A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h = -16t² +90t gives the height h of the ball after t seconds.
a Explain what the a, b, &c mean in this problem.
b. How many seconds will it take for the ball to reach the ground?​

The derivative of y = ln(x√(x² - 6)) is

\(dy/dx = [(x^2 - 6)^{(1/2) }+ x^2] / [(x^2 - 6)^{(1/2)}(x^2 - 6)].\)

The derivative of the function y = ln(x√(x^2 - 6)), we can use the chain rule.

\(y = ln((x(x^2 - 6)^{(1/2)})).\)

1. Differentiate the outer function: d/dx(ln(u)) = 1/u * du/dx, where u is the argument of the natural logarithm.

2. Let \(u = (x(x^2 - 6)^{(1/2)})\).

3. Find du/dx by applying the product and chain rules:

Differentiate x with respect to x,

\(du/dx = (1)(x^2 - 6)^{(1/2)} + x(1/2)(x^2 - 6)^{(-1/2)}(2x)\)

Simplifying,\(du/dx = (x^2 - 6)^{(1/2)} + x^2/(x^2 - 6)^{(1/2)}\)

4. Substitute u and du/dx back into the chain rule:

\(dy/dx = (1/u) * (x^2 - 6)^{(1/2)} + x^2/(x^2 - 6)^{(1/2)\)

Therefore, the derivative of y = ln(x√(x² - 6)) is

\(dy/dx = [(x^2 - 6)^{(1/2)} + x^2] / [(x^2 - 6)^{(1/2)}(x^2 - 6)].\)

To know more about chain rule refer here

https://brainly.com/question/30764359#

#SPJ11

There are 846720 different values possible for the sum of xyx and yxy.

Let's denote the three digits of xyx as a, b, and c, such that xyx = 100a + 10b + c, and the three digits of yxy as d, e, and f, such that yxy = 100d + 10e + f. Note that x and y are distinct non-zero digits, so a, b, c, d, e, and f are all distinct non-zero digits.

The sum of xyx and yxy is (100a + 10b + c) + (100d + 10e + f), which simplifies to 100(a+d) + 20(b+e) + (c+f).

We want to find how many different values are possible for the sum. Since a, b, c, d, e, and f are all distinct non-zero digits, we can consider each of them separately.

For a given value of a, there are 9 choices for d (since d cannot be equal to a), and once we have chosen d, there are 8 choices for e (since e cannot be equal to either a or d). Similarly, there are 7 choices for f (since f cannot be equal to a, d, or e).

So, for a fixed value of a, the number of possible values of the sum is the number of possible values of (100(a+d) + 20(b+e) + (c+f)), which is simply the number of possible values of (20(b+e) + (c+f)), since 100(a+d) is fixed.

There are 8 choices for b (since b cannot be equal to a), and once we have chosen b, there are 7 choices for c (since c cannot be equal to either a or b). Similarly, there are 6 choices for e (since e cannot be equal to either a, d, or b), and 5 choices for f (since f cannot be equal to either a, d, e, or c).

Therefore, the total number of possible values of the sum is:

9 × 8 × 7 × 8 × 7 × 6 × 5 = 846720

Therefore, there are 846720 different values possible for the sum of xyx and yxy.

Learn more about non-zero digits

https://brainly.com/question/13246806

#SPJ4

Answer:

Okay!

Notable things in the problem:

2011 minutes AFTER the beginning of January 1rst.

12:00AM will be our starting time, because that's when January 1rst begins.

It'll be a bit easier to work with if we convert the 2011 minutes into hours.

So take 2011 minutes and divide it by 60 to get the number of hours.

2011 / 60 = 33 hours and 31 minutes

You wouldn't be able to easily get the exact number of minutes from a calculator. You'll need to use long division. The remainder will be the number of minutes. If you want to check you can multiply the number of hours by 60 and add 31 to the product. If it doesn't equal 2011 minutes then something is amiss.

12:00 AM

Since we know this is a 24 hour clock we can subtract 24 from our number of hours. (Just remember that this is the next day)

12:00 AM with 9 hours and 31 minutes left.

9:31 AM a day later is our time!

Step-by-step explanation:

The triangles SAT and SAO are congruent by the Side-Angle-Side (SAS) congruence theorem.

