Trigonometric ratio: find an angle measure​

Answer:

34m = c

Step-by-step explanation:

For every month (m) you pay 34 dollars. However many months youu use that service time 34 equals your total cost (c).

Answer:

[tex]let \: cost \: be \: { \bf{c}} \: and \: months \: be \: { \bf{n}} \\ { \bf{c \: \alpha \: n}} \\ { \bf{c = kn}} \\ 34 = (k \times 1) \\ k = 34 \: dollars \\ \\ { \boxed{ \bf{c = 34n}}}[/tex]

Answer:

15 / 4

Step-by-step explanation:

1 kg = 1000 g

3 kg

= 3 x 1000

= 3000 g

3kg to 800g

= 3kg : 800g

= 3000 : 800

= 30 : 8

= 30 / 8

= 15 / 4

15/4 is the fraction representing the ratio of 3 kilograms to 800 grams.

To express the ratio of 3 kilograms to 800 grams as a fraction in its lowest terms.

we need to convert both the quantities to the same units. Since 1 kg is equal to 1000 g, we can convert 3 kg to grams as follows:

3 kg = 3 * 1000 g = 3000 g

Now, we have the quantities in the same unit, and the ratio becomes:

3000 g to 800 g

To express this ratio as a fraction, we place the quantities over each other:

3000 g

-------

800 g

Now, to simplify the fraction to its lowest terms, we find the greatest common divisor (GCD) of the two numbers (3000 and 800) and divide both the numerator and denominator by this GCD.

The GCD of 3000 and 800 is 200, so dividing both by 200 gives us:

3000 ÷ 200 = 15

800 ÷ 200 = 4

Therefore, the ratio 3 kg to 800 g expressed as a fraction in its lowest terms is 15/4.

In summary, we first converted the units to the same (grams) to make the ratio easier to handle. Then, we represented the ratio as a fraction and simplified it to its lowest terms using the GCD method. The final answer, 15/4, is the fraction representing the ratio of 3 kilograms to 800 grams.

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Answer:

6

Step-by-step explanation:

We have the expression "3x is 18" and we want to find out x, so the easiest way is to isolate x. The way to do this is by dividing both 3x and 18 by 3, leaving us with 6. This means that our answer for x is 6. I hope this helped and please don't hesitate to reach out for clarification!

Answer:

6

Step-by-step explanation:

3x = 18

Divide both sides by 3

3x / 3 ( the 3s cancel out and we're left with x )

18/3 = 6

We get that x = 6

We can then plug in 6 to x in 3x = 18 to check if our answer is correct

3x = 18

Replace x with 6

3(6) = 18

3(6) = 18

18 = 18

This is true hence we can confirm that x = 6

Given:

The graph of a function.

To find:

The range of the given function using interval notation.

Solution:

Range: The set of y-values or output values are known as range.

From the given graph, it is clear that the function is defined for [tex]0<x<4[/tex] and the values of the functions lie between -2 and 2, where -2 is excluded and 2 is included.

Range [tex]=\{y|-2<y\leq 2\}[/tex]

The interval notation is:

Range [tex]=(-2,2][/tex]

Therefore, the range of the given function is (-2,2].

Answer:

Step-by-step explanation:

a = 5

b = 15

c = ?

c^2 = a^2 + b^2

c^2 = 5^2 + 15^2

c^2 = 25 + 125

c^2 = 250

sqrt(c^2) = sqrt(250)

c = sqrt(250)

answer choice a

x^2 - 5x - 1 = 0

a=1, b=-5, and c=-1

next you plug in the numbers into the quadratic formula

-(-5) plus or minus the square root of (-5)^2 - 4(1)(-1)/ 2(1)

after you simply, you should get 5 plus or minus the square root of 29, which is answer choice a

Answer:

[tex]\displaystyle V = \frac{625 \pi}{2}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Shell Method:                                                                                                         [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 5

Step 2: Identify

Find other information from graph.

See Attachment.

Bounds of Integration: [0, 5]

Step 3: Find Volume

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

Unit: Applications of Integration

Book: College Calculus 10e

9514 1404 393

Answer:

  x² +y² -6x -16y +48 = 0

Step-by-step explanation:

Given:

Find:

  general form equation for the circle

Solution;

The standard form equation for the circle is ...

  (x -h)² +(y -k)² = r² . . . . . circle with radius r centered at (h, k)

  (x -3)² +(y -8)² = 5²

Subtracting 25 and expanding this will give the general form.

  x² -6x +9 +y² -16y +64 -25 = 0

  x² +y² -6x -16y +48 = 0

_____

Additional comment

"General form" of an equation is usually the form f(x,y) = 0, where f(x, y) is written in "standard form," with terms in lexicographical order and decreasing degree.

Answer:

90 cause 90 times 10 is 900 and 10% times 10 is 100%

Step-by-step explanation:

Answer: 90

Step-by-step explanation: 900 × .10 = 90

9514 1404 393

Answer:

Step-by-step explanation:

The graph shows the function value is zero for x=5 and x=7. These are the elements of the solution set.

  x ∈ {5, 7}

__

The graph is below the x-axis between these points, so that is the region where f(x) < 0

  5 < x < 7 . . . . . for f(x) < 0

In interval notation: (5, 7).

