Find the value of each of the six trigonometric functions of the
angle theta in the figure
Find the value of each of the six trigonometric functions of the angle 0 in the figure a=10 and b=7

To Find :

The area of triangle whose side are 4 yard, 14 yard and 17 yard.

Solution :

We will use Heron's formula to find area of the triangle.

So,

\(s = \dfrac{a+b+c}{2}\\\\s = \dfrac{4+14+17}{2}\\\\s = 17.5\)

Now, heron's formula is :

\(A = \sqrt{s(s-a)(s-b)(s-c)}\)

Putting all given values in above equation :

\(A = \sqrt{17.5\times (17.5-4)\times(17.5-14)\times(17.5-17)}\\\\A = \sqrt{17.5\times 13.5\times 3.5\times 0.5}\\\\A = 20.33\ yard^2\)

Hence, this is the required solution.

Arteries veins and capillaries distribute blood to the body. Together the heart, blood, arteries, veins, and capillaries make up a(n) 

Organs

1. Quadratic function with range [-2, ∞): One example is f(x) = x² - 2, which opens upward with a vertex at (0, -2) and includes all values greater than or equal to -2.

1. Quadratic function with range [-2, ∞):

A quadratic function can be written in the form f(x) = ax² + bx + c, where a, b, and c are constants. To find a quadratic function with a range of [-2, ∞), we need to ensure that the function outputs values greater than or equal to -2 for all x.

Let's consider the quadratic function f(x) = x² - 2. This function opens upward since the coefficient of x² is positive. The vertex of the parabola is given by (-b/2a, f(-b/2a)). In our case, b = 0 and a = 1, so the vertex is located at (0, -2).

For any value of x, the function f(x) = x² - 2 outputs a value greater than or equal to -2. As x moves further away from the vertex in either direction, the function value increases without bound, ensuring that the range includes all values greater than or equal to -2.

2. Exponential function with range (-∞, 0):

An exponential function can be written in the form f(x) = a^x, where a is a positive constant. To find an exponential function with a range of (-∞, 0), we need to ensure that the function outputs negative values for all x.

Let's consider the exponential function g(x) = -2^x. By multiplying the standard exponential function f(x) = 2^x by -1, we obtain a reflection across the x-axis. As a result, g(x) is negative for all values of x.

As x approaches positive or negative infinity, the function g(x) approaches 0. Therefore, the range of g(x) is the set of all negative real numbers, represented as (-∞, 0).

To learn more about Quadratic function   Click Here: brainly.com/question/18958913

#SPJ11

well, let's move like the crab, backwards, let's start with b), then we'll do a)

b)

\({\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=75 \end{cases}\implies 75=ab^2 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=5\\ y=9375 \end{cases}\implies 9375=ab^5\implies 9375=ab^{2+3}\implies 9375=ab^2 b^3\)

\(\stackrel{\textit{substituting from the 1st equation}}{9375=\underset{ab^2}{(75)} b^3}\implies \cfrac{9375}{75}=b^3\implies 125=b^3 \\\\\\ \sqrt[3]{125}=b\implies \boxed{5=b}\hspace{5em}\stackrel{\textit{we know that}}{75=ab^2}\implies 75=a5^2\implies 75=25a \\\\\\ \cfrac{75}{25}=a\implies \boxed{3=a}\hspace{5em} {\Large \begin{array}{llll} y = 3(5^x) \end{array}}\)

a)

\(\begin{cases} x=0\\ y=j \end{cases}\implies j=3(5^0)\implies j=3(1)\implies j=3 \\\\\\ \begin{cases} x=4\\ y=k \end{cases}\implies k=3(5^4)\implies k=3(625)\implies k=1875\)

Answer:

X+X+100° = 180°

Step-by-step explanation:

X+X+100° = 180°

2X= 180°-100°

2X=80°

X=80/2

X=40°

Answer:

\(2^{-3}\)

Step-by-step explanation:

\(\displaystyle \frac{1}{8}=\frac{1}{2^3}=2^{-3}\)

Answer:

Jamal should find the Length of each leg by Subtracting the x coordinates and the y-coordinates and y-coordinates.