The Side-Angle-Side congruence theorem states that if any of the two sides on a triangle are the same, along with the angle between them, then the two triangles are congruent.

For the triangles SAT and SAO in this problem, we have that:

The common angle are between the common sides, hence the SAS congruence theorem was used to determine the congruence of the two triangles.

More can be learned about congruence theorems at https://brainly.com/question/3168048

#SPJ1

A relation R  is a subset of the Cartesian product. Or simply, a bunch of points (ordered pairs). In other words, the relation between the two sets is defined as the collection of the ordered pair, in which the ordered pair is formed by the object from each set.

a group of some elements of the input set which are passed to a function to obtain some elements of the output set. It is the inverse of the Image. It is denoted as;

f: X → Y.

N be the set of Natural numbers and the relation R be defined as;

R = {(a ,b) : b=a2, a ,b ∈ N}. State whether R is a relation function or not.

From the relation R = {(a ,b) : b=a2, a ,b ∈ N}, we can see for every value of natural number, their is only one image. For example, if a=1 then b =1, if a=2 then b=4 and so on.

Therefore, R is a relation function here.

f:A→B, and D⊆B, the preimage  D of under  f is defined as

\(f^-1\)(D)={x ∈ A∣ f(x)∈D}.(5.4.5)

Hence, \(f^-1\)(D) is the set of elements in the domain whose images are in C. The symbol \(f^-1\)(D) is also pronounced as “f inverse of D.”

To know more about preimage visit brainly.com/question/29001984

#SPJ4

Answer:

solution,                                                                                                                                     cp=Rs150                                                                                                                                        profit=Rs12                                                                                                                              Now,                                                                                                                                                   profit percent=profit% of cp                                                                                              or,profit percent=12/100 x Rs150                                                                                                Therefore,profit percent =18%

Step-by-step explanation:

Answer:

8%

Step-by-step explanation:

We know that

Profit% = Profit/CP × 100

=> 12/150 × 100

=> 12/15 × 10

=> 4/5 × 10

=> 8%

The length of side b is 56m, angle A is 45°, and angle C is 67°.

In the given triangle with side lengths a = 74m, b ≈ 56m, and c = 36m, the length of side b is approximately 56m.

To solve the triangle, we can use the Law of Cosines and the fact that the sum of angles in a triangle is 180 degrees. Given angle B = 67°51', we have:

Using the Law of Cosines, we have:

b² = a² + c² - 2ac * cos(B)

Substituting the known values:

b² = 74² + 36² - 2 * 74 * 36 * cos(67°51')

Calculating the value of b:

b ≈ √(74² + 36² - 2 * 74 * 36 * cos(67°51'))

b ≈ 55.92m (rounded to the nearest whole number, b ≈ 56m)

Using the Law of Cosines again, we have:

cos(A) = (b² + c² - a²) / (2 * b * c)

Substituting the known values:

cos(A) = (56² + 36² - 74²) / (2 * 56 * 36)

Calculating the value of A:

A = cos⁻¹((56² + 36² - 74²) / (2 * 56 * 36))

A ≈ 45° (rounded to the nearest whole number)

Using the fact that the sum of angles in a triangle is 180 degrees:

C = 180° - A - B

Substituting the known values:

C ≈ 180° - 45° - 67°51'

Calculating the value of C:

C ≈ 67°9' (rounded to the nearest whole number, C ≈ 67°)

Therefore, in the given triangle, the length of side b is approximately 56m, angle A is approximately 45°, and angle C is approximately 67°.

Learn more about the Law of Cosines

brainly.com/question/17289163

#SPJ11

When standardizing scores, the standard deviation will always be 1.

The Correct option is B.

As, the standardization involves transforming the scores to have a mean of 0 and a standard deviation of 1 in the new distribution.

By subtracting the mean and dividing by the standard deviation, we rescale the scores to represent how many standard deviations they are away from the mean.

Since the transformed scores will be in units of standard deviations, the standard deviation is standardized to 1 to maintain consistency in the new distribution. This allows for easier comparison and interpretation of the scores across different variables or distributions.

Thus, the standard deviation will always be 1.

Learn more about Standard Deviation here:

https://brainly.com/question/13498201

#SPJ4

The probability that the paint on a sample of 65 test panels will have a mean life before corrosive failure of less than 144 hours is approximately 0.0005 or 0.05%.

