f(x) = 4x² + 3x - 2 g(x) = 6x³ - 3x²-4 Find (f +g) (x)​

Answer:

The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]

Step-by-step explanation:

We are given the following differential equation:

[tex]\frac{dP}{dt} = kP - h[/tex]

Solving by separation of variables:

[tex]\frac{dP}{kP-h} = dt[/tex]

Integrating both sides:

[tex]\int \frac{dP}{kP-h} = \int dt[/tex]

On the left side, by substitution, u = kP - h, du = kDp, Dp = du/k. Then

[tex]\frac{1}{k} \ln{kP-h} = t + K[/tex]

In which K is the constant of integration.

[tex]\ln{kP-h} = kt + K[/tex]

[tex]e^{\ln{kP-h}} = e^{kt + K}[/tex]

[tex]kP - h = Ke^{kt}[/tex]

[tex]kP = Ke^{kt} + h[/tex]

[tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]

The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]

Answer:

[tex]3y - 5x +11=0[/tex]

Step-by-step explanation:

Given

[tex]P(x_1,y_1) = (-1,6)[/tex]

[tex]Q(x_2,y_2) = (9,0)[/tex]

Required

The equation of l

First, calculate the slope (m) of PQ

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{0-6}{9--1}[/tex]

[tex]m = \frac{-6}{10}[/tex]

[tex]m = \frac{-3}{5}[/tex]

Since l is perpendicular to PQ, the slope of l is:

[tex]m_2 = -\frac{1}{m}[/tex]

[tex]m_2= -\frac{1}{-3/5}[/tex]

[tex]m_2 = \frac{5}{3}[/tex]

Next, calculate the midpoint of PQ

[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]

[tex]M = \frac{1}{2}(-1+9,6+0)[/tex]

[tex]M = \frac{1}{2}(8,6)[/tex]

[tex]M = (4,3)[/tex]

The equation of l is:

[tex]y = m(x -x_1) + y_1[/tex]

[tex]y = \frac{5}{3}(x -4) +3[/tex]

Multiply through by 3

[tex]3y = 5(x -4) +9[/tex]

Open bracket

[tex]3y = 5x -20 +9[/tex]

[tex]3y = 5x -11[/tex]

Rewrite as:

[tex]3y - 5x +11=0[/tex]

Answer:

How long is the [shirt] in the air? 3 seconds

How many seconds after launching is the t-shirt at 17 feet? 0.25 seconds

Step-by-step explanation:

Formula to represent the shirt's flight path (given): [tex]h=-16t^2+vt+c[/tex], where [tex]h[/tex] is the height of the shirt, [tex]v[/tex] is the initial velocity of the shirt, [tex]c[/tex] is the shirt's starting height, and [tex]t[/tex] is elapsed time since launch.

The function forms a parabola concave down. Since the shirt is caught at 17 feet, we want to second x-coordinate of a point with a y-coordinate of 17 that the function passes through. This is because the shirt was caught going down, not up.

Therefore, let [tex]h=17[/tex]:

[tex]17=-16t^2+52t+5,\\\\-16t^2+52t-12=0,\\\\ y= \frac{-52\pm\sqrt{52^2-4(-16)(-12)}}{2(-16)},\\\\y=\frac{1}{4},\boxed{y=3}[/tex].

The second x-coordinate is the larger of the two and therefore the shirt was in the air for 3 seconds.

However, the first time the shirt reaches a height of 17 feet is on its way up, which occurs at 1/4 or 0.25 seconds (the first x-coordinate). Therefore, the t-shirt reached a height of 17 feet 0.25 seconds after launching.

Answer:

The time required is of 17.53 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per year, compounded monthly.

This is t for which [tex]A(t) = 14000[/tex], considering [tex]P = 7000, r = 0.04, n = 12[/tex]. So

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]14000 = 7000(1 + \frac{0.04}{12})^{12t}[/tex]

[tex](1.0033)^{12t} = 2[/tex]

[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]

[tex]12t\log{1.0033} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]

[tex]t = 17.53[/tex]

The time required is of 17.53 years.