Step-by-step explanation:

Ansewer for Edmentum:)

Jamal's next step is : Jamal should find the length of each leg by subtracting x coordinate and y coordinate

"It is a triangle whose one the angle measures 90°"

"In a right triangle \(c^{2} =a^{2} +b^{2}\) where c is the hypotenuse and a, b are other two sides of right triangle."

"The distance between two points \((x_1,y_1),(x_2,y_2)\) is given by \(s=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\) "

For given question,

Jamal wants to find the length of 'd'

For right triangle in the figure, 'd' is the hypotenuse.

Jamal should find the other two sides of the triangle.

And then using Pythagoras theorem, Jamal can find the length of 'd'

So, Jamal need to find the length of each leg by subtracting x coordinate and y coordinate.

Therefore, Jamal's next step is : Jamal should find the length of each leg by subtracting x coordinate and y coordinate

Learn more about distance here:

https://brainly.com/question/2287272

#SPJ3

By using the approximation of 62,500 inches to the mile, you can simplify and expedite various calculations involving distances and conversions between inches and miles, providing a convenient tool for numerical analysis and problem-solving

The approximation of 62,500 inches to the mile is commonly used in various calculations, especially in scenarios where conversions between inches and miles are involved. This approximation simplifies the conversion process and allows for easier calculations.

For example, if you need to convert a distance from miles to inches, you can simply multiply the number of miles by 62,500 to obtain the equivalent distance in inches. Conversely, if you have a measurement in inches and want to convert it to miles, you divide the number of inches by 62,500 to get the distance in miles.

Additionally, this approximation can be useful in other applications, such as determining the number of inches in a given number of miles, or calculating the length of a specific distance in miles based on its measurement in inches.

Learn more about measurement here:

https://brainly.com/question/28913275

#SPJ11

.

Answer:

2199.11 (with pi)

2198 (with 3.14)

Step-by-step explanation:

A=2πrh+2πr²

A=2π(14)(11)+2π(14)²

A=2π(154)+2π(196)

A=2(483.56)+2(615.44)

A=967.12+1230.88

In September 2021, the approximate number of citizens incarcerated in jails and prisons is around 2.3 million.

It is important to note that this figure can vary over time due to changes in policies, criminal justice reforms, and other factors. The incarcerated population includes individuals who have been convicted of crimes and are serving their sentences, as well as those who are awaiting trial or have been sentenced but not yet transferred to a correctional facility.

These numbers can vary between different countries and jurisdictions. To obtain the most accurate and up-to-date information on current incarceration rates, it is advisable to refer to official sources such as the U.S. Bureau of Justice Statistics or relevant governmental organizations in your country.

Learn more about number here:

https://brainly.com/question/3589540

#SPJ11

Answer:

8 orange slices

Step-by-step explanation:

The total number of persons = Aiden + 6 friends = 7 persons

7 people are to share 56 orange slices equally.

Hence,

7 persons = 56 slices

1 person = x

Cross Multiply

7x = 56 × 1

x = 56/7

x = 8 slices

Therefore, each person will get 8 orange slices

Answer:

12 sure not sure not sure

=8/12

in reduced fraction= 2/3

its 2/3  

The probability of a Type I error is 0.2 or 20%. This means that there is a 20% chance of rejecting the null hypothesis when it is actually true.

The power of a hypothesis test is the probability of rejecting the null hypothesis when the alternative hypothesis is true. In this case, the power of the test is given as 0.8, and the null hypothesis is that the true value of the parameter is 10, while the alternative hypothesis is that the true value is 8.

We are given the sample size, n = 25, and the standard deviation, σ = 4. To calculate the probability of a Type I error, we need to determine the significance level of the test, denoted by α.

The significance level is the probability of rejecting the null hypothesis when it is actually true. It is usually set before conducting the test, and commonly set at 0.05 or 0.01.