To find the probability that the paint on a sample of 65 test panels will have a mean life before corrosive failure of less than 144 hours, we will use the Central Limit Theorem (CLT). The CLT states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population distribution.

Given:
- Mean life before corrosive failure (μ) = 155 hours
- Standard deviation (σ) = 27 hours
- Sample size (n) = 65 test panels
- Target mean life before corrosive failure (x) = 144 hours

First, we need to calculate the standard error (SE) of the sample mean:

SE = σ / √n = 27 / √65 ≈ 3.343

Next, we will calculate the z-score for the target mean life of 144 hours:

z = (x - μ) / SE = (144 - 155) / 3.343 ≈ -3.293

Now, we will use the standard normal distribution table or a calculator to find the probability that the sample mean life is less than 144 hours:

P(z < -3.293) ≈ 0.0005

Learn more about probability here: brainly.com/question/11234923

#SPJ11

x2 = -2.0000. In this way, we get x2, the second approximation to the root of the equation using Newton's method with an initial approximation x1 = −2.

Newton's method is one of the numerical methods used to estimate the root of a function.

The following are the steps for using Newton's method:

Let the equation f (x) = 0 be given with an initial guess x1, and let f′(x) be the derivative of f(x).

Determine the next estimate, x2, by using the formula x2 = x1 - f (x1) / f'(x1).

Therefore, the given equation is x³ + x + 6 = 0.

Let us use Newton's method to solve the given equation. We have x1 = -2, which is the initial approximation.

Therefore, f(x) = x³ + x + 6, and f'(x) = 3x² + 1.

To find x2, the second approximation to the root of the equation, we need to substitute the values of f(x), f'(x), and x1 into the formula x2 = x1 - f (x1) / f'(x1).

Substituting the given values in the above equation we get, x2 = x1 - f (x1) / f'(x1) = -2 - (-2³ - 2 + 6) / (3(-2²) + 1) = -2 - (-8 - 2 + 6) / (3(4) + 1) = -2 - (-4) / 13 = -2 + 4 / 13 = -26 / 13

To Know more about derivative visit:

https://brainly.com/question/29144258

#SPJ11

Answer:

Im guessing it would be a positive change

Step-by-step explanation:

part a had the cost of $100,000 while part b had the cost of $210,000

therefore, part b increased $110,000 from 2000 to 2008.

this is my guess.

Answer:

A) 60 girls B)80 boys

Step-by-step explanation:

Pretend that the ratio is a fraction. If there are 4 boys for every 4 girls, than pretend that you add the 4 and the 3 together, thus giving you 7 as your denominator. Start with the girls, giving you a fraction of 3/7, multiply by 140, you get 60 as the number of girls. 140-60=80, giving you 80 boys.

1. The given function is growth.

The percent of growth is 43%.

The initial value is 1500.

2. The rate of decay is 20% per day.

3. a. The exponential equation representing the sales after x months for the given situation is 3500000(0.97ˣ).

b. The monthly sales after 8 months will be $274,310.1758.

4. Between months 5 and 6, the website gains more members. The difference between the two sites for this period is 2700 members.

An exponential function is of the form f(x) = (a)(bˣ), where a is the initial value, and b is the exponential factor.

When b > 1, we have growth, and when b < 1, we have decay or depreciation.

1. Given function, f(x) = 1500(1.43ˣ).

The exponential factor in this function is 1.43, which is greater than 1, thus we have growth.

The percent of growth = (1.43 - 1)*100% = 43%.

The initial value = 1500.

2. Given an equation, y = 75(.8ˣ).

The exponential factor in this function is 0.8, and x signifies the days passed.

Thus, the rate of decay = (1 - 0.8)*100% per day = 20% per day.

3. Initial value = $350,000.

Rate of depreciation = 3% per month.

a. Thus, the equation for the sales after x months can be given as:

f(x) = 350000(1 - 0.03)ˣ = 350000(0.97ˣ).

b. To find the monthly sales after 8 months, we substitute x = 8.

Sales = 350000(0.97⁸) = $274,310.1758.

4. Initial members for both sites = 100.

For site a:-

Members double each month.

This makes an exponential equation, f(x) = 100.(2ˣ), where x is the number of months.

The growth between months 5 and 6 can be calculated as:

f(6) - f(5) = 100.(2⁶) - 100.(2⁵) = 6400 - 3200 = 3200.

