The right triangle has legs a and b and hypotenuse c. If b=12 and c=13, then what does a equal?

The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

For similar question on projectile.

https://brainly.com/question/30695754

#SPJ11

Answer:

C = 133.33°

Step-by-step explanation:

Apply the Law of Cosines to find angle C:

\( Cos(C) = \frac{a^2 + b^2 - c^2}{2ab} \)

Where,

a = 8.5 cm

b = 4.1 cm

c = 11.7 cm

Plug in the values

\( Cos(C) = \frac{8.5^2 + 4.1^2 - 11.7^2}{2*8.5*4.1} \)

\( Cos(C) = \frac{-47.83}{69.7} \)

\( Cos(C) = -0.6862 \)

\( C = Cos^{-1}(-0.6862) \)

C = 133.33°

The average distance from the mean is 0.09.

The mean is also known as the average and is calculated by adding up all the values in the set and then dividing the sum by the total number of values.

So, for the given set of data: 24.49, 24.68, 24.77, 24.83, 24.73, the mean would be calculated as follows:

Mean = (24.49 + 24.68 + 24.77 + 24.83 + 24.73) / 5

= 24.70

It tells us what the typical value is within the data set. In this case, the mean value of the data set is 24.70.

Next, let's find the median of the set of data. The median is the middle value of a data set when it is arranged in numerical order. In this case, the data set is already arranged in numerical order, so we can easily find the median.

The median value of the data set is the middle value, which is 24.77.

Now, we will calculate the deviation from the mean for each data point within the set. The deviation from the mean tells us how far each value is from the mean value. This is calculated by subtracting the mean from each value in the set.

Deviation from the mean for each data point:

-0.21, -0.02, 0.07, 0.13, 0.03

As you can see, some values are above the mean, and some are below the mean. The deviation from the mean can be used to determine how spread out the data is from the mean value.

Finally, we will calculate the mean deviation for the set. The mean deviation is the average of the absolute values of the deviation from the mean.

Mean deviation = (|(-0.21)| + |(-0.02)| + |0.07| + |0.13| + |0.03|) / 5

= 0.09

The mean deviation tells us the average distance from the mean value.

To know more about mean here.

https://brainly.com/question/22871228

#SPJ4

Answer:

Step-by-step explanation:

Answer:

The answer is 4³⁰

Step-by-step explanation:

(4⁹/4³)⁵

Here, we will use the property

aᵐ/aⁿ = (aᵐ⁻ⁿ)

(4⁹⁻³)⁵ = (4⁶)⁵ = 4⁶*⁵ = 4³⁰

Thus, The answer is 4³⁰

-TheUnknownScientist 72

Answer:

25 + 9^3

Step-by-step explanation:

Answer:

(L-6)(L+2)

Step-by-step explanation:

Let L be the length of the flower garden.

Then the width will be L-4.

The area of the flower garden = L*(L-4) =L²-4L

The area of the birdbath is 3*4 = 12 ft²

The area of the remaining space for planting is

= Area of flower garden - area of birdbath

We can factor the expression as follows:

taking common frome each two terms

Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.

Answer:

64 marbles

Step-by-step explanation:

The solution is, 24 is the total number of marbles in the bag.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

given that,

A bag of marbles only has red and blue marbles.

The bag has a ratio of blue marbles to red marbles of 3:5,

and there are 24 blue marbles in the bag.

we have to find the total number of marbles in the bag.

let, there are x red marbles .

we have,

blue marbles : red marbles = 3:5

so, we get,

blue marbles : red marbles = 24 : x

i.e. 3:5 = 24 : x

so, x = 24 * 5 / 3

or, x = 8*5

or, x = 40

so, there are 24 red marbles .

so, total = 24 + 40 = 64

Hence, The solution is, 24 is the total number of marbles in the bag.

To learn more on ratio click:

brainly.com/question/13419413

#SPJ2

Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.

Answer:

-2 ≤ x ≤ 14

Step-by-step explanation:

x - 6 + 7 ≥ -1

x + 1 ≥ -1

x ≥ -2

-(x - 6) + 7 ≥ -1

-x + 6 + 7 ≥ -1

-x + 13 ≥ -1

-x ≥ -14

x ≤ 14

Answer:

Joseph- 265 coins

molly- 275 coins

Answer:

The first box : -4  the second one : 6

Step-by-step explanation:

subtract 7 from 3 for the first box, then add 10 to -4 for the second one.

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

for such more question on combinations

https://brainly.com/question/28065038

#SPJ8

Answer:

X = -1

Step-by-step explanation:

f(-1) = 6(-1) + 1

6 * -1 = -6

-6 + 1 is equal to -5

I hope this helps (:

Answer:

P((1 + r)^4) = 1,300

P((1 + r)^7) = 1,525

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

(1 + r)^3 = 61/52, so r = .0547 = 5.47%

P(1.0547^4) = 1,300, so P = $1,050.78

The length of the guy wire is; 74.72 meters and the distance of its anchor point to the base of the tower is; 55.53 meters.

a). The length of the guy wire in discuss as described in the task content can be determined by means of trigonometric ratios as follows;

Sin 42° = 50/x

x = 50/sin 42°

x = 74.72 meters.

b). The distance between the base of the tower and the anchor point of the guy wire can be determined as follows;

Tan 42° = 50/y

y = 50/tan 42°

y = 55.53 meters.

Read more on trigonometric ratios;

https://brainly.com/question/10417664

#SPJ1

Answer:

Hi there!

