MATHEMATICS HIGH SCHOOL

What is the value of cos(x/2) if tan x=1/2 and x is in quadrant III

Answers

Answer 1
Answer:

The value of cos(x/2) is required.

The required value is \cos(x/2)=-\sqrt{(5-2√(5))/(10)}

Trigonometry

The given value is

\tan x=(1)/(2) where x is in quadrant III.

From trigonometricidentities we have

\sec^2x=1+\tan^2x\n\Rightarrow \sec^2x=1+((1)/(2))^2\n\Rightarrow \sec^2x=(5)/(4)\n\Rightarrow \cos^(2)x=(4)/(5)\n\Rightarrow \cos x=(2)/(√(5))

If x lies in quadrant III then x/2 lies in quadrant II.

Cos is negative in quadrantIII so,

\cos x=-(2)/(√(5))=-(2√(5))/(5)

\cos (x)/(2)=\pm \sqrt{(1+\cos x)/(2)}\n =\pm\sqrt{(1-(2√(5))/(5))/(2)}\n =\pm\sqrt{(5-2√(5))/(10)}

Since, x/2 lies in the secondquadrant and cos (x/2) is negative.

The required value is -\sqrt{(5-2√(5))/(10)}

Learn more about trigonometry:

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Answer 2
Answer:

Answer:

Step-by-step explanation:

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What is the missing reason in the two calumn proof

Answers

Answer:

1. b

2. d

3. c

4. a

5. f

6. e

Step-by-step explanation:

If a store uses a selling price-based markup of 40% and an item costs the store $300, what selling price would the store set for the item?

Answers

The store sells a product for 40% more than the what they buy it for.
40% is 0.40 in decimal because all percents are out of 100 (divide by 100)
300×(1+0.40)=$420

At Joe's Pizzeria, small pizzas cost $7.50, and large pizzas cost$11.00. One day between 3:00 PM and 9:00 PM, Joe sold 100 pizzas
and took in $848. How many more small pizzas than large pizzas did
Joe sell during that 6-hour period?
(A) 28
(B) 44
(C) 56
(D) 72

Answers

Answer:

Option B. 44 is the correct answer

Step-by-step explanation:

Let l be the number of large pizzas and s be the number of small pizzas

Then according to the given statement the equations will be:

l+s = 100\ \ \ Eqn\ 1\n11l+7.5s = 848\ \ \ Eqn\ 2

From equation 1

l = 100-s

Putting in equation 2

11(100-s)+7.5s = 848\n1100-11s+7.5s = 848\n-3.5s+1100 = 848\n-3.5s = 848-1100\n-3.5s = -252\n(-3.5s)/(-3.5) = (-252)/(-3.5)\ns = 72

Putting s=72 in equation 1

l+72 = 100\nl = 100-72\nl = 28

How many more small pizzas means we have to find s-l

So,

s-l = 72-28 = 44

Hence,

Option B. 44 is the correct answer

20+ POINTS!!! ANSWER FAST!!!Which sets of numbers are closed under addition?



Choose all answers that are correct.



A.


whole numbers


B.


natural numbers


C.


negative integers


D.


integers

Answers

It is all of them. A. Whole Numbers, B. Natural Numbers, C. Negative Numbers, D. Integers. This is because when ever you add any of these numbers to them selves, the answer will always be from that set of numbers. Like negative + negative = negative, like that.

Hope I helped ya!!!!!!!!!
♥ Which sets of numbers are closed under addition?



♥ Choose all answers that are correct.



A.


whole numbers


B.


natural numbers


C.


negative integers


D.


integers  
♥are all closed under addition. 
♥Therefore ALL are right. 

Which is the best definition of the radius of a circle? A. The distance around the outside of the circle
B. The distance across the middle of the circle
C. The Point at the center of the circle
D. The distance from the center to any point on the circle

Answers

The best definition of the radius of a circle is option D: "The distance from the center to any point on the circle."

The radius is a fundamental geometric concept that is integral to understanding and describing circles. It is a straight line segment that extends from the center of the circle to its outer edge.

This single measurement defines the size of the circle and is consistent from the center to any point on the circumference. It is crucial in various mathematical and geometric calculations, including calculating the circle's area, circumference, and relationships with other elements in geometry. Option D succinctly encapsulates the essence of the radius and its geometric significance in a clear and concise manner.

for such more question on radius

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#SPJ2

D since the radius is the distance between the center and any edge of the circle

if you like my answer vote me for the brainiest.

The cost in dollars, y, of a large pizza with x toppings from Pat’s Pizzeria can be modeled by a linear function. A large pizza with no toppings costs $14.00. A large pizza with 2 toppings costs $17.50. What is the cost of a pizza with 5 toppings? Round to the nearest penny.

Answers

Answer:

The cost a pizza with 5 toppings is $22.75

Step-by-step explanation:

Consider the provided statement.

It is given that A large pizza with no toppings costs $14.00.

A large pizza with 2 toppings costs $17.50.

We can translate the problem and given into data points: (0, 14) and (2,17.50)

Where x coordinates represents the toppings and y is the cost.

Now the use the point-slope form: y - y_1 = (y_2-y_1)/(x_2-x_1) (x-x_1)

Substitute the respective values.

y - 14 = (17.50-14)/(2-0) (x-0)

y - 14 = 1.75 (x)

y= 1.75x+14

Hence, the required equation isy= 1.75x+14

Now find the cost of pizza with 5 toppings by substituting x=5 in above equation.

y= 1.75(5)+14

y= 8.75+14

y= 22.75

Hence, the cost a pizza with 5 toppings is $22.75
First find how much one topping is: subtract the L price from the L2T price: 17.50-14=3.50. Divide by 2: 3.50/2=1.75. Multiply by 5: 1.75•5=8.75. Add the topping cost to the L pizza cost: 8.75+14=22.75. $22.75 :)
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