Trigonometric Equations

Solve the equation over the interval [0°, 360°)

2sin^2theta-5sintheta+3=0

Answer:

Step-by-step explanation:

CONE:

height of cone = h =  12 cm

r =3.5 cm

[tex]Volume \ of \ cone =\dfrac{1}{3}\pi r^{2}h[/tex]

                           [tex]=\dfrac{1}{3}*\dfrac{22}{7}*3.5*3.5*12\\\\\\=22*0.5*3.5*4\\\\= 154 \ cm^{3}[/tex]

Cylinder:

h = 16 cm

r = 3.5 cm

[tex]Volume \ of \ cylinder = \pi r^{2}h\\[/tex]

                                [tex]= \dfrac{22}{7}*3.5*3.5*16\\\\\\= 22*0.5*3.5*16\\\\= 616 \ cm^{3}[/tex]

Total volume = 154 + 616

                       = 770 cm³

Answer:

33

Step-by-step explanation:

let g be Gabrielle age

m be mikhail age.

So according to this problem,

[tex]g + m = 81[/tex]

[tex]m + 15 = g[/tex]

Subsitue m+15 for g.

[tex](m + 15) + m = 81[/tex]

[tex]2m + 15 = 81[/tex]

[tex]2m = 66[/tex]

[tex]m = 33[/tex]

So mikhail age is 33.

Answer:

4) v=kx^2/y^3

2= k(4^2)/(3^3)

2 =k16/27

k = 2(27/16) = 27/8

v = (27/8)(3^2)/(2^3 = (27/8)(9/8) = 243/64

v = 243/64 when x=3 and y=2

Step-by-step explanation:

here

F varies jointly as x and y and the value of x is 3 and y is 2.

We have given that,

1.) m varies directly as a and b  m=10 when a=4 and b=7. Find m when a=11 and b=8.

v=kx^2/y^3

2= k(4^2)/(3^3)

2 =k(16/27)

k = 2(27/16)

k = 27/8

v = (27/8)(3^2)/(2^3)

= (27/8)(9/8)

= 243/64

v = 243/64 when x=3 and y=2.

Therefore we get the value of x is 3 and y is 2.

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Please see Explanation

[tex]a)\ As\ shown\ in\ the\ figure.[/tex]

[tex]b)\ According\ the\ picutre,[/tex]

[tex]we\ know\ only\ 3\ people[/tex]

[tex]sell\ maize\ and\ 5\ people\ sell\ plantain.[/tex]

I hope this helps you

:)

The 3 people sell only maize, 5 people sell only plantain and 4 people sell maize and plantain and the probability that a woman selected at random from the group sells plantain only is 0.147.

It is given that a group of 34 women sells at least one of the following foodstuffs: yam, maize, and plantain.

22 sell yam, 14 sell maize, 18 sell plantain, 7 sell both yam and maize, 9 sell yam and plantain, and no one sells all three items

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

i) Venn diagram is shown in the picture below:

ii) As per the picture 3 people sell only maize, 5 people sell only plantain        

   and 4 people sell maize and plantain.

iii)  Total number of women in the group = 34

     The number of women who sells plantain = 5  

We know the probability = [tex]\rm \frac{favorable \ event}{total \ outcome}[/tex]

Probability [tex]=\frac{5}{34} \\\\\\= 0.147\\[/tex]

Thus, the 3 people sell only maize, 5 people sell only plantain      

and 4 people sell maize and plantain and the probability that a woman selected at random from the group sells plantain only is 0.147.

Learn more about the Venn diagram here:

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Answer: 1

Step-by-step explanation:

Answer:

The Domino Theory suggested that one nation becoming Communist makes it more likely that others will too. Without American involvement, the South would quickly have fallen to the North and the nation, united under Communism, would have joined the Communist bloc.                

Step-by-step explanation:

35% of 120 is :

120 x 0.35 = 42 $ profit

selling cost 120+42=162$

Answer:

325/377×100= 116% it means they completed 116%of the trip

Answer:

40%

Step-by-step explanation:

Givens and Formula

% Good = (number good / total number) * 100

% Good = ?

Number Good = 32

Total Number = 80

Solution

% Good = (32 / 80) * 100

% Good = 2/5 * 100

% Good = 40%

Answer:

(0, -14)

Step-by-step explanation:

Midpoint formula: [tex](x_m, y_m) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]

Answer:

Step-by-step explanation:

39.8 - 32.2 = 7.6

Range is subtracting the highest and lowest numbers by each other .

Based on the calculations, the range for this data set is equal to 7.6.

In Mathematics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.

Mathematically, range is calculated by using this formula;

Range = Highest number - Lowest number

From the given data set, we have:

Substituting the given parameters into the formula, we have;

Range = 39.8 - 32.2

Range = 7.6.