Answer: The ans is imaginary . option c

Answer:

C

Step-by-step explanation:

The triangles are similar and the scale factor can be find out by computing 18/6=15/5=9/3=3

admins, pls delete this, I messed up and don't know how

Answer:

(-2,3,10,8)

Step-by-step explanation:

eg

(x,y)=(domain,range)

x components are domain and y components are range in the given set of ordered pairs

Answer:

= ∑ 6*n*x^n-1

Radius of convergence = 1

Step-by-step explanation:

f(x) = 6(1-x)^-2

Maclaurin series can be expressed using the formula

f(x) =  f(0) + f '(0)x + f ''(0)/ 2!  (x)^2 + f '''(0)/3! (x)^3 + f (4)(0) 4! x4 + .

attached below is the detailed solution

Radius of convergence = 1

The Maclaurin series for f(x) = 6 / (1 - x )^2  = ∑ 6*n*x^n-1  ( boundary ; ∞ and n = 1 )

Answer:

The solution to the equation  log3(x+2)=1 is given by x=1

Step-by-step explanation:

We are given that

[tex]log_3(x+2)=1[/tex]

We have to find the graph which shows the  solution to the equation log3(x+2)=1.

[tex]log_3(x+2)=1[/tex]

[tex]x+2=3^1[/tex]

Using the formula

[tex]lnx=y\implies x=e^y[/tex]

[tex]x+2=3[/tex]

[tex]x=3-2[/tex]

[tex]x=1[/tex]

Answer:

The first one is 2

The second one is 0

I hope this helps!

Answer:

First:

[tex]{ \tt{ = 4 + ( - 2)}} \\ = 4 - 2 \\ = 2[/tex]

Second:

[tex] - 3 + 3 \\ = 0[/tex]

Answer:

30 gallons of each brand

Step-by-step explanation:

1 gallon of 60% + 1 gallon of 80% = 2 gallons 70% (60/2 = 30)

Answer: hi your question is poorly written below is the correct question

answer :

a) y1 = Asint,   y'1 = Acost  , y"1 = -Asint

b) y2 = Bcost,   y'2 = Bsint , y"2 = - Bcost

c) y = Asint + B cost satisfies the differential equation for any constant A and B

Step-by-step explanation:

y" + y = 0

Proves

a) y1 = Asint,   y'1 = Acost  , y"1 = -Asint

b) y2 = Bcost,   y'2 = Bsint , y"2 = - Bcost

c) y3 = y1 + y2 ,   y'3 = y'1 + y'2,  y"3 = y"1 + y"2

∴ y"1 + y1 = -Asint + Asint

  y"2 + y2 = -Bcost + Bcost

  y"3 - y3 = y"1 + y"2 - ( y1 + y2 )

               = y"1 - y1 + y"2 - y2  

               = -Asint - Asint  + ( - Bcost - Bcost )  = 0

Hence we can conclude that y = Asint + B cost satisfies the equation for any constant A and B

Answer:

The area of the square is increasing at a rate of 40 square centimeters per second.

Step-by-step explanation:

The area of the square ([tex]A[/tex]), in square centimeters, is represented by the following function:

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

Where [tex]l[/tex] is the side length, in centimeters.

Then, we derive (1) in time to calculate the rate of change of the area of the square ([tex]\frac{dA}{dt}[/tex]), in square centimeters per second:

[tex]\frac{dA}{dt} = 2\cdot l \cdot \frac{dl}{dt}[/tex]

[tex]\frac{dA}{dt} = 2\cdot \sqrt{A}\cdot \frac{dl}{dt}[/tex] (2)

Where [tex]\frac{dl}{dt}[/tex] is the rate of change of the side length, in centimeters per second.

If we know that [tex]A = 25\,cm^{2}[/tex] and [tex]\frac{dl}{dt} = 4\,\frac{cm}{s}[/tex], then the rate of change of the area of the square is:

[tex]\frac{dA}{dt} = 2\cdot \sqrt{25\,cm^{2}}\cdot \left(4\,\frac{cm}{s} \right)[/tex]

[tex]\frac{dA}{dt} = 40\,\frac{cm^{2}}{s}[/tex]

The area of the square is increasing at a rate of 40 square centimeters per second.

Answer:

[tex]9 + 7i[/tex]

Step-by-step explanation:

[tex]7i^5+9i^8[/tex]

[tex]i^5 = i\\ i^8 = 1[/tex]

Answer:

8.50 cm²

Step-by-step explanation:

The dimension of each square is given as 0.5cm by 0.5cm

The area of the a square is, a²

Where, a = side length

Area of each square = 0.5² = 0.25cm

The number of blue colored squares = 34

The total area of the blue colored squares is :

34 * 0.25 = 8.50cm²

Answer:

It has a difference of x=2 of -4

Step-by-step explanation:

It has a difference of x=2 of -4

Given ,

           x ≠ 2 ,

           x - 2 =0

So, we put x = -2 because in question x ≠ 2 .

Then,      x - 2 = 0

              -2 -2 = 0

               - 4 =0

Therefore, it has a difference of x= -2 of -4.

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the graph would steeper, meaning more savings over time

Answer:

-5 it is

Step-by-step explanation:

Answer:

i think you answer is correct as it has to be less that 64 yards since it is not on a big slant. using reference from the first section forty yards is not as big as the sectuon you are looking for therefore using estimation, the answer is most likely b 53 and 1 thirds

Answer:

the answer should be e^3

Step-by-step explanation:

i hope it helps you

Answer:

Growth: y = 1700(1.25)^t, y = 4000(1.0825)^t, y = 1.5(10)^t

Decay: y =240(1/2)^t, y = 12,000(0.72)^t,  y = 8000(0.97)^t

Step-by-step explanation:

In an exponential equation, growth and decay are determined by the factor you are multiplying by exponentially. If it's under 1 you're basically exponentially dividing the initial value. Over 1 and you are increasing the value.

Answer:

[tex]90[/tex] [tex]ft^3[/tex]

Step-by-step explanation:

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

The formula to find the volume of a rectangular prism is   [tex]V=lwh[/tex]

Let's substitute the number for the length, width, and height now.

[tex]V=(6)(5)(3)[/tex]

[tex]V=(30)(3)[/tex]

[tex]V=90[/tex]

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

Hope this is helpful.