Your answer is;

-2= x

Step-by-step explanation:

12= -5x +2

-2

10= -5x

/-5

-2 = x

Hope this helps

Answer: x = -2 give me brainliest

Step-by-step explanation:

The value of x after solving (2.3x + 8) = (-1.7x-8) is -4.

According to the question,

We have the following expression:

(2.3x + 8) = (-1.7x-8)

Now, moving -1.7x from the right hand side to the left hand side will result in the change of its sign from minus to plus:

2.3x+1.7x +8 = -8

4x+8 = -8

Now, moving 8 from the left hand side to the right hand side will also result in the change of the sign from plus to minus:

4x = -8-8

4x = -16

x = -16/4 (4 was in multiplication on the left hand side. So, it is in division on the right hand side.)

x = -4

Hence, the value of x is -4.

To know more about solving here

https://brainly.com/question/315182

#SPJ1

Answer:

The answer to this problem would be D

Step-by-step explanation:

Hope this helped!!

Tell me if im wrong

Answer:

(a) and (b)

\(f(g(x)) = g(f(x)) = x\)

(c) and (d)

\(f(g(x)) =-x + 8\)

\(g(f(x)) = x + 8\)

Step-by-step explanation:

Given

(a) to (d)

Required

Find f(g(x)) and g(f(x)) for each pair

For (a) and (b), we have:

\(f(x) = \frac{3}{x}\)

\(g(x) = \frac{3}{x}\)

Calculate f(g(x))

\(f(x) = \frac{3}{x}\)

\(f(g(x)) = \frac{3}{g(x)}\)

Substitute 3/x for g(x)

\(f(g(x)) = \frac{3}{3/x}\)

Rewrite as:

\(f(g(x)) = 3/\frac{3}{x}\)

\(f(g(x)) = 3*\frac{x}{3}\)

\(f(g(x)) = x\)

Since f(x) = g(x), then:

\(f(g(x)) = g(f(x)) = x\)

For (c) and (d)

\(f(x) =x + 4\)

\(g(x) =-x + 4\)

Solving f(g(x)), we have:

\(f(x) =x + 4\)

\(f(g(x)) =g(x) + 4\)

Substitute \(g(x) =-x + 4\)

\(f(g(x)) =-x + 4 + 4\)

\(f(g(x)) =-x + 8\)

Calculating g(f(x))

\(g(x) =-x + 4\)

\(g(f(x)) = -f(x) + 4\)

Substitute: \(f(x) =x + 4\)

\(g(f(x)) = x + 4 + 4\)

\(g(f(x)) = x + 8\)

Answer: C. 5/6+7/6i

Step-by-step explanation: just did it on Edg

The equation in the form of i will be 5/6 + (7/6)i. Then the correct option is C.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The equation is given below.

\(x = \dfrac{5 + \sqrt{-49}}{6}\)

We know that √(-1) = i, then we have

x = 5/6 + (√49 / 6)i

x = 5/6 + (7/6)i

Then the correct option is C.

More about the simplification link is given below.

https://brainly.com/question/12616840

#SPJ2

Answer: -81a^2 + 27a + 10

Step-by-step explanation: We can do this question by using FOIL (first, outer, inner, last)

(-9a-2)(9a-5)

First, multiply the first two terms in the parentheses

-9a times 9a is -81a^2

Second, multiply the outer terms

-9a times -5 is 45a

Third, multiply the inner terms

-2 times 9a is -18a

And lastly, multiply the last terms

-2 times -5 is 10

After doing this we end up with -81a^2 + 45a - 18a + 10 = -81a^2 + 27a + 10

Answer:

-3, 2 , 3.3 , 4.6, 5.9

Step-by-step explanation:

I just counted where the dots were for example "-5"

Answer:

-3, 2 , 3.3 , 4.6, 5.9

The margin of error is defined as follows:

M = 1.9z/sqrt(n).

In which:

The bounds of the confidence interval are given as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

The margin of error is then given as follows:

\(M = z\frac{\sigma}{\sqrt{n}}\)

The problem is incomplete, hence the general procedure to obtain the sample size was presented.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer:

x = 5/2

Step-by-step explanation:

(4^3x)/(2^4x) = 32

(2^6x)/(2^4x) = 32

2^2x = 32

2^2x = 2^5

2x = 5

x = 5/2

Answer:

14 kg

Step-by-step explanation:

Set up a proportion:

9/238.5 = x/371

Cross multiply.

9 x 371 = 3339

238.5 times x = 238.5x

238.5x = 3339

Divide by 238.5 on both sides.

3339/238.5 = 14

The value of y when x = -4 for the given proportion will be 8/5 and the value of the k for the given equation is (-8/20).

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

y = -8 when x = 20

The ratio of y and x = -8/20

With the same ratio value of y if x = -4

y/(-4) = -8/20

y = (-8/20)(-4) = 8/5

As per the given equation,

-8 = k(20)

k = (-8/20)

Hence "The value of y when x = -4 for the given proportion will be 8/5 and the value of the k for the given equation is (-8/20)".

For more information about ratios and proportions,

brainly.com/question/26974513

#SPJ1

The length of the altitude is 3√6.

According to Right Triangle Altitude Theorem

The altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse has a length that is the geometric mean of the lengths of the two segments of the hypotenuse.

So, AD = √CD.  DB

Here we have CD=6 and DB=9 so

AD = √6 x 9

AD = √54

AD = 3√6

Learn more about Right Triangle Altitude Theorem here:

https://brainly.com/question/3128215

#SPJ1

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

Read more about Partial Differential Equations at: https://brainly.com/question/28099315

#SPJ1