Read more on range here: https://brainly.com/question/9393969

Answer:

  {−1.47596288535, 1.73968983949, 9.73627304586}

Step-by-step explanation:

The roots of this cubic are real and irrational, as indicated by a graph of it. (Rational roots would be divisors of 25.) The same graphing calculator can provide an iterative solution to 12 significant figures. Here, we have used Newton's method iteration. The iteration function is ...

  g(x) = x -p(x)/p'(x) . . . where p'(x) is the derivative: 3x^2-20x

We started each iteration using the value shown on the graph.

  x ∈ {−1.47596288535, 1.73968983949, 9.73627304586}

__

The second attachment shows another calculator's solution. The values of x that are roots are the opposite of the constant in each binomial factor. You will notice this solution has a couple more significant figures than the one shown above.

__

Additional comment

There are several formulas for finding the "exact" roots of the cubic. Here's a trig approach that works reasonably well for cubics with 2 or 3 real roots.

We can define, for p(x) = x³ +ax² +bx +c, ...

  s = -a/3 = 10/3

  t = b -a²/3 = -100/3

  r = a(2a² -9b)/27 +c = -10(200)/27 +25 = -1325/27

  d = √(-4t/3) = √(400/9) = 20/3

  h = 4r/d³ = -53/80

Now, the roots are ...

  x = s +d·sin(arcsin(h)/3 +2nπ/3) . . . . for n=-1, 0, 1

  = 10/3 +20/3·sin(arcsin(-53/80)/3 + n(2π/3)) . . . . . "exact solution"

  = (10/3)(1 +2·sin(-13.8303° +n(120°))

  = -1.47596..., or 1.73969..., or 9.73627...

Answer:

[tex]\displaystyle [0, 2][/tex]

Step-by-step explanation:

First, find the rate of change [slopes]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-6 + 3}{8 - 2} = m; \frac{-3}{6} \\ \\ -\frac{1}{2} = m[/tex]

We now plug the above information into the Slope-Intercept Formula. It does not matter which ordered pair is selected:

[tex]\displaystyle y = mx + b \\ \\ 3 = -\frac{1}{2}[-2] + b \hookrightarrow 3 = 1 + b; \boxed{2 = b} \\ \\ y = -\frac{1}{2}x + 2[/tex]

OR

[tex]\displaystyle y = mx + b \\ \\ 6 = -\frac{1}{2}[-8] + b \hookrightarrow 6 = 4 + b; \boxed{2 = b} \\ \\ y = -\frac{1}{2}x + 2[/tex]

Therefore, the line passes through the y-intercept of [tex]\displaystyle [0, 2].[/tex]

I am joyous to assist you at any time.

Answer:

[tex]\rightarrow \boxed{\sf{8x+16}}[/tex]

Step-by-step explanation:

You have to isolate the term of x from one side of the equation.

Distributive property:

A(B+C)=AB+AC

5x+(x+12)+(2x+4)

5x+(x+12)+(2x+4)=5x+x+12+2x+4

5x+x+12+2x+4

Group and combined like terms.

5x+x+2x+12+4

Add the numbers from left to right.

12+4=16

Rewrite the problem down.

5x+x+2x+16

Then, you solve.

5x+x=6x

6x+2x=8x

8x+16

As a result, the final answer is 8x+16.

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

mm what's that?

Step-by-step explanation:

wala akong pake char

Line BF is one of the three angle bisectors that meet at point F (incenter), hence, line BF as it relates to ABC is called the: interior angle bisector.

An interior angle bisector can be described as the line segment that divides an interior angle into two halves.

When the three interior angle bisector of a triangle meet at a point, the point is referred to a the incenter.

The diagram guven shows the incenter where the three interior angle bisectors meet.

Therefore, line BF as it relates to ABc is called the: interior angle bisector.

Learn more about the interior angle bisector on:

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Answer:

t=9

Step-by-step explanation:

Solve -

Distribute :7-(5t - 13) = - 25

7 - 5t + 13 = - 25

Add the numbers :7 – 57 + 13 = -25

20-51 = -25

Rearrange terms :20-51 = -25

-51+ 20 = -25

Subtract 20 from both sides :-51 + 20 = -25

-51+20-20-25-20

Simplify :Subtract the numbers

-51+ 20-20-25-20

-5:=-25-20

Subtract the numbers

-51 = -25-20

-51 = -45

-51 = -45

Divide both sides by the same factor : -51 = -45 -5t -5 -45- -5 =

Simplify : Cancel terms that are in both the numerator and denominator :: -5t - = -45 - -5

t = - 45 - -5

Divide the numbers :

t = - 45 - -5 ” t=9 ” here’s the answer

Answer:

Point A

Step-by-step explanation:

It can be seen from the image that the chosen value for N is greater than zero but less than 1, i.e,

[tex]0 < n < 1[/tex]

The square of such numbers will always result values less than N since they're decimals with zeroes on the whole number parts.

