given that sinθ=-3/4 in quadrant 4 find cosθ

The length of the function y = 3x over the given interval [0, 2] is 3.2 units

For given question,

We have been given a function  y = 3x

We need to find the length of the function on the interval x = 0 to x = 2.

Let f(x) = 3x where f(x) = y

We have  f'(x) = 3,  so  [f'(x)]² = 9.  

Then the arc length is given by,

[tex]\int\limits^a_b {\sqrt{1+[f'(x)]^2} } \, dx\\\\= \int\limits^2_0 {\sqrt{1+9} }\, dx\\\\=\sqrt{10}\\\\ =3.2[/tex]

This means, the arc length is 3.2 units.

Therefore, the length of the function y = 3x over the given interval [0, 2] is 3.2 units

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Answer:

4x-3y+4z

Step-by-step explanation:

There are lot's of process to answer it but i will show one easy way to find the answer.

To find the required answer we need to subtract 5x - 4y + 8z by  x-y + 4z, we get

5x - 4y + 8z

-x   +  y - 4z  [Note: while subtracting we must change the sigh that one       ___________who we are subtracting]

4x-3y+4z which is a required answer

Answer:

4x - 3y + 4z

Step-by-step explanation:

Let the unknown value that we have to add be 'a'.

Let us make an expression like this.

x -y + 4z + a = 5x - 4y + 8z

Now make 'a' the subject of the equation.

a = 5x - 4y + 8z - x + y - 4z

Now combine like terms.

a = 5x - x - 4y + y + 8z - 4z

a = 4x - 3y + 4z

Now let us check whether the answer is correct or wrong.

We can replace 'a' with ( 4x - 3y + 4z ).

Let us see.

x - y + 4z + 4x - 3y + 4z

Combine like terms.

5x - 4y + 8z

Yes, we are getting the same answer!

Therefore,

we need to add 4x - 3y + 4z to get 5x - 4y + 8z to  x - y + 4z.

Answer:

√s(s-a) (s-b) (s-c)

Step-by-step explanation:

123456

herons formula

Based on the shape shown on the graph, the reflection of the shape would be b) A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. A triangle is shown on ordered pair 2, negative 2 and 4, negative 2, and 2, negative 6.

The coordinate grid that the shape would be reflected across is the y axis to get a reflection in the negative side of the x axis.

The first reflection would be of the point that is (2,2). It would be reflected to become (-2, 2).

The second reflection would be of point (2, 6) which would then be reflected to become (-2, 6).

Finally the third point would be of point (4, 2) which would then become (-4, 2).

In conclusion, the reflection was across the y axis.

Options include:

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Answer: Point D

Reason:

The circumcenter is found by intersecting the perpendicular bisectors of each segment of the triangle.

As you can see, the circumcenter is the center of the circumcircle. This special circle is the smallest possible that wraps the triangle so to speak. The vertices of the triangle are on the circle.  The distances AD, BD and CD are all the same.

The two stadiums are 2,871 meters

A blimp    = point A

stadium 1  = point B

stadium 2 = point C

height of the blimp ,  AD = 1600

depression angle of stadium 1 , ∠y = 71.7°

depression angle of stadium 2 , ∠x = 25.2°

distance between the two stadiums  = d

So, it forms 2 triangles  ABD and ACD,

Using the trigonometric ratios,

tan θ = Altitude / Base

DC = AD × tan (90° - x)

= 1600 × tan( 90° - 25.2° )

= 1600 × cot(25.2°)

= 1600 × 2.13

DB = AD × tan (90° - y)

= 1600 × tan( 90° - 71.7° )

= 1600 × cot(71.7°)

= 1600 × 0.33

∴ d = DC - DB

     = 1600 * [ tan( 90° - 25.2° ) - tan( 90° - 71.7° ) ]

    = 2,871 meters

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Answer:

2000

Step-by-step explanation:

let the sum of the two terms be,x

Then,

x/100=20

where

100=no. of terms

20=mean

Then,

x/100=20

x=20×100

x=2000

So,

Sum of terms=2000

Answer:

42

Step-by-step explanation:

let the number be x

4/7 of x

(4/7) × x

4x/7

As stated in the question:

x=4x/7+18

=x-4x/7=18

=(7x-4x)/7=18

=3x/7=18

3x= 18×17

3x= 126

x=126/3

x=42

The balance after 8 years is $22,942.67

We know that the savings account earns 15% annually, and the initial deposit is $7500, then the balance as a function of time in years is:

B = $7500*(1 + 15%/100%)^t

B = $7500*(1.15)^t

The balance after 8 years is what we get when we evaluate the above function in t = 8, so we get:

B = $7500*(1.15)^8 = $22,942.67

So the correct option is the last one.

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Answer:

[tex]\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]

Step-by-step explanation:

Setting the expression equal to zero to find the roots,

[tex]3x^2 +2=0\\\\3x^2 =-2\\\\x^2 =-\frac{2}{3}\\\\x=\pm i\sqrt{\frac{2}{3}}[/tex]

This means that

[tex]3x^2 +2=\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]

Answer: Yes

Step-by-step explanation:

Each value of y maps onto one value of x.

Answer:

35-17=3y

Step-by-step explanation:

3y+17=35

    -17  -17

3y=35-17

Each sample has an equal chance of being picked as part of the sampling procedure known as random sampling. A randomly selected sample is intended to provide a fair reflection of the entire population.

Step 1: He should identify and decide which population he wants to study

Step 2: He should decide the size of the sample. He can do this using a sample size calculator.

Step 3: Select the Sample Randomly using:

It is to be noted that the lottery and Random Techniques can be manual or computer simulated.

The sample bar graph for the above sample is attached.

40% of 60% is not likely to catalyze a change in the needed change. A more proper percentage should be 90%.

Based on the figures given, 72% of the students agree that the dress code is nice (that is , it requires not change).

This means that it is highly unlikely that any changes will be made to the dress code soon.

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Answer:

Since <ABC ~= <DBE and <BAC ~= <BDE, the triangle s are similar by angle-angle.

Answer:

379.94

Step-by-step explanation:

3.14 x 11^2 =  379.94

The area of the given circle is 95 square ft.

Calculation for the Area of the Circle:

It is given in the diagram that,

The diameter of the circle, d = 11 ft.

Now, we know that the radius of a circle is equal to half of the diameter.

Therefore, radius of the given circle, r = 11/2 ft.

The formula for the area of the circle is given as follows,

A = π × r²

Substituting the values, π = 3.1, and r = 11/2, we get,

A = (3.14) × (11/2)²

A =  (3.14) × 30.25

A = 94.985

A ≈ 95

Hence, the area of the given circle with diameter 11 ft. comes out to be 95 ft².

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Answer:

160

Step-by-step explanation:

I multiplied the amount of each item to get to the answer:

- 8 shirts

- 4 pairs of pants

- 5 pairs of shoes

8 x 4 x 5 = 32 x 5

32 x 5 = 160

hope this helps!

Answer:

1. Given.

2. <5 is supplementary to <4.

2. Angles 5 and 4 are consecutive angles, and by the consecutive angles theorem, the two are supplementary.

3. m<4 + m<5 = 180

3. By the definition of supplementary angles, m<4 + m<5 = 180.

4. m<2 = m<4

4. Angles 2 and 4 are corresponding angles, and by the corresponding angles postulate, the two are congruent. By the definition of congruent angles, m<2 = m<4.

5. m<5 + m<2 = 180

5. Substitution property of equality.

Answer:

Step-by-step explanation:

Let l and w be the dimensions of rectangle.

The length of fencing is 100 ft:

Then:

The area is:

In order to have the maximum area we need to find the vertex of the quadratic function:

The vertex has x-coordinate:

or

So the width is 25 ft.

Find the length:

The area is:

See the attached graph.

Step-by-step explanation:

let's say one integer is X ....

so , Another one is (X -4).....

so , X × (X - 4) = 45

x² - 4x - 45 = 0

x² - 9x + 5x - 45 = 0

x(x - 9) +5(x - 9) = 0

(x-9) × (X+5) = 0

x-9 = 0 OR x+5 = 0

X= 9 X= -5

X is not a negative integer ......

so , X = 9

X-4 = 5 .......

r = 6
A=πr^2

A = 113.09734

Quarter circle formula = πr^2 / 4

113.09734 / 4 = 28.274335

113.09734 - 28.274335 = 84.824005 is the answer

Answer: 17

Step-by-step explanation:

substitute -3 for a and -5 for b. the equation will be[tex]\frac{(-3)^{2}+(-5)^{2} }{-3-(-5)}[/tex]. then when you simplify, you will get [tex]\frac{9+25}{-3+5}[/tex]. finally, add and you will get [tex]\frac{34}{2}[/tex] which is 17.

The base area of cube B is 25/9  times larger than the base area of cube A.

What is area cubic?

We know that volume of cube with each side of  units is equal to .

First of all, we will find the each side of cube A and B as:

[tex]A^{3} = 27[/tex]

[tex]\sqrt[3]{A^{3} } = \sqrt[3]{27}[/tex]

A = 3

[tex]B^{3} = 125[/tex]

[tex]\sqrt[3]{B^{3} } = \sqrt[3]{125}[/tex]

B = 5

Now, we will find base area of both cubes as:

[tex]\frac{Base area of B}{Base area of A} = \frac{B^{2} }{A^{2} }[/tex]

[tex]\frac{Base area of B}{Base area of A} = \frac{5^{2} }{3^{2} }[/tex]

[tex]\frac{Base area of B}{Base area of A} = \frac{25}{9}[/tex]

Therefore, the base area of cube B is 25/9  times larger than the base area of cube A.

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Work Shown:

(x hours strength)/(4 hours endurance) = 5/3

x/4 = 5/3

3x = 4*5

3x = 20

x = 20/3

x = (18+2)/3

x = 18/3 + 2/3

x = 6 + 2/3

x = 6 & 2/3

He needs to spend 6 full hours, plus an additional 2/3 of an hour, on strength training.

1 hr = 60 min

2/3 hr = (2/3)*60 min

2/3 hr = 40 min

6 hr + 2/3 hr = 6 hr + 40 min

Therefore, he needs to spend 6 hours, 40 minutes on strength training.

This is equivalent to 6*60+40 = 360+40 = 400 minutes.

Answer:

a polygon with an interior angle of 108 is a pentagon

While E will increase, C and D won't change.

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.

Due to the fact that the circle's equation is,

Nevertheless, we are aware of the circle's equation.

                           [tex]x^{2}+y^{2}+C x+D y+E=0[/tex]

(By figuring out the circle's equation[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex], where r is the radius and (h,k) is the center)

                         [tex]x^{2}+y^{2}+2 h x+2 k y+\left(h^{2}+k^{2}-r^{2}\right)=0[/tex]

The following equation is compared to the generic equation above.

Our results are C = 2h, D = 2k, and E [tex]=\left(h^{2}+k^{2}-r^{2}\right)[/tex]

As a result, C will be unchanged if r lowers ( because C is free from r)

D won't be effected ( because D is also free from r)

E will, however, rise if r falls.

E[tex]=\left(h^{2}+k^{2}-r^{2}\right)[/tex]

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The correct option is (B) yes because all the elements of set R are in set A.

Given sets:

So,

Therefore, the correct option is (B) yes because all the elements of set R are in set A.

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The complete question is given below:
Consider the sets below. U = {x | x is a real number} A = {x | x is an odd integer} R = {x | x = 3, 7, 11, 27} Is R ⊂ A?

(A) yes, because all the elements of set A are in set R

(B) yes, because all the elements of set R are in set A

(C) no because each element in set A is not represented in set R

(D) no, because each element in set R is not represented in set A

Ileana  have to invest for 8 years :

Simple interest is a simple and straightforward formula for figuring out how much interest will be charged on a loan. Simple interest is calculated by dividing the daily interest rate by the principle and the number of days between payments.

The principal amount must be multiplied by the time, interest rate, and time period in order to calculate simple interest. Simple Interest = Principal x Interest Rate x Time is the written formula.

Principal amount = $15,500

interest = $5,084

Time = ?

Rate = 4.1% simple interest

to find the simple interest :

                                         I = [tex]\frac{(p*t*r)}{100}[/tex]

       Then:

         Time = [tex]\frac{I*100}{P*R}[/tex]

                  = [tex]\frac{(5084*100)}{(15500*4.1)}[/tex]

                  = [tex]\frac{508400}{63,550}[/tex]

                  = 8 years

Ileana  have to invest for 8 years

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