What is the area of a sector when r = 2 and 0 = 1.75 radians? [?] sq units Round your answer to the nearest tenth. Enter​

By using trigonometric properties, we will see that:

tan(x) = 3/4.

Remember that the sine of the difference is:

sin(a - b) = sin(a)*cos(b) - sin(b)*cos(a).

Here we have:

sin(90° -x ) = 0.8

Expanding the sine:

sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°)

We know that:

sin(90°) = 1 and cos(90°) = 0, then:

sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°) = cos(x).

Then we have:

cos(x) = 0.8

And we want to find the tangent of x, which is:

[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]

We already know that cos(x) = 0.8

Now, remember that:

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

Because x is an acute angle, sin(x) > 0, that is why we choose the positive root.

Replacing cos(x) we get:

[tex]sin(x) = \sqrt{1 - 0.8^2} = \sqrt{1 - 0.64} = \sqrt{0.36} = 0.6[/tex]

Then the tangent of x is:

[tex]tan(x) = \frac{0.6}{0.8} = \frac{6}{10}*\frac{10}{8} = 6/8 = 3/4[/tex]

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Step-by-step explanation:

Answer:

Adults: 79 tickets

Students: 237 tickets

Step-by-step explanation:

a + b = 316    Eq. 1

b = 3a            Eq. 2

a = adults

b = students

Replacing Eq. 2 in Eq. 1

a + 3a= 316

4a = 316

a = 316/4

a = 79

from the Eq. 2

b = 3a

b = 3*79

b = 237

Check:

from the Eq. 1

a + b = 316

79 + 237 = 316

A function assigns the values. The statement "The rate of population growth each year is 166%" is true.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function of the population for the town is [tex]P (t) = 45,000(2.66)^t[/tex], where t is the time in years. Comparing the given function to the general function of the population,

P(x) = a(1+b)ˣ

Then, the value of b will be 166%.

Hence, the statement "The rate of population growth each year is 166%" is true.

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Answer: -2

Step-by-step explanation:

We can combine the fundamentals of mental math and the brain to calculate the problem when x is -2. You wake up noticing x is -2 and you instantly know the answer and solved in less than a second.

The answer is (A) f(x) = x+4.

The probability that a randomly selected person from the sample will be female or left-handed will be 0.05.

Probability is synonymous with possibility. It is concerned with the occurrence of a random event.

Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.

Given data;

Total number of sample,n(S) = 100 person

No of female or left-handed is,n(E) =5

P(E) is the probability that a randomly selected person from the sample will be female or left-handed

The probability that a randomly selected person from the sample will be female or left-handed is found as;

P(E) = n(E)/n(S)

P(E) = 5 / 100

P(E) = 0.05

Hence the probability that a randomly selected person from the sample will be female or left-handed will be 0.05.

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Answer: B

Step-by-step explanation:

Plug in x for 3. Then solve.

4*(1/3)^3

4*1/9

4/9

Answer:

Probability of rolling a sum of 5 is 1/9.

There are 36 different combinations because 6(first roll)*6(second roll) = 36. The only possible combinations are {1,4},{2,3}{2,3}and{4,1}

4/36 = 1/9

The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the profit (P) in thousands for security camera with price of x, hence for a profit of at least $471, 000:

-(x - 32)² + 1000 ≥ 471

-(x² - 64x + 1024) + 1000 ≥ 471

-x² + 64x - 1024 + 1000 - 471 ≥ 0

-x² + 64x - 495 ≥ 0

x = 55 or x = 9

The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9

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Answer:

b.) 0

Explanation:

⇒ f(g(-1))

go from right to left while solving such function questions.

⇒ f(-1 + 2)

⇒ f(1)

⇒ (1)² -2(1) + 1

⇒ 0

Step-by-step explanation:

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

[tex]f(x) = {(x - 1)}^{2} [/tex]

[tex]g(x) = x + 2[/tex]

[tex] \: [/tex]

[tex] = f(g( - 1))[/tex]

[tex] = {(x - 1)}^{2} [/tex]

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

[tex] = {(( - 1 + 2) - 1)}^{2} [/tex]

[tex] = {(1 - 1)}^{2} [/tex]

[tex] = {0}^{2} [/tex]

[tex] = 0[/tex]

The answer is B.