Hence, the value for N squared will be in the region of Point A.

Answer:

D.) there is 9a and 6b ,3c and 1 thats four different terms

Step-by-step explanation:

Have a nice day! :D

Answer:

109.375

Step-by-step explanation:

We need to multiply all of the lengths and widths by 2 1/2 in order to make the dimensions 2 1/2 times larger.

For length:

[tex]5\frac{1}{4}[/tex]  x  [tex]2\frac{1}{2}[/tex] = 13.125 or [tex]13\frac{1}{8}[/tex]

For width:

[tex]3\frac{1}{3}[/tex]  x  [tex]2\frac{1}{2}[/tex] = 8.333 or [tex]8\frac{1}{3}[/tex]

Then to find the area use the equation:

A = l x w (Area = length x width)

And plug in the values:

A = [tex]13\frac{1}{8}[/tex]  x  [tex]8\frac{1}{3}[/tex] = [tex]\frac{875}{8}[/tex] or [tex]109\frac{3}{8}[/tex] or 109.375

Step-by-step explanation:

Using the section formula , if a point ( x , y ) divides the line joining the points ( x1 , y1 ) and ( x2 , y2 ) into the ratio m : n , then

( x , y ) = ( mx2 + nx1 / m + n , my2 + ny1 / m + n)

Let the points be A(-8,−2) and B(6,19). Let a point P(x,y) divides AB in the ratio 5:2

Therefore, we have

[tex]P(x,y) =( \frac{5 \times 6 + 2 \times - 8}{5 + 2} , \: \frac{5 \times 19 + 2 \times - 2}{5 + 2}) [/tex]

[tex]P(x,y) = ( \frac{30 + ( - 16)}{7} , \: \frac{95 + ( - 4)}{7} )[/tex]

[tex] P(x,y) = (2, 13)[/tex]

Answer:

(2, 13)

Step-by-step explanation:

Let P be the point that partitions the segment.

Let M = (-8, -2)

Let N = (6, 19)

If point P partitions the segment MN in a 5 : 2 ratio, then to calculate the x and y values of point P:

x-value of P:

[tex]\sf \implies \left(\dfrac{x_N-x_M}{5+2}\right)\cdot5+x_N[/tex]

[tex]\sf \implies \left(\dfrac{6-(-8)}{5+2}\right)\cdot5+(-8)=2[/tex]

y-value of P:

[tex]\sf \implies \left(\dfrac{y_N-y_M}{5+2}\right)\cdot5+y_N[/tex]

[tex]\sf \implies \left(\dfrac{19-(-2)}{5+2}\right)\cdot5+(-2)=13[/tex]

[tex]\sf P=(2,13)[/tex]

Answer: 6.

Step-by-step explanation: The total number of seats is 328.  There are 14 rows with 23 seats in each row.  To solve this, we need to multiply the amount of rows with the amount of seats in each row, which would look like this:

14 x 23 = 322.

As you can see, there are only 322 seats.  However, there are 328 seats in total, so there are 6 extra seats that aren't in a specific row.  Therefore, there are 6 extra seats.

Hope this helps! :)

Answer:

Step-by-step explanation:A. h(x) = √(x-2)

Step-by-step explanation:

To translate a function right by p units and up by q units, the function becomes ...

g(x) = f(x -p) +q

Here, there is no translation upward, but there is a translation of 2 units to the right. The transformed function's name is given as h (not g), so you have ...

(p, q) = (2, 0)

h(x) = f(x -2) +0

h(x) = √(x -2)

The function h(x) , a transformation of the parent function f(x) = √x is √(x+1). Option A is correct option.

The transformation of the function is a function that curves a graph formed by the moving the original graph to left / right / up / down or by expansion or compression.

The transformation is of type horizontal shift when the curve moves to left or right. For y = f(x) , when this curve moves left or right the transformation  is given by y = f(x +c), c > 0 moves y=f(x) to the left by c units

and if c < 0 , moves  y =f(x) to the right by c units

Given that the graph of the f(x) = √x by dotted line and the graph of its transformation h(x) given by solid line.

h(x) is clearly formed by moving f(x) one units to the left as it is moved to left by 1 on origin

Then transformation of y =f(x) moving one unit to left will be given by

y = f(x+1) =√(x+1)

Therefore , transformation h(x) of f(x) is h(x) =√(x+1) and option A is correct option.

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[tex]\sf 2^{-6}[/tex]

these two options apply

[tex]\rightarrow \sf \dfrac{1}{2^6}[/tex]

[tex]\rightarrow \sf 2^{-2} \ * \ 2^4 \ * \ 2^{-8}[/tex]

in decimals : 0.015625

Answer:

Option C and D

Step-by-step explanation:

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

Example:

If the given exponent is a⁻ᵇ, then the result will be 1/aᵇ.