For site b:-

500 new members are added each month.

This makes a linear equation, f(x) = 100 + 500x, where x is the number of months.

The growth between months 5 and 6 can be calculated as:

f(6) - f(5) = (100 + 500*6) - (100 + 500*5) = 3100 - 2600 = 500.

Thus, between months 5 and 6, the website a gains more members. The difference between the two sites for this period is 2700 members.

Learn more about exponential functions at

https://brainly.com/question/2456547

#SPJ4

\( \frac{ \sin(20 \degree) }{ \cos(70\degree) } + \frac{ \cos(35\degree) }{ \sin( 65\degree)} \)

\( \frac{ \sin(20 \degree) }{ \cos(70\degree) } + \frac{ \cos(35\degree) }{ \sin( 65\degree)} \)

\( \sin( \theta) = \cos(90 - \theta) \\ \\ \cos( \theta) = \sin(90 - \theta) \)

So putting down the value

\( \frac{ \cos(90 - 20 \degree) }{ \cos(70\degree) } + \frac{ \sin(90 - 35\degree) }{ \sin( 65\degree)} \)

\( \frac{ \cos(70\degree) }{ \cos(70\degree) } + \frac{ \sin(65\degree) }{ \sin( 65\degree)} \)

\(\frac{\cancel{\cos(70\degree)}}{ \cancel{\cos(70\degree)}} + \frac{\cancel{\sin(65\degree)}}{\cancel{\sin( 65\degree)}} \)

\( \frac{1}{1} + \frac{1}{1} \\ 1 + 1 = 2 \: \: ans\)

Answer:

cool im fatter

Step-by-step explanation:

Answer:

(D)$81

Step-by-step explanation:

Given that the number of purses a vendor sells daily has the probability distribution represented in the table.

Expected Value, \(E(x)=\sum_{i=1}^{n}x\cdot p(x)\)

Therefore:

\(E(x)=(0X0.35)+(1X0.15)+(2X0.2)+(3X0.2)+(4X0.03)+(5X0.07)\\=0+0.15+0.4+0.6+0.12+0.35\\E(x)=1.62\)

If each purse sells for $50.00, the number of expected daily total dollar amount taken in by the vendor from the sale of purses

=Expected Value X $50

=1.62 X $50

=$81

The correct option is D.

Assuming no deposits or withdrawals are made, the time it would take for the value of the account to reach $182,800 is 13.5 years.

Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:

B = P(1 + r/n)^t

where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded monthly, and t is the time in number of months

Based on the given information, t is the unknown and

B = $182,800

P = $75,000

r = 6.8% = 0.068

n = 1

Plug in the values and solve for the time it would take for the value to reach $182,800.

B = P(1 + r/n)^t

$182,800 = $75,000(1 + 0.068/1)^t

$182,800 = $75,000(1.068)^t

(1.068)^t = $182,800 / $75,000

(1.068)^t = 914/375

t = 13.5 years

Learn more about compound interest here: brainly.com/question/24924853

#SPJ4

Para encontrar las razones trigonométricas, debemos recordar su definición:

donde, co denota el cateto opuesto, ca el cateto adyacente y h la hipotenusa.

Como vemos de las definiciones, necesitamos saber todos los lados del triángulo. Para encontrar el lado a del triángulo es necesario utilizar el teorema de Pitágoras:

En este caso, c=100 y b=85. Sustituyendo los valores y resolviendo la ecuación para a, tenemos que:

Una vez que tenemos todos los lados, podemos encontrar las funciones trigonométricas del ángulo 55°. Notamos que para este angulo:

Entonces:

Answer:

Step 2

Step-by-step explanation:

(100 + 3)² = 100² + 2 x 100 x 3 + 3²

This is by the law of squares
(a + b)² = a² + 2ab + b²

the unit vector is given by:

N1(Uii^ + Ujj^) = 1/√5242 (61i - 39j)

the required unit vector is 1/√5242 (61i - 39j).

Given two vectors A and B: A = 13i + 15j and B = 16i - 18j.

We need to find the unit vector that points in the same direction as the vector A + 2B.