The number of cases of flu on day 15 will be 1001 flus

Exponential functions are expressed as y = ab^x

Given the expression below

[tex]f(x)=10001+999e^{-0.6030x}[/tex]

In order to determine the number of cases of flu on day 15, we will substitute x = 15 into the expression to have:

[tex]f(x)=10001+999e^{-0.6030(15)}\\f(x)=10001+999e^{-9.045}\\f(15) = 10001+0.11786\\f(15) \approx 10001[/tex]

Hence the number of cases of flu on day 15 will be 1001 flus

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Answer:

Step-by-step explanation:

Evaluate the function for the value x=15.

f(x)f(15)f(15)=10001+999e−0.6030x=10001+999e−0.603(15)≈894.565217

Rounded to the nearest whole number, there will be 895 cases on day 15.

Answer:

0

Step-by-step explanation:

[tex]10 + ( - 8) - 2 \\ = 1 0 - 8 - 2 \\ = 2 - 2 \\ = 0[/tex]

Answer: 0

Step-by-step explanation: -8+-2 is -10 and -10+10 is 0

The way to solve the polynomial using the methods is given below.

Polynomial by factoring:

An example is (t² + 5t + 4) / +t + 4)

= (t + 1)(t + 4)/(t + 4)

= t + 1.

Dividing polynomial by long division:

Divide the first term of the dividend by the first term of the divisor.

Put this as the first term in the quotient.

Subtract to create a new polynomial.

Continue until you can't divide anymore.

Dividing polynomial by synthesic division:

Step 1: Set up the synthetic division.

Step 2: Bring down the leading coefficient to the bottom row.

Step 3: Multiply c by the value just written on the bottom row.

Step 4: Add the column created in step 3.

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76.89 sjsbs austere. Sisson whenever. Ebenezer oe eie h rur fuf 8r r earned e 3epoe9 r rur 8e e aonwowne e7 rjr or

Answer:

3

Step-by-step explanation:

AD/AB = AE/AC

8/10 = 12/AC

AC = 12(10/8)=15

EC = 15 - 12 = 3

Answer:

x + 7 and x + 5 are possible dimensions

Step-by-step explanation:

x² + 12x + 35 ← factor the quadratic

consider the product of the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (+ 12)

the factors are + 7 and + 5 , since

7 × 5 = + 35 and 7 + 5 = + 12 , then

x² + 12x + 35 = (x + 7)(x + 5) ← in factored form

now the area A = length × breadth , that is

A = x² + 12x + 35 = (x + 7)(x + 5) , then

length = x + 7 or x + 5

breadth = x + 5 or x + 7

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equivalent to -(1/6)y + 1/3 is,

-(1/6)y + 1/3

Take 1/6 common from both first and the last term,

1/6 (-y + 2)

Hence, the correct option is C.

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The volume of the piece of the metal Gina is found to be 22.82 cubic cm.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of cube or cuboid.

Given the density of the metal = 9.2g/cm3

Given the mass of the piece of the metal = 210 g

Assuming the volume of a piece of metal to be V

The expression for the density is shown below:-

Density = Mass / Volume

9.2 = 210 / V

V = 210 / 9

V =  22.82 cubic cm.

Therefore the volume of the piece of the metal Gina is found to be 22.82 cubic cm.

The complete question is given below:-

Gina was given an irregularly shaped piece of metal and was told that the density of the metal was 10 g/cm3. She measured the mass of the piece to be 210 g. What was the volume of the piece of metal Gina was given?

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Step-by-step explanation:

The value of X is given so put the value of X in 1/4 (2)^x

=========================================================

Explanation:

This is the given piecewise function

[tex]h(a) = \begin{cases}3a+2 \text{ when } a > 3\\4a+5 \text{ when } a = 3\\3 \text{ when } a < 3\\\end{cases}[/tex]

We can rewrite things like this

[tex]\text{when } a > 3, \ \ h(a) = 3a+2\\\text{when } a = 3, \ \ h(a) = 4a+5\\\text{when }a < 3, \ \ h(a) = 3\\[/tex]

I personally prefer this format better because it mentions the inputs first, and that leads to which function definition we go for.