Answer:

30

Step-by-step explanation:

Complementary angles add to 90

x+60 = 90

x+60-60 = 90-60

x = 30

Answer: A

Step-by-step explanation:

Complementary angles sum up to 90 degrees. Thus, we can write that:

90=angle1+angle2

90-angle1=angle2

90-60=angle2

angle2=30

Answer:

[tex]\displaystyle y' = -5(3x-1)^4(4 - x^4)^4(15x^4 - 4x^3 - 12)[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

Derivative Rule [Product Rule]:                                                                                [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:                                                                                    [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

y = (3x - 1)⁵(4 - x⁴)⁵

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

850

Step-by-step explanation:

Given that :

Initial population = 170

Percentage rise in population within 3 years = 400%

Hence, the current population of the town will be ;

Current population = Initial population * (1 + rate)

Current population = 170(1 + 400%)

Current population = 170(1 + 4)

Current population = 170(5)

Current population = 850

QUESTION :- . A board that measures feet long is cut into 6 equal pieces. What is the length of each piece?

A. 1 inches

B. 3 inches

C. 2 inches

D. 9 inches

ANSWER:- 1 FEET -->12 INCH

ATQ ->

1 FEET IS divided into 6 parts so

1 feet = 12 inches

[tex] \frac{1}{6} feet = \frac{12}{6} inches \\ \frac{1}{6} feet = 2 inches [/tex]

so each part will be equal to 2 inches

1 ft = 12 in

12 inch can be devided into 6 equal parts resulting in 2 inches each.

I guess you mistyped either B or C..

hope it helps

kind regards

Alex

Answer:

False

Step-by-step explanation:

Take the point (2, 3)  = (x, y)

Rotated 90º clockwise (3, -2) = (y, -x)

Rotated 90º counter clockwise (-3, 2) = (-y, x)

Neither rotation becomes (-3, -2)

Answer:

The answer is " The sequence converges to infinity. "

Step-by-step explanation:

Given:

[tex]\to a_n=\frac{n^3-n}{n^2+5n}[/tex]

[tex]\lim_{n \to \infty} a_n= \lim_{n \to \infty} \frac{n^3-n}{n^2+5n}[/tex]

                   [tex]= \lim_{n \to \infty} \frac{n(n^2-1)}{n(n+5)}\\\\= \lim_{n \to \infty} \frac{(n^2-1)}{(n+5)}\\\\= \lim_{n \to \infty} \frac{n(n-\frac{1}{n})}{n(1+\frac{5}{n})}\\\\= \lim_{n \to \infty} \frac{(n-\frac{1}{n})}{(1+\frac{5}{n})}\\\\[/tex]

Denominator[tex]= \lim_{n \to \infty} 1+\frac{5}{n}=1+\lim_{n\to \infty} \frac{5}{n}=1+0=1[/tex]

Numerator [tex]=\lim_{n\to \infty}n-\frac{1}{n}=\infty[/tex]

[tex]\therefore\\\\\lim_{n\to \infty}a_n=\frac{\infty}{1} =\infty[/tex]

Answer:

x = 590/11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

50 + x + 10 + 8x + 2x = 650

Step 2: Solve for x

Answer:

x= 590/11

Step-by-step explanation:

Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.

Answer:

M < X + M < Y  < 90

Step-by-step explanation:

Answer:

Set the expression inside the square root greater than or equal to zero. We do this because only nonnegative numbers have a real square root, in other words, we can not take the square root of a negative number and get a real number, which means we have to use numbers that are greater than or equal to zero.

Step 2: Solve the equation found in step 1. Remember that when you are solving equations involving inequalities, if you multiply or divide by a negative number, you must reverse the direction of the inequality symbol.

Step 3: Write the answer using interval notation.

