\\\angle B=55^o\\\angle C = 55^o[/tex]

Answer:

Step-by-step explanation:

(b-(a-a)) ÷ 3

a = 6 , b = 3

Substitute the values into the above formula

That's

[tex](3 - (6 - 6)) \div 3[/tex]

Using PEDMAS solve the terms in the bracket first

That's

[tex](3 - 0) \div 3[/tex]

We have

3 ÷ 3

Hope this helps you

Answer:

Step-by-step explanation:

[tex]4 - 2(3 + 2) ^{2} \\ 4 - 2( {5}^{2} ) \\ 4 - 2(25) \\ 4 - 50 = - 46[/tex]

Answer:

(x-4)*(x+5) : x =4,-5

Step-by-step explanation:

a= 1

b= 1

c= -20

x1,2 = (-1+-(1 - (4*1*-20))^0.5)/2

x1,2 = (-1+-(1+80)^0.5)/2

x1,2 = (-1+-(81^0.5))/2

x1,2 =(-1+-9)/2

x1 = 8/2 = 4 x2 = -10/2 = -5

Answer:

What

Step-by-step explanation:

What Do You Mean Bro

There are four levels of measurement – nominal, ordinal, and interval/ratio – with nominal being the least precise and informative and interval/ratio variable being most precise and informative.

solve from here by understanding what i have write

Answer:

[tex] y = 0 [/tex]

Step-by-step explanation:

To find the given asymptote of the given function, [tex] f(x) = \frac{x^2 - 2x + 1}{x^3 + x - 7} [/tex], first, compare the degrees of the lead term of the polynomial of the numerator and that of the denominator.

The numerator has a 2nd degree polynomial (x²).

The denominator has a 3rd degree polynomial (x³).

The polynomial of the numerator has a lower degree compared to the denominator, therefore, the horizontal asymptote is y = 0.

Answer:

a) Sample size need to be greater than 30

b) The probability is approximately 0.0571

Step-by-step explanation:

a) For a normal distribution, the sample size has to be greater than 30. A sample size greater than 30 makes it to be an approximate normal distribution.

b) Given that:

μ = 11.2 minutes, σ = 4.5 minutes, n = 35

The z score determines how many standard deviations the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma} \\For\ a\ sample\ size(n)\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]

For x < 10 minutes

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\ z=\frac{10-11.2}{4.5/\sqrt{35} }= -1.58[/tex]

Therefore from the normal distribution table, P(x < 10) = P(z < -1.58) =  0.0571

The probability is approximately 0.0571

Answer:

100 ounces(hope it help)

Step-by-step explanation:

because there is only 100 ounces in the jar.

Answer:

apples:bananas: strawberries

3     :             6       :         7

Step-by-step explanation:

apples:bananas: strawberries

6              12                  14

Divide each by 2

6/2           12/2               14/2

3                 6                      7

The ratio is

3     :             6       :         7

Answer:

3:6:7  

Step-by-step explanation

The answer is 3:6:7 because if you divide the numbers by 2, you will get a answer of 3, 6, and 7, the simplest form of the ratio.

Hope this helped!

~Emilie Greene

Answer:

Hello! Answer below.

Step-by-step explanation:

The answer to your question is:

18 9/10 or 18.9

Steps below...

You have to do this first.

1. Convert the mixed number to fraction.

2. [tex]7/2[/tex]

Multiplied by

[tex]27/5[/tex]

This will equal, 189/10

If you divide this the answer will be 18 9/10

So the answer is 18 9/10 or 18.9

Hope this helps!

By, BrainlyMagic

Answer:

.= 157

Step-by-step explanation:

There are three clock summing up to 21

One clock=21/3

One clock= 7

There are three calculator summing up to 30

One calculator= 30/3

One calculator= 10

There are three light bulb summing up to 15

One light bulb =15/3

One light bulb= 5

So the problem expression is

Clock +calculator *3bulb

= Clock +(calculator*3bulb)

= 7+(10*3(5))

= 7 +(10*15)

= 7 + 150

.= 157

Answer:

Step-by-step explanation:

Let the amount spent by Tim be x and the amount spent by Nikko be y

If Tim spent $55 more than 2/3 of the amount that Nikko spent for his computer, then amount spent by Tim will be x = 55+2/3 y

Since the total amount that Tim and Nikko spent for their computers was $2,870 then;

x+y = $2,870

Substituting  x = 55+2/3y into the equation above, we will have;

55+2y/3 + y = 2,870

(165 + 2y)/3 + y = 2,870

(165 + 2y+3y)/3 = 2,870

cross multiply

165 + 2y+3y =  3*2870

165+5y = 8610

5y = 8610-165

5y = 8445

y = 8445/5

y = 1689

Hence Nikko spent  a sum of $1,689.00 on his computer.

Divide distance walked by time:

2 1/4 miles / 2/3 hours = 3 3/8 miles per hour

Answer:

Net

Step-by-step explanation:

The definition of "Net Income" is a person's income after deductions and taxes. Hence it is also sometimes know as the "Take-Home" income. i.e the amount of money that you actually take home.

Answer:

1) What is the average score of the student surveyed?

b. 52.5

2) What is the median of the student's surveyed?

52.5

3) How many students were surveyed?

20 students

Step-by-step explanation:

1) What is the average score of the student surveyed?

Average score of the student's been surveyed means we should calculate the mean of the above scores

The formula for Mean = Sum of the number of terms/ Number of terms

Number of terms = 20

Average(Mean score) =

25 + 30 + 35 + 40 + 40 + 45 + 45 + 50 + 50 + 50 + 55 + 55 + 55 + 60 + 60 + 65 + 65 + 70 + 75 + 80/20

= 1050/20

= 52.5

2) What is the median of the student's surveyed?

25, 30, 35, 40, 40, 45, 45, 50, 50, 50, 55, 55, 55, 60, 60, 65, 65, 70, 75, 80

From the above data, we can see that 20 students were surveyed. To find the Median, we find the sum of the 10th value and the 11th value and we divide by 2

Hence,

25, 30, 35, 40, 40, 45, 45, 50, 50,) 50, 55, (55, 55, 60, 60, 65, 65, 70, 75, 80

10th value = 50

11th value = 55

Median = 50 + 55/2

= 105/2

= 52.5

3) How many students were surveyed?

Counting the results of the survey, the number of students that were surveyed = 20 students