Which equation should be used to find the volume of the figure?

Answer:

[tex]-3/\sqrt{58}[/tex]

Step-by-step explanation:

tan = opposite / adjacent

opposite side is the y-coordinate of a point on the terminal side

adjacent side is the x-coordinate of a point on the terminal side

if the terminal side is in the second quadrant (the top-left quadrant), a coordinate on the terminal side would have a negative x-coordinate and a positive y-coordinate

This being the case:

the opposite side (y) would be -3 and the adjacent side (x) would be 7

using the Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex]

[tex]7^2+(-3)^2=c^2[/tex]

The hypotenuse is c, so it equals [tex]\sqrt{58}[/tex]

sin = opposite / hypotenuse

so sin(theta) = [tex]-3/\sqrt{58}[/tex]

For the provide inquilty problem,

a) The feasible region lies in between the following equations,

b) The extreme points of feasible region are (2,5) , (6,1) ,(0,0),(6,0),(0,5).

Let consider, x = A and y = B, this changes your inequalities and equations as follows: Maximize x + 2y, such that:

x ≤ 6

y ≤ 5

2x + 2y = 14

x,y ≥ 0

We use graphical method, for getting the solution of problem. So, first change the Inequalities into equality equations.

we would then find the region of feasibility by looking at the areas on the graph that satisfy the inequalities and equations,

x ≤ 6

y ≤ 5

2x + 2y = 14 (this is an equation)

x ≥0

y ≥ 0

a) The graph will look like as present above : we can see that the feasible region is the area on the graph that is:

on or below the line y = 5

on or to the left of the line x = 6

on or above the line y-axis , y = 0

on or to the right of the x-axis, x = 0

on the line 2x + 2y = 14

This says is that your solution has to be on the line of 2x + 2y = 14, have an x-coordinate that is greater than or equal to 0 and less than or equal to 5 and have a y-coordinate that is greater than or equal to 0 and less than or equal to 5. The maximum or minimum value should be at the corner points of the feasible region.

b) The corner points would be at (x,y) = (2,5) and (x,y) = (6,1). Also, plotted some other points on the line just to show the max/min value of function on the corner points of the feasible region.

(2,5) = 12

(4,3)= 10

(3,4) = 11

(6,1) = 8

the maximum solution is at the coordinate of (2,5) and all of your constraints have to be satisfied at the this point. The solution is that the maximum value is when x = 2 and y = 5, that is one of the corner points of the feasible region.

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Complete question:

Consider the following linear program:

Max. 1A+2B , s.t.

1A ≤6

1B≤5

2A+2B=14

A,B>0

a. Show the feasible region.

b. What are the extreme points of the feasible region?

Answer:

the 2 positive of number is

Step-by-step explanation:

2_:3+23*3⅔+09=2465

Answer:

Solutions given:

4sin B=3sin (2A+B)............(1)

let B=A+B-A

and

2A+B=A+B+A

again

substituting value we get

Or, 4sin[ A+B-A]=3sin[ A+B+A]

Or,4Sin [(A+B)-A]=3sin[ (A+B)+A]

Or,4(Sin(A+B)cosA-Cos(A+B)sinA)=

3(Sin(A+B)cosA+Cos (A+B)sin A)

Or,4Sin(A+B)Cos A-4Cos(A+B)sinA=

3Sin(A+B)cosA+3cos(A+B)sinA

Or, 4Sin(A+B)CosA-3Sin(A+B)cosA=

3cos(A+B)sinA+4Cos(A+B)sinA

OrSin(A+B)CosA=7Cos(A+B)sinA

or

7cos(A+B)/Sin (A+B)=Cos A/Sin A

7Cot (A+B)=CotA.

7Cot (A+B)=CotA.Proved.

The irrational numbers to children can be explained as the numbers  that can be written as a nonrepeating or nonterminating decimal .

What are Irrational Numbers ?

The real numbers that can be represented as a nonrepeating or a nonterminating decimal but not as a fraction, and the decimal that goes on forever without repeating.

For Example : [tex]\sqrt{2} , \sqrt{5} , \sqrt{7}[/tex] are few example of irrational numbers .

In simpler words : the irrational number is a number that is not rational. which means It is a number which cannot be written as a ratio of two integers or cannot be written as fraction.

and If a fraction has a 0 in the denominator , it is an irrational number .

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Answer:

15

Step-by-step explanation:

To find f(-3), substitute x with (-3)

f(x) = -x² - 8x

f(-3) = - (-3)² - 8*(-3)

      = - (9) + 24

       = - 9 + 24

       = 15

Answer:

15

Step-by-step explanation:

f ( x ) = - x² - 8x

Accordingly, to find the value of f ( -3 ) you have to replace x with ( - 3 ).

f ( -3 ) = - (-3)² - 8 × -3

f ( -3 ) = - 9 + 24

f ( -3 ) = 15

Answer:The student needs to score 20 points

Step-by-step explanation:

? /50= 40/100Cross multiply:100*? = 40*50⇒? = 40*50/100= 20

The slope of the line is given by the equation slope m = 3/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , let the first point be P = P ( 0 , 1 )

Let the second point be Q = Q ( 2 , 4 )

Now , the slope of the line between the two points is

Slope m =  ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 4 - 1 ) / ( 2 - 0 )

On simplifying the equation , we get

Slope m = ( 3 / 2 )

Therefore , the value of m is 3/2

Hence , the slope of the line is 3/2

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Answer:

37.7 cm

Step-by-step explanation:

C=2πr=2·π·6≈37.69911

Answer:

37.68 cm.

Step-by-step explanation:

The formula for circumference of a circle is: πd (diameter)

The radius of this circle is 6 centimeters.

To find the diameter, multiply the radius by 2.

6 × 2 = 12.

12 is the diameter.

Lastly, multiply the diameter by pi.

**3.14 IS A SUBSTITUTE FOR PI**

3.14 = 37.68.

Therefore, the circumference of this circle is 37.68 cm.

Answer:

1. A 2.C 3.D 4.B 5. A PORK-U-PINE

Step-by-step explanation:

a^2+b^2=c^2

Answer:

28x^2+3x-18

Step-by-step explanation:

Formula: (a+b)(a+b) = a^2 + a*b + a*b + b*b

Following this: 28x^2 -21x +24x -18

Then you combine like terms: 28^2 +3x-18

hope this helped!! :)

Answer:

[tex]28x^{2} + 3x - 18[/tex]

Answer:

5

Step-by-step explanation:

The process of solving the 3 variable with 2 equation is explained below.

The term equation is defined as a relationship between two terms on either side of an equal sign.

Here we have the following steps to solve the 3 variable for two equation is solved accordingly.

First of all we have to take any two equations and solve it for one variable.

And then again we have to take another two pair of equations and solve for the same variable.

Now, we have a system of two equations with two unknown variables.

Then we have to solve the equation by using the appropriate arithmetic operations.

and then substitute it accordingly until all the value of the variable are solved.

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The linear equation for jj is ($7.46 - $2.66) / 5 and the cost of each bottle of juice is $0.96.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                   Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The first step to take in order to determine jj, is to determine the total cost of the  5-pack of juice bottles.

Cost of the  5-pack of juice bottles = Total cost before tax - cost of the bag of oranges

Cost of the  5-pack of juice bottles = $7.46 - $2.66 = $4.80

The second step is to determine the cost of each bottle of juice

The cost of each bottle of juice = Cost of the  5-pack of juice bottles / total number of bottles

$4.80 / 5

= $0.96

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Answer: c = P - a - 5

Step-by-step explanation:

P= a + 5 + c

P - a - 5= c

Here the exact values of circle is not given.so in general .Area of Circle = πr² or πd2/4 in square units, where (Pi) π = 22/7 or 3.14.

The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r2, where r is the circle's radius, is the formula for c

Area of Circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of circumference to diameter of any circle. It is a special mathematical constant.

Area of Circle:

[tex]\pi[/tex]×r²

Where [tex]\pi[/tex]=3.14

But Here we need correct values to find the area of the circle.

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A verbal expression for the given algebraic expression are as follows:

10. The product of a and b

11. Four times the sum of x and seven

12. Twice the value of x

13. The cube of m

14. The difference between x and six

15. Eight hundred twelve

16. The value of y

17. The average of x and y

18. Three times x minus four

19. Five times the difference of a and b

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Answer:

2.275%

Step-by-step explanation:

z = (x-μ)/σ, where

x is the raw score = 14.9 ft

μ is the population mean = 12.5 ft

σ is the population standard deviation = 1.2 ft

We are to find the percentage of the apple trees are taller than 14.9 ft,

This means x > 14.9, x greater than 14.9

Hence,

z = (14.9 - 12.5)/1.2

z = 2

Probability value from Z-Table:

P(x<14.9) = 0.97725

P(x>14.9) = 1 - P(x<14.9) = 0.02275

Converting to Percentage

= 0.02275 × 100

= 2.275%

Therefore, the percentage of the apple trees that are taller than 14.9 ft is 2.275%

Answer:

D. 3600ft^3

Step-by-step explanation:

First you have to find the volume of one box:

Volume = Length*Width*Height

Volume = 48ft^3

Multiply 48 by 75 to find the volume of 75 boxes:

48*75 = 3600ft^3

y=1200(1+.3)⁶

initial value =

y=5792.1708

6 represent time.

Answer:

What he did right was doing the first part correctly, wher it;s 46000x1.05, which is 48300. But then the student thought that every year, Carlos' salary will increase by 48300, and after 3 years it got to 144900, which is nuts. The real thing is to do 46000 x 1.15, because on the 3rd year, your salary will be 115% of your salary, if that makes sense, you do 5x3 = 15, then you add 15% to 100 which is 115 % =1.15. then you do 46000x1.15= 55545$

hope that answers your question

comment if your confused about something.

Step-by-step explanation:

Salary after 3 years of increment by 5% annual rate is given as $53,250.

Carlos accepts a new job with a starting salary of $46,000. He will earn a 5% increase after each year. What will be his salary after 3 years.

It is defined as the fee you pay to borrow money or the fee you levy to lend money. Interest is considerable and frequently recalled as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

Incorrect solution,
$46,000 • 1.05 • 3 = $144,900 is Carlos’ salary after 3 years.

Correct solution,
Principal amount = $46,000
rate of increase in salary each year = 5%
After t = 3 years what will be the salary = ?

following identity is used to calculate the increments in principal amount.
[tex]Amount = principal(1+r)^t[/tex]

[tex]Amount = 46000(1+0.05)^3\\Amount = 46000(1.05)^3\\[/tex]
Amount = 456000 * 1.16
Amount = 53,250

Thus, salary after 3 years of increment is given as $53,250.

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Using trigonometric ratios, the value of x is as follows:

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the angle of a right angle triangle can be found using trigonometric ratios as follows:

Hence, let's find angle x

Therefore,

sin x = opposite / hypotenuse

opposite side = 7 ft

hypotenuse side = 18 ft

Hence,

sin x = 7 / 18

x = sin⁻¹ 7 / 18

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Answer:

D)

Step-by-step explanation:

all vertical lines have an undefined slope because their denominator (after using the slope formula) is zero

Answer:

pls can you explain further

Answer:

63

Step-by-step explanation:

1/3 of 63= 21

and the reverse of 63 is 36

so 1/2 of 36 =18

so 21-18 =3

hence proven

The two-digit number will be 63 for the given condition.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

1/3 of 63= 21

And the reverse of 63 is 36

so 1/2 of 36 =18

so 21-18 =3

Therefore the two-digit number will be 63 for the given condition.

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The total number of quizzes in 9 weeks will be 45.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Baldwin took a total of 35 quizzes over the course of 7 weeks. After attending 9 weeks of school this quarter.

The number of quizzes in 9 weeks will be,

7 weeks = 35 quizz

1 week = 35 / 9 quizz

9 week = ( 35 x 7 ) / 9

9 weeks = 45 quizzes.

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Answer:

4.30 inches

Step-by-step explanation:

Given data

Volume of basket ball= 334cubic inches

We know that the expression for the volume of a sphere is given as

Volume of sphere= 4/3πr^3

334= 4/3πr^3

334=4/3*3.142*r^3

334=4.189*r^3

r^3= 334/4.189

r^3=79.73

cubic root both sides

r= ∛79.73

r=4.30 inches