Answer:

= 56.43

Step-by-step explanation:

= 3.42 × 16.5

= 56.43

Answer:

1-90

2-80

3-033

Step-by-step explanation:

Answer:

-6 < y < ∞

Step-by-step explanation:

The range is the values that y can take

y goes from  almost -6 to infinity ( there is an asymptote at -6)

-6 < y < ∞

Answer:

A suitable estimate of all families who own their home is 42%.

Step-by-step explanation:

42% reported that they own their home.

This means that the sample proportion is of 42%. So that an estimate for the percentage of all families who own their home is of 42%., and that the first option is correct.

Answer:

The correct answer is: The survey suffers from undercoverage and may not provide a suitable estimate of homeownership.

Step-by-step explanation:

I just took the review test. The person above me is wrong

Answer:

Step-by-step explanation:

2143.57

Answer:

A U B={1,2,3,4,5,6,7,8,9,10} represents A union B

(includes all the members of set Sand the members of set Bout together, do not repeat anyone that comes twice)

A n B={1,4} represents A interception B( this refers to the members that sets A and B have in common)

Answer:

A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }

Step-by-step explanation:

A = { 1 , 3 , 4 , 5 , 7 , 9 }

B = { 1 , 2 , 4 , 6 , 8 , 10 }

A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }

           It represents the whole numbers between 0 and 11

          [ A ∪ B is the elements of both A and B , without any repetition ]    

A ∩ B = { 1 , 4 }

            It represents the common numbers in both A and B

Answer:

QUALITATIVE DATA-type of data states that every value in the set is a number.

Step-by-step explanation:

QUALITATIVE DATA-type of data states that every value in the set is a number.

Answer:

QUALITATIVE DATA-type of data states that every value in the set is a number.

Step-by-step explanation:

[tex]\begin{aligned} -5x+4y &= 3\\\\ x&=2y-15 \end{aligned}[/tex]

Answer:

x = -1/2 , y = -5/2

x = 4, y = 29

Step-by-step explanation:

y = 2x² - 3

y = 7x + 1

------------------

set equal

2x² - 3 = 7x + 1

Subtract 7x + 1 from both sides

2x² - 7x - 4 = 0

Factor

(2x + 1)(x - 4) = 0

x = {-1/2, 4}

For x = -1/2

y = 7(-1/2) + 1

y = -5/2

(-1/2 , -5/2)

For x = 4

y = 7(4) + 1

y = 29

(4, 29)

Answer:

The correct answer is "168 students".

Step-by-step explanation:

According to the question,

Graduation probability,

[tex]P_g=\frac{1}{4}[/tex]

Major probability,

[tex]P_m=\frac{1}{21}[/tex]

Now,

The probability of having both graduation as well as major will be:

= [tex]\frac{1}{4}\times \frac{1}{21}[/tex]

= [tex]\frac{1}{84}[/tex]

hence,

The number of students having guarantee two graduations throughout the same year and major will be:

⇒ [tex]\frac{x}{84}=2[/tex]

By applying cross-multiplication, we get

⇒ [tex]x = 84\times 2[/tex]

⇒    [tex]=168[/tex]

Answer:

-45 1/2

Step-by-step explanation:

Answer:

300 square feet

Step-by-step explanation:

Area is found by multiplying the length and width of a surface

Answer:

hope it helps you..........

Im sorry but what I got was x=1.5 I don't know if this helps or not.

Answer:

Option C

Step-by-step explanation:

n = 81  

s2 = 625  

H0: σ2 = 500  

Ha: σ2 ≠ 500  

Test Statistics X^2 = (n-1)s^2/ σ2 = (81-1)*625/500

X^2 = 100

P value = 0.0646 for degree of freedom = 81-1 = 80

And X^2 = 100

At 95% confidence interval  

Alpha = 0.05 , p value = 0.0646  

p < alpha, we will reject the null hypothesis

At 95% confidence, the null hypothesis