This exponent includes a negative sign. To make the exponent positive, take the exponent's reciprocal and change the negative sign to a positive sign. The same will be done to the given expression.

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

First, take the exponent's reciprocal as said above.

⇒ [tex]2^{-6}[/tex]

⇒ [tex]\frac{1}{2^{-6} }[/tex]

Now, change the exponent's sign.

⇒ [tex]\frac{1}{2^{-6} }[/tex]

⇒ [tex]\frac{1}{2^{6} }[/tex]

Now, simplify the term.

⇒ [tex]\frac{1}{2^{6} }[/tex]

⇒ [tex]\frac{1}{2 \times 2 \times 2 \times 2 \times 2 \times 2} }[/tex]

⇒ [tex]\frac{1}{8 \times 8}[/tex]

⇒ [tex]\frac{1}{64}[/tex]

Using the simplified result we obtained, let's verify all the options to see which is equivalent to the term.

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

A)------------------------------------------------------------------------------------------------------

Keep in mind that the exponent is the number of times the base needs to multiply itself.

[tex]-2^{6} \rightarrow -2 \times -2 \times -2 \times -2 \times -2 \times -2[/tex]

NOTE: If there are even number of "-", then the result should be positive. If there are odd number of "-", then the result should be negative.

[tex]-2 \times -2 \times -2 \times -2 \times -2 \times -2[/tex]

⇒ [tex]2 \times 2 \times 2 \times 2 \times 2 \times 2[/tex]

⇒ [tex]64[/tex]

[tex]-2^{6} = 64 \neq \frac{1}{64}[/tex]

B)------------------------------------------------------------------------------------------------------

Since -64 is already a simplified term, we can compare this with the simplified result.

[tex]-64 \neq \frac{1}{64}[/tex]

C)------------------------------------------------------------------------------------------------------

[tex]\frac{1}{2^{6}}[/tex]

⇒ [tex]\frac{1}{2 \times 2 \times 2 \times 2 \times 2 \times 2 }[/tex]

⇒ [tex]\frac{1}{8 \times 8 }[/tex]

⇒ [tex]\frac{1}{64}[/tex]

[tex]\frac{1}{2^{6} } = \frac{1}{64} = \frac{1}{64}[/tex]

D)------------------------------------------------------------------------------------------------------

[tex]2^{-2} \times 2^{4} \times 2^{-8}[/tex]

⇒ [tex]\frac{1}{2^{2}} } \times 16 \times \frac{1}{2^{8} }[/tex]

⇒ [tex]\frac{1}{4} \times 16 \times \frac{1}{256}[/tex]

⇒ [tex]\frac{1}{4} \times 1 \times \frac{1}{16}[/tex]                                                                               [16² = 256]

⇒ [tex]\frac{1}{4} \times \frac{1}{16}[/tex]

⇒ [tex]\frac{1}{64}[/tex]

[tex]2^{-2} \times 2^{4} \times 2^{-8} = \frac{1}{64} = \frac{1}{64}[/tex]

E)------------------------------------------------------------------------------------------------------

[tex]2^{3} \times 2^{-2}[/tex]

⇒ [tex]2^{3 - 2}[/tex]

⇒ [tex]2^{1} = 2[/tex]

[tex]2^{3} \times 2^{-2} = 2 \neq \frac{1}{64}[/tex]

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

Step-by-step explanation:

tbh I don't know I need help with that too please like this comment

The measure of the marked central angle of the sector will be 280°.

Let r is the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

The figure addresses 7/9 of a complete circle. Then the arc length of the circle will be given as,

Arc / P = 7/9

Simplify the equation, then we have

(θ/2π) 2πr / 2πr = 7/9

θ/2π = 7/9

θ = 14π / 9

θ = 280°

The central angle of the sector will be 280°.

More about the arc length of the sector link is given below.

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well it would be very helpful thank you

Answer:

448 ft ^2

Step-by-step explanation:

[tex]A = \frac{b_{1} + b_{2}}{2} * h\\A = \frac{17 + 39}{2} * 16\\A = \frac{56}{2} * 16\\\\A = 28 * 16\\\\A = 448 ft^{2}[/tex]

Hope this helps,

If best, mark brainliest, if not, hope it helps anyway.

Answer:

Cost of Computer: $734

Cost of Printer: $367

Step-by-step explanation:

These two equations can represent the costs; x = price of computer; y = price of printer.

x + y = 1101

2y = x

If you graph these, you get an intersection point of (734, 367). This means that the only place that both equations are fulfilled is on (734, 367).

Then you can check your work:

734+367=1101

367*2=734

Answer:

7pm

Step-by-step explanation:

1pm + 24 = 1pm

30 - 24. = 6

1pm + 6 = 7pm