To calculate α, we can use the following formula:

α = 1 - power = 1 - 0.8 = 0.2

So, the probability of a Type I error is 0.2 or 20%. This means that there is a 20% chance of rejecting the null hypothesis when it is actually true.

for such more question on  probability

https://brainly.com/question/13604758

#SPJ11

Answer:

85

Step-by-step explanation:

The trigonometric ratio for sin Z is 3/5 in the given right triangle.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The right triangle is given in the question, as shown.

As we know the cosine ratio, is as follows:

cos Z = base/hypotenuse

cos Z = YZ/XZ

cos Z = 32/40

cos Z = 4/5

Now, as we know the sine ratio, is as follows:

sin Z = √(1 - cos² Z)

sin Z = √(1 - (4/5)²)

sin Z = √(1 - 16/25)

sin Z = √(9/25)

sin Z = 3/5

Thus, the trigonometric ratio for sin Z is 3/5.

Learn more about Trigonometric functions here:

brainly.com/question/6904750

#SPJ1

Answer:

a,e

Step-by-step explanation:

Answer:

A, E

Step-by-step explanation:

lets first solve the equation using distributive property:

-3(x-2)=4x-2(x-1)

-3x+6=4x-2x+2

-3x+6=2x+2    (E)

Now move the like terms on one side:

-3x-2x=2-6

-5x=-4             (A)

The mean and variance of the reward of the runner-up is 7/3 and Variance is 89/9

What is Variance?

Variance is the anticipated squared variation of a random variable from its population mean or sample mean in probability theory and statistics. Variance serves as a proxy for dispersion, or the degree to which a set of numbers deviates from their mean.

Here, a=0 and b=12. So,

f(x) = 1 / (12 - 0)

     = 1/12

A runner receives $10 if he or she is between 0 and 1 minute behind the leader. The corresponding probability is stated as

\(\int\limits^1_0 {1/12} \, dx\)=1/12(\(x^1_{0}\))

             = 1/12

A runner receives $6 if he or she is between one and three minutes behind the leader. The corresponding probability is stated as

\(\int\limits^3_1 {1/12} \, dx\) = 1/12(\(x^3_{1}\))

               = 1/6

A runner receives $2 if he or she is between three and six minutes behind the leader. The corresponding probability is stated as

\(\int\limits^6_3 {1/12} \, dx\) = 1/12(\(x^6_{3}\))

               = 1/4

A runner receives nothing if he or she is more than six minutes behind the leader. The corresponding probability is stated as

12

∫ 1/12 dx = 1/12 (\(x^{12}_6\))

6

             = 1/2

We can produce the following table:

X P(X)  X(P(X) X^2 P(X)

10 1/12   5/6         25\3

6 1/6         1     6

2 1/4      1/2  1

0 1/2      0     0

Sum: 1      E(X)=7/3  E(X^2)=46/3

Thus the expected value of X is given as

E(X) = 7/3

The variance is given as

σ² = E(X)² - [E(X)]²

    = 46/3 - (7/3)²

 σ²   = 89/9

Hence, Mean of the reward runner up is 7/3 and Variance is 89/9

To learn more about Variance click on the link

https://brainly.com/question/9304306

#SPJ4

Answer:

y=3 x=2/5

Step-by-step explanation:

5x + 3y =11

5x - 3y =-1

ok for the first one when 3y way positive the answer is positive and when it was negative the answer was negative meaning it is freater then 5x

the difference between the answer 11--1= 12 shows how much the difference between the negative and positive y  is so 12 has to equal 4y

4y=12

so y has to be 3

and if y is 3  we plug it back into the equations

5x+3(3)=11

5x+9=11

5x=2

Answer:

11+11+13+5+5+4+4=53

Step-by-step explanation:

so 4 is the answer

(a) The least integer n for which f(x) is o(\(x^n\)) is 4

(b) f(x) is not o(\(x^n\)) for any integer n.

(c) The least integer n for which f(x) is o(\(x^n\)) is 2.

(d) The least integer n for which f(x) is \(o(x^n)\) is 4.

