What is the value of the expression, written in standard form?

Answer:

y = 6·sin(3·(x - 1)) + c

Step-by-step explanation:

The general form of an equation for a sinusoidal function is presented ad follows;

y = a·sin(b·(x - h) + c

Where;

a = The amplitude of the equation

T = The period = 2·π/b

h = The phase shift

c = The vertical shift

From the question, we have;

a = 6,

2·π/3 = 2·π/b

∴ b = 3

h = 1

We get;

y = 6·sin(3·(x - 1)) + c.

Answer:

Answer:

6 sqrt(3) = x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin 60 = x/12

12 sin 60 =x

12 ( sqrt(3)/2) =x

6 sqrt(3) = x

Answer:

x=6[tex]\sqrt{3}[/tex]

Step-by-step explanation:

take 60 degree as reference angle

using sin rule

sin 60=opposite/hypotenuse

[tex]\sqrt{3[/tex]/2=x/12

do cross multiplication

2*x=12*[tex]\sqrt{3}[/tex]

x=12[tex]\sqrt{3}[/tex] /2

x=6[tex]\sqrt{3}[/tex]

Answer:

SMALLER NUMBER = 14

BIGGER NUMNER = 34

Step-by-step explanation:

Two equations can be derived from the question

a + 2b = 62 equation 1

3a - b = 116  equation 2

a = bigger number

b = smaller number

multiply equation 1 by 3

3a + 6b = 186 equation 3

subtract equation 2 from 3

5b = 70

b = 14

substitute for b in equation 1

a + 28 = 62

a = 34

Answer:

5.78

19

Step-by-step explanation:

Let original population be, P = x

Growth in 12 years, A = 2x

Rate be = r

Time = 12years

Find the rate :

   [tex]A = P(1 + \frac{r}{100})^t[/tex]

 [tex]2x = x(1 + \frac{r}{100})^{12}\\\\\frac{2x}{x} =(1 + \frac{r}{100})^{12}\\\\2 = (1 + \frac{r}{100})^{12}\\\\ \sqrt[12]{2} = (1 + \frac{r}{100})\\\\\sqrt[12]{2} - 1 = \frac{r}{100}\\\\2^{0.08} - 1 = \frac{r}{100}\\\\1.057 - 1 = \frac{r}{100}\\\\0.057 \times 100 = r\\\\r = 5.7 \%[/tex]

The annual rate of increase of the population of this city is approximately 5.78.

Find  time in which the population becomes 3 times.

That is A = 3x

P = x

R= 5.78%

               [tex]A = P( 1 + \frac{r}{100})^t\\\\3x = x ( 1 + \frac{5.78}{100})^t\\\\3 = (1.0578)^t\\\\log \ 3 = t \times log \ 1.0578 \\\\t = \frac{log \ 3}{ log \ 1.0578 }\\\\t = 19.55[/tex]

The population will grow to three times its current size in approximately 19years .

5.78% ,19 years are the answers.

2=(1+r)^12

r=(2)^(1÷12)−1

R=0.0578*100=5.78%

3=(1+0.0595)^t

t=log(3)÷log(1.0595)

t=19 years

Exponential growth and exponential decay are two of the most common uses of exponential functions. Systems with exponential growth follow a model of the form y = y0ekt. In exponential growth, the growth rate is proportional to the amount present. In other words, for y'= ky

exponential function, multiply a by x to produce y. The exponential graph looks like a curve that starts with a very flat slope and becomes steep over time.

The exponential model, like the sphere model, starts at the origin and operates linearly near it. However, the increasing slope of the curve is less than the slope of the spherical model.

Learn  more about exponential function here:https://brainly.com/question/2456547

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Answer:

B

Step-by-step explanation:

tan28=tan (90-62)=cot 62=1/tan 62

Answer:

30°

Step-by-step explanation:

it is the alternating angle.

Answer and Step-by-step explanation:

The last answer choice is correct.

Set the product of 7 and 24 equal to the product of 8 and x, and then solve for x

The process being used in the last answer choice is called Cross multiplication, and is used to find the unknown value in fractions.

[tex]\frac{7}{8}[/tex] × [tex]\frac{x}{24}[/tex]

7 × 24 = 8x

168 = 8x

21 = x

#teamtrees #PAW (Plant And Water)

Answer:

B. [tex]^{5} P_{5}[/tex] × [tex]^{20} P_{15}[/tex]

Step-by-step explanation:

No. of students from first grade = 15

No. of students from second grade = 5

There are 5 rows of seats

Each row contains 5 seats

Total seats = 25

No. of ways for second-grade students to occupy the first row (i.e first 5 seats) = [tex]^{5} P_{5}[/tex]

Remaining seats = 20

So, now we are left with 15 first grade students  

So, No. of ways for first-grade students occupy remaining seats = [tex]^{20} P_{15}[/tex]

Using the counting rule principle,

No. of ways for the students can be seated if all of the second-grade students occupy the first row = [tex]^{5} P_{5}[/tex] × [tex]^{20} P_{15}[/tex]

So, Option B is the correct answer

Hence, no. of ways for the students can be seated if all of the second-grade students occupy the first row is ×

There are ¹⁵P₁₅ x ¹⁰P₅ possible way to seat, if all of the second-grade students occupy the first row.

