Ieda bakes 73 cupcakes and accidentally drops 5 of them. She divides them equally into 13 containers for a bake sale for the school band. How many cupcakes does Ieda have left

Answers

Answer 1

Answer:

3 left

Step-by-step explanation:

If she starts out with 73 and drops 5 she is left with 68, an you cannot evenly divide 68 and 13 so you divide it as much as you can evenly which is five containers leaving 3 extra cupcakes.

Answer 2

For this case we have that initially there are 73 cupcakes, if Leda dropped 5 then we are left with:

[tex]73-5 = 68[/tex]

Now, you must equally divide the 68 cupcakes into 13 containers:

putting 5 cupcakes in each of the 13 containers we have;

[tex]13 * 5 = 65[/tex]

[tex]68-65=3[/tex]

So, we have 3 cupcakes left.

Answer:

3 cupcakes


Related Questions

A fish tank has a length of 14cm, a width of 25cm, and a height of 15cm. It is only filled with water up to a height of 7 centimeters. How much more water is needed to fill the tank to the brim?

Answers

Answer:

2800 cm^3, or 2.8 liters

Step-by-step explanation:

The base of the tank remains 14 cm × 25 cm. The remaining height is 15 -7 = 8 cm, so the remaining volume is ...

(14 cm)(25 cm)(8 cm) = 2800 cm^3 = 2.8 liters

_____

1 liter = 1000 cm^3

This Data set represents the number
of children in 8 families

4,2,1,2,4,2,6,3

The mean of this data set is 3. what is the mean absolute deviation

A. 1.25
B. 3
C. 3.3
D. 8

Answers

Answer:

The answer would be A. 1.25

Given that (-8,-8) is on the graph of f(x), find the corresponding for the function f(x)+5.

Answers

ANSWER

[tex](-8, - 3)[/tex]

EXPLANATION

Given that: (-8,-8) is on f(x).

Then we can write (-8,f(-8)) is on f(x).

The corresponding point on

[tex]f(x) + 5[/tex]

will be

[tex](-8,f(-8)+5)[/tex]

We substitute f(-8)=-8 to obtain;

[tex](-8, - 8+5)[/tex]

This simplifies to

[tex](-8, - 3)[/tex]

Therefore the corresponding point on f(x)+5 is (-8,-3).

a maple tree is 4.2 meters tall. A pine tree is 1.02 shorter that the maple tree. An oak tree is 1.89 taller than the pine tree . How tall is the oak tree?

Answers

Answer:

7.782352941

Step-by-step explanation:

4.2 divided by 1.02 the multiply the out come of that by 1.89 to get 7.782352941

factor the expression below x^2 + 12x + 36

Answers

Answer:

(x + 6)²

Step-by-step explanation:

This is a perfect square of the form

(x + a)² = x² + 2ax + a²

here a² = 36 ⇒ a = 6 and 2ax = 2 × 6x = 12x

Hence

x² + 12x + 36 = (x + 6)²

Answer:

(x+6)(x+6)

Step-by-step explanation:

The inequality x + 2y ≥ 3 is satisfied by which of the following points? (Select all that apply.)

(1, 1)
(-3, 4)
(-2, 2)
(5, -2)

Answers

Answer:

First option: (1, 1)

Second option: (-3, 4)

Step-by-step explanation:

Substitute each point into the inequality:

Point (1,1):

[tex]x + 2y \geq3\\\\(1) + 2(1) \geq3\\\\3\geq3[/tex]

(The inequality is satisfied with this point)

Point (-3, 4):

[tex]x + 2y \geq3\\\\(-3) + 2(4) \geq3\\\\5\geq3[/tex]

 (The inequality is satisfied with this point)

Point (-2, 2):

[tex]x + 2y \geq3\\\\(-2) + 2(2) \geq3\\\\2\geq3[/tex]

(The inequality is not satisfied with this point)

Point (5, -2):

[tex]x + 2y \geq3\\\\(5) + 2(-2) \geq3\\\\1\geq3[/tex]

(The inequality is not satisfied with this point)

Answer:

Your answer would be A and B

Step-by-step explanation:

If two distinct lines intersect, which is NOT necessarily true? A) The lines are not parallel. B) The lines are perpendicular. C) The lines form angles at the intersection. D) The intersection of the two lines is a point.

Answers

Answer:

B is not necessarily true

Step-by-step explanation:

A) This is always true

B) This is not necessarily true

When two lines intersect, they form angles at the intersection as D says, but that does not mean that the angle will always be 90 degrees as is required for the two intersecting lines to be perpendicular

C) This is always true

D) This is always true

Option B) The lines are not perpendicular is not necessarily true.

What is the Intersection of Two lines?

When two lines intersect and following are the three different possibilities:

1) They are parallel, if lines are parallel they can never intersect.

2)They cross each at an angle and the point of intersection is unique that is they intersect at only one point.

3) Two lines coincide, that is every point on line 1 is a point on line 2.

Now

In option B it is given that lines are perpendicular that is the specific case of (2) When angle is 90°.

Therefore, it is not necessarily true.

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17) There are 15 boys and 18 girls in seventh grade. Find the ratio of boys to girls in seventh grade.

18) Janet bought 12 guavas and 16 apples. What is the ratio of guavas to apples?

19) Sandy has 8 candies and Tabitha has 10 candies. Find the ratio of Sandy’s candies to Tabitha’s candies.

20) For a birthday party, Evelyn orders 10 chicken pizzas and 15 vegetable pizzas. Find the ratio
of chicken pizzas to the vegetable pizzas.

21) In a local animal sanctuary, there are 48 deer and 64 monkeys. Find the ratio of deer to monkeys.

22) Gerry scored 56 in Math and 84 in Science. Find the ratio of his scores in Math to Science.

23) A fruit seller bought 75 mangoes and 125 apples from vendor. Find the ratio mangoes to apples bought.

24) Yulee primary school maintains a library with 81 English books to every 90 Math books. Find the ratio of English books to the Math books.

Answers

17) 5:6

18) 3:4

19) 4:5

20) 2:3

21) 3:4

22) 2:3

23) 3:5

24) 9:10

These answers are all simplified ratios

Final answer:

The questions involve finding the ratio of two quantities and simplifying them by dividing both numbers by their greatest common divisor. Each ratio gives a comparative relationship between two different counts of items or scores in different subjects.

Explanation:

The questions provided all relate to finding the ratio of two quantities.

The ratio of boys to girls in seventh grade is 15:18, which can also be simplified to 5:6 by dividing both numbers by 3.The ratio of guavas to apples Janet bought is 12:16, which simplifies to 3:4 after dividing both numbers by 4.For Sandy and Tabitha's candies, the ratio is 8:10, which simplifies to 4:5 once both numbers are divided by 2.Evelyn orders chicken and vegetable pizzas at a ratio of 10:15, which is equal to 2:3 after dividing both numbers by 5.In the animal sanctuary, the ratio of deer to monkeys is 48:64, simplifying to 3:4 after dividing by 16.Gerry's scores in Math to Science are at a ratio of 56:84, which can be reduced to 2:3 by dividing by 28.The ratio of mangoes to apples the fruit seller bought is 75:125, simplified to 3:5 after dividing both by 25.Lastly, the ratio of English books to Math books in Yulee primary school's library is 81:90, which simplifies to 9:10 upon division by 9.

In each case, the ratio is found by comparing two quantities and simplifying by dividing both numbers by their greatest common divisor (GCD).

Which answer shows 0.00897 written in scientific notation?

Answers

Answer:

8.97*10^-3

Step-by-step explanation:

just did the question and got it right.

Can someone help me with this I’ll give brain

Answers

Answer:

-65/2

Step-by-step explanation:

I am just a natural genius ;)

Answer:

see explanation

Step-by-step explanation:

Evaluate the parenthesis before multiplication

4² = 4 × 4 = 16 and

( [tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex]

Thus 16 + [tex]\frac{1}{4}[/tex] = 16 [tex]\frac{1}{4}[/tex] = [tex]\frac{65}{4}[/tex]

Hence

- 2 × [tex]\frac{65}{4}[/tex] = [tex]\frac{-2(65)}{4}[/tex] = - [tex]\frac{65}{2}[/tex] = - 32 [tex]\frac{1}{2}[/tex]

Help help help math image:

Answers

Answer:

13. 90

14. 43

15. 146

a hula hoop has a radius of 19 inches. what is the length of the arc subtending 1/4 of the hoop?
A. 43.8
B. 14.9
C. 29.8
D. 59.7

Answers

Find the circumference:

Circumference = 2 x PI x radius

Circumference = 2 x 3.14 x 19 = 119.32

Divide by 4: 119.32 / 4 = 29.83 rounded to 29.8

The answer is C.

Answer:

C. 29.8 inches

Step-by-step explanation:

Length of complete hula hoop(L)= circumference of hoop

=>[tex]L=2\pi r[/tex]

where radius, r= 19 inches

Therefore length of arc(l) subtending 1/4 of the hoop is

=>[tex]l=\frac{1}{4}\times L=\frac{1}{4}\times2\pi r=\frac{\pi r}{2}[/tex]

=>[tex]l=\frac{\pi \times 19}{2}inches=29.8 inches[/tex]

Thus the length of the arc subtending 1/4 of the hoop is 29.8 inches

Solve the equation

3x-1/2y=2

Answers

Answer:

Step-by-step explanation:

Without a second equation relating x and y, we can solve 3x - 1/2y = 2 ONLY for x in terms of y or for y in terms of x:

x in terms of y:    Multiply all three terms of 3x - 1/2y = 2 by 2, to eliminate the fraction:  6x - y = 4.  Now add y to both sides to isolate 6x:  6x = 4 + y.

Last, divide both sides by 6 to isolate x:

x = (4 + y)/6

y in terms of x:    

y = 6x - 4

If you want a numerical solution, please provide another equation in x and y and solve the resulting system.

HELP!!!!!! READ BELOWW

Answers

Answer:

The missing words

# x ⇒ # y ⇒ # 4 ⇒ # 0

Step-by-step explanation:

* Lets revise how to find the inverse function

- At first write the function as y = f(x)

- Then switch x and y

- Then solve for y

- The domain of f(x) will be the range of f^-1(x)

- The range of f(x) will be the domain of f^-1(x)

* Now lets solve the problem

∵ f(x) = √(x - 4)

∴ y = √(x - 4) ⇒ switch x and y

x = √(y - 4) ⇒ square the two sides

∴ x² = [√(y - 4)]² ⇒ cancel the root by squaring

∴ x² = y - 4 ⇒ add 4 to the both sides

y = x² + 4

∴ f^-1(x) = x² + 4

* To find the domain of the inverse, find the range of the function

∵ The domain of f(x) is ⇒ x - 4 ≥ 0 (no negative value under√)

∴ the domain is x ≥ 4

- Substitute this value in the function to find the range

∵ x = 4

∴ y = √(4 - 4) = 0

∴ y ≥ 0

- The range of f(x) is y ≥ 0

∴ The domain of the inverse f^-1(x) is x ≥ 0

- The missing words

# x

# y

# 4

# 0

1. m+ 10< 16
2. -2g28_
3. y-22 < 19
4. -7b>-28
5. h+30 < 0
6. -5x < 10
7. t+13 > 22
8. w-12 <16​

Answers

Answer:

[tex]1.\ m<6\\2.\ g\leq-4\\3.\ y<41\\4.\ b<4\\5.\ h<-30\\6.\ x>-2\\7.\ t>9\\8.\ w<28[/tex]

Step-by-step explanation:

1. Subtract 10 from both sides. Then:

[tex]m+ 10< 16\\ m+ 10-10< 16-10\\m<6[/tex]

2. Divide both sides by -2. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-2g\geq8\\\\\frac{-2g}{-2}\geq\frac{8}{-2}\\\\g\leq-4[/tex]

3. Add 22 to both sides. Then:

[tex]y-22< 19\\ y-22+22<19+22\\y<41[/tex]

4. Divide both sides by -7. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-7b>-28\\\\\frac{-7b}{-7}>\frac{-28}{-7}\\\\b<4[/tex]

5. Subtract 30 from both sides. Then:

[tex]h+30<0\\ h+30-30<0-30\\h<-30[/tex]

6. Divide both sides by -5. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-5x<10\\\\\frac{-5x}{-5}<\frac{10}{-5}\\\\x>-2[/tex]

7. Subtract 13 from both sides. Then:

[tex]t+13>22\\ t+13-13>22-13\\t>9[/tex]

8. Add 12 to both sides. Then:

[tex]w-12< 16\\ w-12+12<16+12\\w<28[/tex]

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 The length of a rectangle is 6 inches, and the width is 5 inches. When each dimension is increased by x inches, the area triples. Which equation models this situation?

A)(6x)(5x) = 60B)(6x)(5x) = 90C)(x + 6)(x + 5) = 60D)(x + 6)(x + 5) = 90​

Answers

Answer:

D

Step-by-step explanation:

Before the increase, the length is 6 and the width is 5, so the area is 5×6 = 30.