The input a = 2 fits the description of [tex]a < 3[/tex] since [tex]2 < 3[/tex] is a true statement. Therefore we go for the third line and can see that [tex]h(a) = 3[/tex] becomes [tex]h(2) = 3[/tex]

-----------

As another example, if we had the input a = 7, then we'd go for the first line (since 7 > 3) and get

h(a) = 3a+2

h(7) = 3(7)+2

h(7) = 23

Using the midpoint formula, the coordinates of the intersection of the diagonals of the parallelogram is: (1, 2.5).

The diagonals of a parallelogram bisect each other, therefore, the coordinates of their intersection can be determined using the midpoint formula, which is: [tex]M(\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2})[/tex].

A diagonal is XZ.

X(2, 5) = (x1, y1)

Z(0, 0) = (x2, y2)

Plug in the values

[tex]M(\frac{0 + 2}{2}, \frac{0 + 5}{2})[/tex]

= (1, 2.5).

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The transformed function is y = 1/3(log(x/3 + 4)) + 1

The parent logarithmic function is

y = log(x)

When shifted left by 4 units, we have:

y = log(x + 4)

When shifted up by 3 units, we have:

y = log(x + 4) + 3

When compressed vertically by 1/3, we have:

y = 1/3(log(x + 4) + 3)

This gives

y = 1/3(log(x + 4)) + 1

When stretched horizontally by 3, we have:

y = 1/3(log(x/3 + 4)) + 1

Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1

We have:

f(x) = log[-(x – 5)] + 4

Set the radicand greater than 0

-(x - 5) > 0

Divide by -1

x - 5 < 0

Add 5 to both sides

x < 5 -- this represents the domain

A logarithmic function can output any real number.

So, the range is [tex]-\infty < f(x) < \infty[/tex]

In the domain, we have:

x < 5

This means that the interval of decrease is [tex]-\infty < x < 5[/tex]

Rewrite as an equation

x = 5 --- this represents the equation of asymptote

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Answer:

Volume of a cylinder = 1,100cm³

Step-by-step explanation:

Volume of a cylinder = πr²h

Given

π = 22/7

r = 5cm

h = 14cm

Substitute the given information in the problem.

Volume of a cylinder = 22/7 × (5cm)² × 14cm

Volume of a cylinder = 22/7 × 25cm² × 14cm

Volume of a cylinder = 1,100cm³

the original height of the plant was 2mm. The correct option is the second one.

We know that the function:

y = 2 + 4x

Represents the height of a plant in mm, as a function of x, the hours kepts in sunlight.

The y-intercept is the value that y takes when we evaluate in x = 0.

So, the y-intercept is the height of the plant when it is exposed to zero hours of light.

In this case:

y = 2 + 4*x

Evaluating in x = 0

y = 2 + 4*0 = 2

This means that the original height of the plant was 2mm. The correct option is the second one.

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Answer:

A. 81

Step-by-step explanation:

F(x)=[tex]3^{x}[/tex]

if x=4, then F(4) = [tex]3^{4}[/tex] = 3×3×3×3=81

[tex] - 4(n - 6) = 12 \\ (n - 6) = \frac{12}{ - 4} \\ n - 6 = - 3 \\ n = - 3 + 6 \\ n = 3[/tex]

Answer:

  A.  KM

Step-by-step explanation:

A circle is named by its center. Circle K has its center at point K.

A radius is a line segment that extends from the center of the circle to a point on the circle. Point K must be one end of any radius.

Segment KM is a radius.

Segments between points on the circle are chords. The other named segments in the answer choices are all chords of the circle.

Answer: A

Step-by-step explanation:

The expressions are equivalent by the distributive property.

Answer:$986,4000



Step-by-step explanation: