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3 years ago

Find all solutions to the equation. cos x = - 1/2

Mathematics

1 answer:

madam [21]3 years ago

4 0

Answer:

$x = 2\pi /3 + 2\pi n\\x= 4\pi /3 + 2\pi n$

Step-by-step explanation:

Radian: x = 2\pi /3 + 2\pi n\\x= 4\pi /3 + 2\pi n

Degree: x = 120 + 360n , x = 240 + 360n

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Cate wants to buy calzones and sodas for her friends she finds that when she buys two calzones and three sodas she pays $13 when

IceJOKER [234]

Answer:

The prices for a calzone and for soda as an ordered pair (c,s) is (5,1)

Step-by-step explanation:

Let c be the prize of calazone

Let s be the prize of soda

She buys two calzones and three sodas she pays $13

So, 2c+3s=13

She buys three calzones and two sodas she pays $17

So, 3c+2s=17

Plot the equations on graph

2c+3s=13 --- Green

3c+2s=17 --- Blue

Intersection point will give the intersection point

So,(c,s)=(5,1)

So, Option c is correct

The prices for a calzone and for soda as an ordered pair (c,s) is (5,1)

4 0

3 years ago

Find the volume of a cylinder made by rotating a rectangle with a width of 2.5 feet and a length of 8 feet as shown in the figur

asambeis [7]

<span>the question does not present the picture, but this does not interfere with the resolution</span>

we know that
When a rectangle with a width of 2.5 feet and a length of 8 feet rotates it makes a cylinder with a radius r = 2.5 ft and a height h = 8 ft

volume of a cylinder=pi*r²*h-----> pi*2.5²*8----> 157 ft³

the answer is
157 ft³

7 0

3 years ago

A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric

larisa86 [58]

Answer:

525 x 1,050

A = 551,250 m²

Step-by-step explanation:

Let 'L' be the length parallel to the river and 'S' be the length of each of the other two sides.

The length of the three sides is given by:

$2S+L=2,100\\ L=2100-2S$

The area of the rectangular plot is given by:

$A=S*L\\A=S(2100-2S)\\A=2100 S -2S^2$

The value of 'S' for which the area's derivate is zero, yields the maximum total area:

$\frac{dA(S)}{dS}=\frac{d(2100 S -2S^2)}{dS}\\0= 2100 - 4S\\S=525$

Solving for 'L':

$L=2100-(2*525)\\L=1,050$

The largest area enclosed is given by dimension of 525 m x 1,050 and is:

$A = 525*1,025\\A=551,250\ m^2$

5 0

3 years ago

The scientist creates an equation that models her data for each tree so that she can predict the diameter in the future. Complet

otez555 [7]

Answer:

y = 0.3X + 18.3

Step-by-step explanation:

Given that data :

x = year ;

y = trunk diameter, in inches

Year ________trunk diameter

1 __ 18.6

3 __ 19.2

5 __ 19.8

7 __ 20.4

9 ___21.0

11 __ 21.6

13 __ 22.2

Using the linear regression calculator :

The linear equation obtained is :

y = 0.3X + 18.3

Where ;

Slope = 0.3 ; intercept, c = 18.3

8 0

3 years ago

In 2010, there were 311 middle schools in Virginia. In 2016, there were 306. By what percent did the number of middle schools in

Nataly_w [17]

Answer:1.6%

Step-by-step explanation: no of students in 2010=311

no of students in 2016=306

difference=311-306

%decrease=5/311 x 100

3 0

2 years ago