Step 1: Find the vector A + 2B:

A + 2B = A + B + B (using the distributive property)

A + 2B = 13i + 15j + 16i - 18j + 32i - 36j

A + 2B = 61i - 39j

Step 2: Find the magnitude of the vector A + 2B:

Magnitude of A + 2B = √((61)^2 + (-39)^2)

Magnitude of A + 2B = √(3721 + 1521)

Magnitude of A + 2B = √5242

Step 3: Find the unit vector in the same direction as A + 2B:

The unit vector is a vector with magnitude 1 in the same direction as the given vector.

Let N = Ui

N = Ui = 61/√5242

Uj = -39/√5242

Therefore, the unit vector that points in the same direction as the vector A + 2B is N1(Uii^ + Ujj^),

where N = 61/√5242, Ui = 61/√5242, and Uj = -39/√5242.

Thus, the unit vector is given by:

N1(Uii^ + Ujj^) = 1/√5242 (61i - 39j)

So, the required unit vector is 1/√5242 (61i - 39j).

To know more about distributive property

https://brainly.com/question/30321732

#SPJ11

-4y-1

Step-by-step explanation:

If you subtract \({ \green{ \tt{8y + 7}}} \)from \({ \red{ \tt{4y - 8}}}\) then the resultant answer will be as follows

\( \: \: \: \: \: { \red{ \tt{4y - 8}}} \\ - \ \: { \green{ \tt{8y + 7}}} \\ = -{ \blue{ \tt{ 4y - 1}}}\)

Answer:

70 sq. in

Step-by-step explanation:

Area of the figure

= ( 10 x 5 ) + ( 5 x 4 )

= 50 + 20

= 70

= 70 sq. in

To find the orthogonal projection of a vector onto a subspace, we can use the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ,

where A is a matrix whose columns span the subspace, and u is the vector we want to project.

In this case, the subspace W is spanned by the vector v = [0, 0, 0, 1].

Let's calculate the orthogonal projection of u onto W using the formula:

A = [v]

The transpose of A is:

Aᵀ = [vᵀ].

Now, let's substitute the values into the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ

= v⁻¹[vᵀ]u

= [v][(vᵀv)⁻¹vᵀ]u

Substituting the values of v and u:

v = [0, 0, 0, 1]

u = [1, 0, 0, 0]

vᵀv = [0, 0, 0, 1][0, 0, 0, 1] = 1

[(vᵀv)⁻¹vᵀ]u = (1⁻¹)[0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 0]

Therefore, the orthogonal projection of u onto the subspace W is [0, 0, 0, 0].

To learn more about orthogonal projection visit:

brainly.com/question/2264817

#SPJ11

Step-by-step explanation:

34−1.9 + 1234-1.9 + 12

Find the common denominator.

Click to see fewer steps ...

Write −1.9-1.9 as a fraction with denominator 11.

34 + −1.91 + 1234 + -1.91 + 12

Multiply −1.91-1.91 by 4444.

34 + −1.91⋅44 + 1234 + -1.91⋅44 + 12

Multiply −1.91-1.91 by 4444.

34 + −1.9⋅44 + 1234 + -1.9⋅44 + 12

Multiply 1212 by 2222.

34 + −1.9⋅44 + 12⋅2234 + -1.9⋅44 + 12⋅22

Multiply 1212 by 2222.

34 + −1.9⋅44 + 22⋅234 + -1.9⋅44 + 22⋅2

Multiply 22 by 22.

34 + −1.9⋅44 + 2434 + -1.9⋅44 + 24

Combine the fractions.

Click to see fewer steps ...

Combine the fractions that have a common denominator.

3−1.9⋅4 + 243-1.9⋅4 + 24

Multiply −1.9-1.9 by 44.

3−7.6 + 243-7.6 + 24

Simplify the numerator.

Click to see fewer steps ...

Subtract 7.67.6 from 33.

−4.6 + 24-4.6 + 24

Add −4.6 - 4.6 and 22.

−2.64-2.64

Divide −2.6-2.6 by 44.

−0.65-0.65

The point-slope form of the line is y - (3/4) = 5(x - (3/4)).

The point-slope form of a line is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. To find the point-slope form of a line that has a slope of 5 and passes through the point (3/4, 3/4), we can plug in the values for the slope and the point into the point-slope formula. This gives us y - (3/4) = 5(x - (3/4)). This is the point-slope form of the line.

Learn more about Point-Slope Form here:

https://brainly.com/question/24907633

#SPJ4