After the increase, the length is x+6, the width is x+5, and the area is tripled: 30×3 = 90.

Therefore:

(x+6) (x+5) = 90

A sports store had a 60% off sale. Justin bought a pair of sneakers that were on sale for $22.40. What was the original price ?

Answers

Hello wendywagor!

Let x = the original price of the sneakers

x - .60x = 22.40

.40x = 22.40

x = $56

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Have A Great rest of Your Day!

Without calculating, which has a bigger volume. A cube that has a length, width, and height of 18 m. Or a sphere with a radius of 9 m? Explain.

Answers

Weird. A period appears above this... huh.

Answer:

[Th]e cube has a greater value.

Step-by-step explanation:

What the word problem really wants us to get [is ]the question of 'Which is greater, A=6a^2 when 'a' [is] 18 or A=4[tex]\pi[/tex]r^2 when r = 9? And here's how to solve that.

Starting with the[ c]ube we have A=6a^2. A bit t[o]o simple, right?

A=6(18)^2 Substitute numbers.

A=6(324) Solve ex[p]onents.

A=1944 Mult[i]ply.

So w[e] know that the cube is 1944 meters cube[d ] in area. But what about the more [f]ormidable sphere? Fo[r] it we need a slightly m[o]re co[m]plicated formula, A=4[tex]\pi[/tex]r^2. However, instead of using the real pi I will be rounding to 3.14, since we have no calculator so anything more would take way too long and fry your[ bra]in.

A=4(3.14)(9)^2 Subst[i]tute numbers.

A=4(3.14)(81) Solve expone[n]ts.

A=12.56(81) Multip[ly].

A=1017.36 Multiply again[.]

Now, since I'm sure all of us can count, we know that 1944 is greater than 1017.36. Or in other words, the cube is bigger than the sphere.

And PLEASE don't copy this guys. Make your own iteration. Change it up!

What is the distance of the segment formed by joining the following two points on a coordinate plane? (8,4) and (-7,-4)

Answers

Answer:

17

Step-by-step explanation:

Use the distance equation.

d² = (x₁−x₂)² + (y₁−y₂)²

The order doesn't matter.  If I choose (x₁, y₁) to be (8, 4) and (x₂, y₂) to be (-7, -4), then:

d² = (8−(-7))² + (4−(-4))²

d² = 15² + 8²

d² = 289

d = 17

Final answer:

The distance between the points (8,4) and (-7,-4) on a coordinate plane is 17 units.

Explanation:

In order to find the distance between two points on a coordinate plane, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the points (8,4) and (-7,-4), we can substitute the x and y values into the formula:

d = √((-7 - 8)^2 + (-4 - 4)^2)

d = √(225 + 64)

d = √289

d = 17

Therefore, the distance of the segment formed by joining the two given points is 17 units.

The center of Circle D is (0,0). The circumference of the circle passes through Point E (-7,-4).
Find the length of the radius of Circle D.

Answers

Answer:

[tex]\boxed{\sqrt{65}}[/tex]

Step-by-step explanation:

The radius of circle D is the distance from the origin to (-4, -7).

In math, the distance formula gives us the distance between two points, (x₁, y₁) and x₂, y₂):

[tex]d = \sqrt{(x _{2}-x_{1})^{2} +(y _{2}-y_{1})^{2}}[/tex]

You are really using Pythagoras' Theorem to find the distance. You are building a right triangle whose hypotenuse connects two given points.  

For example, in the blue triangle below, the distance between the points (0,0) and (-4, -7) is

[tex]d = \sqrt{(0 - (-4))^{2} +(0 -(- 7))^{2}}\\\\ = \sqrt{4^{2} +7^{2}}\\ = \sqrt{16 + 49}\\=\sqrt{65}[/tex]

[tex]\text{The radius of the circle is }\boxed{\mathbf{\sqrt{65}}}[/tex]

help me with this too and god bless :3 o,o

Answers

Answer:

For the first pic its mode interval and median for the second pic its frequency table.

Step-by-step explanation:

Find f(-3) for f(x) = 4(2)^x

Answers

Hey there! :D

f(-3)= 4(2)^x

Just plug in -3 as x and solve.

4(2)^-3

First do the exponent, and then multiply the four on the outside.

4(1/8)

=1/2

I hope this helps!

