MATHEMATICS
HIGH SCHOOL

Answer: I did this test b4, yours is answer #number 12

Convert things to their basic forms.

Remember a few identities

sin^2 + cos^2 = 1 so

sin^2 = 1 - cos^2 and

cos^2 = 1 - sin^2

I'm going to skip typing the theta symbol, just to make things faster. Just assume it is there and fill it in as you work the problems.

Follow along to see how each problem was worked out. You'll catch on to the general technique.

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1. sec θ sin θ

1/cos * sin = sin/cos = tan

2. cos θ tan θ

cos * sin/cos = sin

3. tan^2 θ- sec^2 θ

sin^2 / cos^2 - 1/cos^2

(sin^2 - 1)/cos^2

-(1-sin^2)/cos^2

-cos^2/cos^2

-1

4. 1- cos^2θ

sin^2

5. (1-cosθ)(1+cosθ)

Remember (a+b)(a--b) = a^2 - b^2

1-cos^2 = sin^2

6. (secx-1) (secx+1)

sec^2 -1

1/cos^2 - 1

1/cos^2 - cos^2/cos^2

(1-cos^2)/cos^2

sin^2/cos62

tan^2

7. (1/sin^2A)-(1/tan^2A)

1/sin^2 - 1/(sin^2/cos^2)

1/sin^2 - cos^2/sin^2

(1-cos^2)/sin^2

sin^2/sin^2

1

8. 1- (sin^2θ/tan^2θ)

1-sin^2/(sin^2/cos^2)

1 - sin^2*cos^2/sin^2

1-cos^2

sin^2

9. (1/cos^2θ)-(1/cot^2θ)

1/cos^2 - 1/(cos^2/sin^2)

1/cos^2 - sin^2/cos^2

(1-sin^2)/cos^2

cos^2/cos^2

1

10. cosθ (secθ-cosθ)

cos *(1/cos - cos)

1-cos^2

sin^2

11. cos^2A (sec^2A-1)

cos^2 * (1/cos^2 - 1)

1 - cos^2

sin^2

12. (1-cosx)(1+secx)(cosx)

(1-cos)(1+1/cos)cos

(1-cos)(cos + 1)

-(cos-1)(cos+1)

-(cos^2 - 1)

-(-sin^2)

sin^2

13. (sinxcosx)/(1-cos^2x)

sin*cos/sin^2

cos/sin

cot

14. (tan^2θ/secθ+1) +1

(sin^2/cos^2)/(1/cos) + 2

sin^2/cos + 2

sin*tan + 2

Convert things to their basic forms.

Remember a few identities

sin^2 + cos^2 = 1 so

sin^2 = 1 - cos^2 and

cos^2 = 1 - sin^2

I'm going to skip typing the theta symbol, just to make things faster. Just assume it is there and fill it in as you work the problems.

Follow along to see how each problem was worked out. You'll catch on to the general technique.

======

1. sec θ sin θ

1/cos * sin = sin/cos = tan

2. cos θ tan θ

cos * sin/cos = sin

3. tan^2 θ- sec^2 θ

sin^2 / cos^2 - 1/cos^2

(sin^2 - 1)/cos^2

-(1-sin^2)/cos^2

-cos^2/cos^2

-1

4. 1- cos^2θ

sin^2

5. (1-cosθ)(1+cosθ)

Remember (a+b)(a--b) = a^2 - b^2

1-cos^2 = sin^2

6. (secx-1) (secx+1)

sec^2 -1

1/cos^2 - 1

1/cos^2 - cos^2/cos^2

(1-cos^2)/cos^2

sin^2/cos62

tan^2

7. (1/sin^2A)-(1/tan^2A)

1/sin^2 - 1/(sin^2/cos^2)

1/sin^2 - cos^2/sin^2

(1-cos^2)/sin^2

sin^2/sin^2

1

8. 1- (sin^2θ/tan^2θ)

1-sin^2/(sin^2/cos^2)

1 - sin^2*cos^2/sin^2

1-cos^2

sin^2

9. (1/cos^2θ)-(1/cot^2θ)

1/cos^2 - 1/(cos^2/sin^2)

1/cos^2 - sin^2/cos^2

(1-sin^2)/cos^2

cos^2/cos^2

1

10. cosθ (secθ-cosθ)

cos *(1/cos - cos)

1-cos^2

sin^2

11. cos^2A (sec^2A-1)

cos^2 * (1/cos^2 - 1)

1 - cos^2

sin^2

12. (1-cosx)(1+secx)(cosx)

(1-cos)(1+1/cos)cos

(1-cos)(cos + 1)

-(cos-1)(cos+1)

-(cos^2 - 1)

-(-sin^2)

sin^2

13. (sinxcosx)/(1-cos^2x)

sin*cos/sin^2

cos/sin

cot

14. (tan^2θ/secθ+1) +1

(sin^2/cos^2)/(1/cos) + 2

sin^2/cos + 2

sin*tan + 2

MIDDLE SCHOOL

The Split Ends Salon orders 10 cases of hand-made hairbrushes. If it takes 26 hours to produce 4 cases of hairbrushes, how many

hours will it take to produce enough hairbrushes to fill the order?

Answer:

it would take 65 hours to produce all of the order.

Step-by-step explanation:

1. you already would figure out that 26 hours=4 cases or 6.5 hours per case of hairbrushes.