(a) To determine the order of growth of f(x), we need to find a function g(x) such that limx→∞ f(x)/g(x) = 0. Let g(x) = \(x^4\). Then:

limx→∞ f(x)/g(x) = limx→∞ (\(2x^2 / x^4\) log(x)) = limx→∞ (2 / (\(x^2\) log(x)))

Using L'Hopital's rule:

limx→∞ (2 / (\(x^2\) log(x))) = limx→∞ (\(2x^{(-2)}\) / log(x) +\(4x^{(-3)} / log(x)^2\)) = 0

Therefore, f(x) is o(\(x^4\)). The least integer n for which f(x) is o(\(x^n\)) is 4.

(b) Let g(x) = \(x^7\). Then:

limx→∞ f(x)/g(x) = limx→∞ (\(3x^7 / x^7 (log(x))^4\)) = limx→∞ (\(3 / (log(x))^4\))

Using L'Hopital's rule four times:

limx→∞ (\(3 / (log(x))^4\)) = limx→∞ (\(3 (4!) / (log(x))^4\)) = ∞

Therefore, f(x) is not o(\(x^n\)) for any integer n.

(c) Let g(x) = \(x^2\). Then:

limx→∞ f(x)/g(x) = limx→∞ \((x^4 / (x^2 + 1)(x^4 + 1))\) = 0

Therefore, f(x) is o\((x^2)\). The least integer n for which f(x) is o(\(x^n\)) is 2.

(d) Let \(g(x) = x^4\). Then:

limx→∞ f(x)/g(x) = limx→∞ \((x^3 (5log(x)) / x^4)\) = limx→∞ (5 log(x) / x) = 0

Therefore, f(x) is\(o(x^4)\). The least integer n for which f(x) is \(o(x^n)\) is 4.

Learn more about order of growth

brainly.com/question/14661014

#SPJ11

Answer: two congruent segments.

Step-by-step explanation:

idlk im not smart

Answer:

Step-by-step explanation:

Step-by-step explanation:

Example, i have 1 equation and i want to find x

2x - 1 = 5

2x = 5 + 1

2x = 6

x = 6/2

x = 3

So, value of x is 3

So, the solution to the initial value problem is:

y(x) = 6x² - 3x³ + 7x + 7.

'To solve the initial value problem given, first, integrate the second-order differential equation with respect to x:

1. ∫(d²y/dx²) dx = ∫(12 - 18x) dx

After integrating, we get:

y'(x) = 12x - 9x² + C₁

Now, apply the initial condition y'(0) = 7:

7 = 12(0) - 9(0)² + C₁

C₁ = 7

So, y'(x) = 12x - 9x² + 7.

Next, integrate y'(x) with respect to x:

2. ∫(dy/dx) dx = ∫(12x - 9x² + 7) dx

After integrating, we get:

y(x) = 6x² - 3x³ + 7x + C₂

Now, apply the initial condition y(0) = 7:

7 = 6(0)² - 3(0)³ + 7(0) + C₂

C₂ = 7

So, the solution to the initial value problem is:

y(x) = 6x² - 3x³ + 7x + 7.

learn more about initial value problem

https://brainly.com/question/30547172

#SPJ11

Step-by-step explanation:

(10, 9), (5 , 4)

Use the distance formula to determine the distance between the two points.

Distance

=√(x2−x1)² +(y2 - y1)²

Substitute the actual values of the points into the distance formula.

√(5−10)² +(4−9)²

Simplify.

5√2

Exact Form:

5√2

Decimal Form:

7.07106781

Hope it will help :)❤

Answer:

Exact form: 6/2

Decimal form: 8.48528137

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

2:5 is the ratio for this problem. Divided 2 by 2 and divide 5 by 2. 1:2.5. Next, do 6.5 x 2.5.

In physics lab, when you measure three quantities of x, y, and z, you can use these mathematical combinations to find meaningful relationships between these quantities:  

In this case, x=2.5 kg, y=0.8 m, and z=4.9 kg/m.

Based on the given quantities' scale, we know that x, y, and z have a relationship where:

z = x/y

Then, the mathematical combinations that might be meaningful are:

- (x/y) - z: This combination gives you the difference between the ratio of x and y, and z. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- (x/z) - y: This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- x - (yz): This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

Learn more about Mathematical Combinations here: brainly.com/question/23327429

#SPJ11