~kaikers

Final answer:

To calculate f(-3) for the function f(x) = 4(2)ˣ, substitute -3 into the function, yielding f(-3) = 1/2 after simplifying 4 times 2 raised to the power of -3.

Explanation:

To find f(-3) for the function f(x) = 4(2)ˣ, simply substitute -3 for x in the equation. Here's How:

Start with the original function f(x) = 4(2)ˣ.

Replace every x with -3 to get f(-3) = 4(2)⁻³.

Calculate 2⁻³, which equals 1/8 because negative exponents represent the reciprocal of the base raised to the positive exponent.

Now, multiply 4 by 1/8 to get f(-3) = 4 * 1/8 = 1/2.

Therefore, f(3) for the given function equals 1/2.

z + mx = yx , for x can you pls give me the answer I need it fast

Answers

z=yx-mx
z=x(y-m)
z/(y-m)=x
Final answer:

To solve the equation Z + mx = yx for x, we first move 'mx' to the right side to get 'yx - mx = Z'. We then factor out 'x' to get 'x(y - m) = Z'. Finally, we divide by '(y - m)' to get 'x = Z / (y - m)'. This solution holds as long as y ≠ m.

Explanation:

Here, we're going to solve the equation for x: Z + mx = yx.

We can start by grouping the terms with 'x' together. This gives us: yx - mx = Z. Now, we can factor x out of the left side of the equation. This results in: x(y - m) = Z. Finally, to solve for x, we divide both sides of the equation by (y - m). This gives us the solution: x = Z / (y - m).

Note: This solution is under the assumption that y ≠ m because division by zero is undefined.

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on monday, carly walked 3 miles and ran 2 miles for a total of 78 minites on a treadmill. on thursday she walked 2 miles and ran 3 miles for atotal of 72 minutes using the same speed setting for the treadmill as she did on Monday. let wand r represent the rates, in minutes per mile , that carly walked a d ran on the treadmill, respectivelsy​

Answers

Answer:

w=18 minutes per mile, r=12 minutes per mile

Step-by-step explanation:

Let w and r represent the rates, in minutes per mile, that Carly walked and ran on the treadmill, respectively.

1. On Monday, Carly walked 3 miles and spent 3w minutes, ran 2 miles and spent 2r minutes. In total Carly spent 78 minutes, so

3w+2r=78

2. On Thursday, Carly walked 2 miles and spent 2w minutes, ran 3 miles and spent 3r minutes. In total Carly spent 72 minutes, so

2w+3r=72

Solve the system of two equations:

[tex]\left \{ {{3w+2r=78} \atop {2w+3r=72}} \right.[/tex]

Multiply the first equation by 2, the second equation by 3 and subtract them:

[tex]2(3w+2r)-3(2w+3r)=2\cdot 78-3\cdot 72\\ \\6w+4r-6w-9r=156-216\\ \\-5r=-60\\ \\r=12[/tex]

Substitute it into the first equation:

[tex]3w+2\cdot 12=78\\ \\3w=78-24\\ \\3w=54\\ \\w=18[/tex]

Solve the equation !!!! HELP PLEASE

Answers

Answer:

x=-1/2

Step-by-step explanation:

Given:

8x^3+12x^2+6x+1=0

Making factors of the given polynomial by using cube formula, given as

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Re-writting the given polynomial:

(2^3.x^3) + 3(2^2.x^2)(1)+3(2x)(1) + (1^3)=0

Hence (2^3.x^3) + 3(2^2.x^2)(1)+3(2x)(1) + (1^3) can be written as (2x+1)^3

(2x+1)^3= 0

2x+1= 0

2x= -1

x= -1/2 !

The president of a certain University receives a salary that is three times the salary of one of the department heads the total of the two salaries is 190000 what is the salary of the president of the University

Answers

Answer:

$142500

Step-by-step explanation:

We are given that the resident of a certain University receives a salary that is three times the salary of one of the department heads.

Assuming [tex]x[/tex] to be the salary of the department head, if the total of the two salaries is $190000, we are to find the salary of the president of the University.