2. You would figure out that 26+26 is 52 so 52 hours for 8 cases

3. Then you remember u have 8 cases of hairbrushes now. Set up a mental equation where you can solve in your mind: if I need 10 cases, but have figured out I only calculated 8, how much more would I still need to meet the order?

4. After mentally solving the hypothetical problem, you then would conclude you needed 2 more cases from 8 to equal 10.

5. you then divide 26 hours per 4 cases and you get 13 hours for 2 cases.

6. finally you multiply 26+26+13 which you would get 65 as the answer

MIDDLE SCHOOL

Barbara received a music gift card $35. she used the card to download songs for 99 cents each can Barbara download another song?

Yes, she can because 99 cents= $1 dollar. Barbara has $35

COLLEGE

Jack drives an 18 wheeler. The truck's gas tank holds 105 gallons of gasoline. The driver begins the trip with a full tank. At his first stop his tank is 65% full. How much gasoline did he use?

Jack drives an 18 wheeler. The truck's gas tank holds 105 gallons of gasoline. The driver begins the trip with a full tank.

Tank holds 105 gallons

65% of gasoline is 0.65 * 105 = 68.25

so 68.25 gallons left in the tank

Tank holds 105 gallons and left out with 68.25 gallons

So gasoline used = 105 - 68.25= 36.75

36.75 gallons of gasoline used

MIDDLE SCHOOL

Write the statement in the if then form perpendicular lines intersect to form right angles

Answer: If perpendicular lines intersect, then they form right angles.

Step-by-step explanation:

You take the first part, "perpendicular lines intersect", and add the "if" to it. Then, you take the second part, "to form right angles", and add the "then" in front of it to get your answer, "If perpendicular lines intersect, then they form right angles."

Hope it helps! :)

MIDDLE SCHOOL

A rectangular prism has a length of 6 cm, a width of 3 cm, and a height of 4 1/2 cm. The prism is filled with cubes that have edge lengths of 1/2 cm.

How many cubes are needed to fill the rectangular prism?

For 15 points plz help

It is either 117 or 58.5 would be the answer

COLLEGE

The sides and hypotenuse of a right triangle are strictly increasing with time. At the instant when x is 24 inches and y is 32 inches, dy/dt = 2 dx/dt. If dθ/dt = −0.01 radians per minute at the same instant, what is the value of dy/dt at that same instant ?

Answer:

Step-by-step explanation:

Did you perhaps mean what is the value of dx/dt at that instant? You have a value for dy/dt to be 2dx/dt. I'm going with that, so if it is an incorrect assumption I have made, I apologize!

Here's what we have:

We have a right triangle with a reference angle (unknown as of right now), side y and side x; we also have values for y and x, and the fact that dθ/dt=-.01

So the game plan here is to use the inverse tangent formula to solve for the missing angle, and then take the derivative of it to solve for dx/dt.

Here's the inverse tangent formula:

and its derivative:

We have values for y, x, dy/dt, and dθ/dt. We only have to find the missing angle theta and solve for dx/dt.

Solving for the missing angle first:

On your calculator you will find that the inverse tangent of that ratio gives you an angle of 53.1°.

Filling in the derivative formula with everything we have:

We can simplify the left side down a bit by breaking up that secant squared like this:

We know that the secant is the same as 1/cos, so we can make that substitution:

and

We can square that and then multiply in the -.01 so that the left side looks like this now, along with some simplification to the right:

We will muliply both sides by 576 to get:

We can now factor out the dx/dt to get:

(16 is the result of subtracting 32 from 48)

Now we divide both sides by 16 to get that

The negative sign obviously means that x is decreasing

MIDDLE SCHOOL

10.00cm by 2.35 cm by 1.10 cm

Answer:

I think you would divide all of your numbers.

Step-by-step explanation:

Answer:

13.45 is your answer

Step-by-step explanation:

MIDDLE SCHOOL

What does this sign mean:

^

Answer:

To the power of, Exponents.

Examples:

5^3, 5 x 5 x 5 = 125

6^4, 6 x 6 x 6 x 6 = 1296

The symbol basically means the exponent, of how many times to multiply the Base Number.

5 is the base.

5 ^ 3. The symbol means the exponent, 3. It tells you to multiply the 5 by it's self 3 times.

Answer:

It means exponent. For example 2^3. is 2*2*2. An exponent is multiplying the base by itself, which in my previous example would be 2, as many times as the exponent says. the exponents was 3 in 2^3. so I multiplied 2, 3 times

COLLEGE

A modem transmits over an error-prone channel, so it repeats every "0" or "1" bit transmission five times. We call each such group of five bits a "codeword." The channel changes an input bit to its complement with probability p =1/10 and it does so independently of its treatment of other input bits. The modem receiver takes a majority vote of the five received bits to estimate the input signal. Find the probability that the receiver makes the wrong decision.

Answer:

0.00111

Step-by-step explanation:

Since the modem receiver takes a majority vote of the five

received bits to estimate the input signal, it will only make a wrong decision if 3, 4 or 5 of the 5 bits received are wrong.

Given that the channel changes an input bit to its complement with probability p =1/10 and it does so independently of its treatment of other input bits, the probability of changing 3 bits out of five is 0.1*0.1*0.1 = 0.001, of changing 4 is 0.0001 and of changing 5 is 0.00001

So, the probability that the modem makes a wrong decision is 0.001+0.0001+0.00001 = 0.00111