A permutation in math is the number of ways in which a set of data or objects can be ordered or arranged, where the order matters.

Given that, a school bus has 25 seats, with 5 rows of 5 seats. 15 students from the first grade and 5 students from the second-grade travel in the bus.

Since you have to place all first-grade students in the first three rows,

Therefore,

For the 15 first-graders of the first three rows (15 seats), we have ¹⁵P₁₅ since all 15 places have to be occupied by all 15 first-graders.

Then we have 10 remaining seats left to be assigned to the 5 second-graders = ¹⁰P₅

We then multiply the permutation numbers of those two arrangements to get the total ways:

¹⁵P₁₅ x ¹⁰P₅

Hence there are ¹⁵P₁₅ x ¹⁰P₅ possible way to seat, if all of the second-grade students occupy the first row.

Learn more about permutation click;

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Answer:

4th answer

Step-by-step explanation:

g(h(x)) means to put the formula for h(x) into the formula for g(  ).

[tex]g(h(x))=g(2x-2)=-3(2x-2)^3-2(2x-2)^2\\=-3(8x^3-24x^2+24x-8)-2(4x^2-8x+4)\\=-24x^3+72x^2-72x+24-8x^2+16x-8\\=-24x^3+64x^2-56x+16[/tex]

Cubing the binomial 2x - 2 can take some time!

We know that :

⊕  Sum of the interior angles in a Pentagon should be equal to 540°

⇒  x° + (2x)° + (2x)° + 90° + 90° = 540°

⇒  (5x)° = 540° - 180°

⇒  (5x)° = 360°

[tex]\sf{\implies x^{\circ} = \dfrac{360^{\circ}}{5}}[/tex]

⇒ x° = 72°

Answer:

gotta be  answer A

Step-by-step explanation:

you can search up f(x) = square root of x

Answer:

XY=6

Step-by-step explanation:

13-7=6

Answer:

XY = 6

Step-by-step explanation:

We know that the whole line (XZ) is equal to 13, and we know that YZ + XY is equal to XZ.

XZ = XY + YZ

13 = XY + 7

6 = XY

Hope this helped :)

Answer:

I think it would be 36, if you use Area=Length×Width×Height

Answer:

Step-by-step explanation:

Answer:

1. mean: 5

2. median: 6

3. mode: 80% or 8

4. range: 7

Step-by-step explanation:

Answer:

mean = 5

median = 6

mode = 80%(aka 8)

range = 7

Step-by-step explanation:

it should be

9x+1y+8

      ^it could be just y instead of 1y

Answer:

the answer is = 9x+y+8

Step-by-step explanation:

...

Answer:

x = 121°

Step-by-step explanation:

∠ 1 + 115° = 180°

∠ 1 = 180 - 115

∠ 1 = 65°

∠ 2 + 304° = 360°

∠2 = 360 - 304

∠ 2 = 56°

∠ 1 + ∠ 2 + ∠ 3 = 180°

65° + 56 ° + ∠ 3 = 180°

∠3 = 180 - 65 - 56

∠ 3 = 59°

∠3 + x = 180°

59° + x = 180°

x = 180 - 59

x =  121 °

Answer:

Aseem’s : 8.3, Stana’s : 11.6

Step-by-step explanation:

Aseem: x

Stana: 2x-5

X+2x-5=20

3x=25

X = 8.3

Answer:

4*4=16+7=23

Step-by-step explanation:

4 inches x 4 weeks is 16 inches

7 + 16 = 23

Answer:

SA= 882cm^2

Step-by-step explanation:

SA=2( width*length + hight*length + hight*width )

SA=2( 9*20+ 9*20+ 9*9)

SA= 2*441

SA=882cm^2

Answer:

-1 and 3

Step-by-step explanation:

The real roots of a function are located where the function passes through the x-axis. In this case, the function passes through x=-1 and x=3, making them the real roots of the function.

Answer: (I am not a maths moderator)

x=4

Step-by-step explanation:

Multiply the exponents

(2x-4)^12=(4^2)^6 (exponents multiply so)

(2x-4)^12=4^12

4^12 = 16777216

(2x-4)^12= 16777216

Take the 1/12 exponent for both sides

that will remove the ^12 exponent from the left side and will take the 12th root for the right.

2x-4=4

add 4 to both sides

2x=8

divide both sides by 2

x=4