We can write an equation in terms of [tex]x[/tex]:

[tex]3x+x=190000[/tex]

[tex]4x=190000[/tex]

[tex]x=47500[/tex]

Salary of the president of the University = [tex]3(47500)[/tex] = $142500

what is the relationship between turning points of a graph and its derivative function​

Answers

Answer:

see explanation

Step-by-step explanation:

Given a function f(x)

Then at the turning points the derivative of f(x) equals zero, that is

f'(x) = 0 at the turning points

PLEASE HELP ME NOW URGENT

Answers

ANSWER

[tex]y = 3 \pm \sqrt{21} [/tex]

EXPLANATION

The quadratic equation is:

[tex] {y}^{2} - 6y - 12 = 0[/tex]

Group variable terms:

[tex] {y}^{2} - 6y = 12[/tex]

Add the square of half, the coefficient of y to both sides.

[tex] {y}^{2} - 6y + ( - 3) ^{2} = 12 + ( - 3) ^{2} [/tex]

[tex] {y}^{2} - 6y + 9= 12 + 9[/tex]

The LHS us now a perfect square trinomial:

[tex]{(y - 3)}^{2}= 21[/tex]

Take square root:

[tex]y - 3 = \pm \sqrt{21} [/tex]

[tex]y = 3 \pm \sqrt{21} [/tex]

The first choice is correct.

3±√21. The equation [tex]y^{2}-6y-12=0[/tex] has two possible solutions 3+√21 y 3-√21.

If we have a general quadratic equation [tex]ay^{2} +by+c=0[/tex] we can solves the equation by completing the square. First, we divide the quadratic equation by a, we obtain [tex]y^{2} +\frac{b}{a} y+\frac{c}{a} =0[/tex].

For this problem, we have [tex]y^{2}-6y-12=0[/tex]

We can skipped division in this example since the coefficient of [tex]x^{2}[/tex] is 1.

Move the term c to the right side of the equation

[tex]y^{2}-6y=12[/tex]

Completing the square on the left side of the equation and balance this by adding the same number to the right side of the equation, with b = -6.

[tex](\frac{b}{2})^{2} =(\frac{-6}{2})^{2}=(-3)^{2} =9[/tex]

[tex]y^{2}-6y+9=12+9[/tex]

[tex](y-3)^{2}=21[/tex]

Take the square root on both sides of the equation:

y - 3 = ±√21

Add 3 from both sides:

y = 3 ± √21

DUDE washed 5 windows in 35 minutes. At this rate, how long
will it take DUDE to wash 12 windows?

Answers

Answer:

35/5 = 7 Minutes per Window thus: 12*7 = 84 Minutes

Step-by-step explanation:

Answer:

84 minutes or 1 hour and 24minutes

Step-by-step explanation:

12*35=420

420/5=84

I need both really bad please and thank you

Answers

Answer:

15. Option A is correct

16. Option B is correct.

Step-by-step explanation:

Question 5:

sin2Ф = 2sinФcosФ

We are given sinФ = 9/13

and we need to find cosФ in order to find sin2Ф

We know that sin^2Ф + cos^2Ф= 1

so, cos^2Ф = 1- sin^2Ф

cos^2Ф = 1- (9/13)^2

cos^2Ф = 88/169

taking √ on both sides:

√cos^2Ф = √88/169

cosФ = (2√22)/13

Now

sin2Ф = 2sinФcosФ

          = 2 (9/13) (( 2√22)/13)

sin 2Ф = 36√22 / 169

Now we find cos2Ф

The formula for cos2Ф = cos^2Ф - sin^2Ф

cos2Ф = ((2√22)/13)^2 - (9/13)^2

cos2Ф = 4*22 /169 - 81/169

cos2Ф = 7/169

So, Option A is correct

Question No 6

We need to find sin2Ф and cos2Ф where cosФ = 6/13

We are given cosФ = 6/13

and we need to find sinФ in order to find sin2Ф and cos2Ф

We know that sin^2Ф + cos^2Ф= 1

so, sin^2Ф = 1- cos^2Ф

sin^2Ф = 1- (6/13)^2

sin^2Ф = 133/169

taking √ on both sides:

√sin^2Ф = √133/169

sinФ = √133/13

Now

sin2Ф = 2sinФcosФ

          = 2 (√133/13) (6/13)

sin2Ф  = 12√133 / 169

Now we find cos2Ф

The formula for cos2Ф = cos^2Ф - sin^2Ф

cos2Ф =  (6/13)^2 - (√133/13)^2

cos2Ф = 36/169 - (133/169)

cos2Ф = -97/169

Since the quadrant is 1st so, cos2Ф will be Positive i.e. 97/169

cos2Ф = 97/169

So, Option B is correct.

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