Mathematics College

Given that tan^2 e= 3/8 what is the value of sec e? A. +√8/3 B.+ √11/8 C. 11/8 D. 8/3

Answers

Answer 1

ANSWER

[tex]{ \sec}(e) = \pm \: \sqrt{\frac{11}{8} } [/tex]

EXPLANATION

We use the Pythagorean Identity,

[tex] { \sec}^{2} (e) = 1 + { \tan}^{2} (e)[/tex]

It was given that,

[tex] { \tan}^{2} (e) = \frac{3}{8} [/tex]

We substitute the values into the identity to obtain,

[tex] { \sec}^{2} (e) = 1 + \frac{3}{8} [/tex]

[tex]{ \sec}^{2} (e) = \frac{11}{8} [/tex]

We take square root of both sides to get,

[tex]{ \sec}(e) = \pm \: \sqrt{\frac{11}{8} } [/tex]

Answer 2

Answer:

sec e = √(11/8) ⇒ answer B

Step-by-step explanation:

* Lets revise some identities in trigonometry

# sin²x + cos²x = 1

- Divide both sides by cos²x

∴ sin²x/cos²x + cos²x/cos²x = 1/cos²x

∵ sinx/cosx = tanx

∴ sin²x/cos²x = tan²x

∵ cos²x/cos²x = 1

∵ 1/cosx = secx

∴ 1/cos²x = sec²x

* Now lets write the new identity

# tan²x + 1 = sec²x

- Let x = e

∴ tan²e + 1 = sec²e

- Substitute the value of tan²e in the identity

∵ tan²e = 3/8

∴ 3/8 + 1 = sec²e

- Change the 1 to the fraction 8/8

∴ 3/8 + 8/8 = sec²e ⇒ add the fractions

∴ 11/8 = sec²e

- Take square root for the two sides to find sec e

∴ sec e = √(11/8)

∴ The answer is B

Related Questions

Estimate the size of a crowd standing along 1 mile section of parade route that is 10 feet deep on both sides of the street assume that each person occupies 2.5 square feet
A) 21,120
B) 42,240
C) 84,480
D) 168,960

Answers

The correct answer is option B). The size of a crowd standing along 1 mile section of parade route that is 10 feet deep on both sides of the street is 42,240.

To estimate the size of the crowd, we need to calculate the total area occupied by the crowd and then divide by the area occupied by each person.

First, let's calculate the total area available for the crowd on both sides of the street:

The length of the parade route is 1 mile. Since there are 5280 feet in a mile, the length in feet is 5280.

The depth of the crowd on both sides of the street is 10 feet.

Therefore, the total area available for the crowd on both sides is:

Total area = 2 [tex]\times[/tex] (Depth of crowd) [tex]\times[/tex] (Length of parade route)

Total area = 2 [tex]\times[/tex] 10 feet [tex]\times[/tex] 5280 feet

Total area = 105,600 square feet

Next, we need to calculate how many people can fit in this area:

Each person occupies 2.5 square feet.

The number of people that can fit in the total area is:

Number of people = Total area / Area per person

Number of people = 105,600 square feet / 2.5 square feet per person

Number of people = 42,240.

Clabber company has bonds outstanding with a par value of $113,000 and a carrying value of $105,100. if the company calls these bonds at a price of $101,500, the gain or loss on retirement is:

Answers

Gain on retirement of bonds = book value of bonds - the amount paid to the bondholders =  105,100 - 101,500 = $3600

So, $3600 should be the gain or loss on the retirement.
   


Solve for x
in the equation x^2-12x+36=90

Answers

This can be rewritten as
   (x -6)² = 90 . . . . . the left side is already a perfect square
   x -6 = ±√90 . . . . . take the square root
   x = 6 ±3√10 . . . . add 6

Answer:

Using the identity rule:

[tex](a-b)^2 = a^2-2ab+b^2[/tex]

Given the equation:

[tex]x^2-12x+36 = 90[/tex]

Rewrite the above equation as:

[tex]x^2-2 \cdot x \cdot 6+6^2 = 90[/tex]

Apply the identity rule:

[tex](x-6)^2 = 90[/tex]

Take square root to both sides we have;

[tex]x-6 = \pm \sqrt{90}[/tex]

Add 6 to both sides we have;

[tex]x = 6\pm \sqrt{90}[/tex]

or

[tex]x = 6 \pm 3\sqrt{10}[/tex]

Therefore, the value of x are:

[tex]6+3\sqrt{10}[/tex] and [tex]6-3\sqrt{10}[/tex]

The first term in a sequence is -2 and the common ratio is 3. What is the sixth term of the sequence?

Answers

It's the Geometric Sequence.

The n-th term of a geometric sequence with initial value a and common ratio r is given by:

[tex]a_n=a_1\cdot r^{n-1}\ for\ n\in\mathbb{N^+}[/tex]

We have:

[tex]a_1=-2;\ r=3;\ n=6[/tex]

Substitute:

[tex]a_6=-2\cdot3^{6-1}=-2\cdot3^5=-2\cdot243=-486[/tex]

Answer: The sixth term is equal -486.

The height of a triangle is increasing at a rate of 2 2 centimeters/minute while the area of the triangle is increasing at a rate of 3.5 3.5 square centimeters per minute. at what rate is the base of the triangle changing when the height is 10 10 centimeters and the area is 80 80 square centimeters?

Answers

The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 20 cm2/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm2. = 2, namely, the base of the triangle is increasing at a rate of 2 cm/min.

If we reject the null hypothesis, h0: ρ = 0 , what can we conclude about the population correlation coefficient?

Answers

If the null hypothesis, [tex]H_0:\:\rho =0[/tex] is rejected, then we can conclude that the correlation coefficient is significant. This means that there is enough evidence to conclude that a relationship exists between the two (or more) variables involved in the regression. 

Jim picked a card from a standard deck. What is the probability that Jim picked a heart or an ace?

Answers

Answer:

The answer is actually 16/52.

Step-by-step explanation:

There are 13 hearts and 4 aces. However, one of the 4 aces is a heart, so there would only be 3 other aces.

13 hearts + 3 other aces = 16

There are 52 cards in a deck, so the probability would be 16/52.

Simon has a scale model of the Concorde airplane. The actual length of the Concorde is approximately 200 feet. If the ratio of the actual length in feet to the length of the model in centimeters is 5 : 1, what is the approximate length of Simon's model?

Answers

The answer is:  "40 cm " .
_________________________________________________________
Note:
_________________________________________________________

[tex] \frac{200 ft }{ (x) cm} = \frac{5}{1} [/tex]  ;

Solve for "x" (in "cm" ) ; 


→  5x = 200 * 1 ; 

→  5x = 200 ; 

Divide each side of the equation by "5" ; 
   to isolate "x" on one side of the equation; & to solve for "x" ; 

→  5x / 5 = 200 / 5 ; 

to get:

→  x = 40 .
___________________________________________________________
The answer is:  " 40 cm " .
___________________________________________________________

Answer:

yur

Step-by-step explanation:

hello can you please help me posted picture of question

Answers

The sample space will be: {1, 2, 3, 4, 5, 6}

Event A is: {Rolling 1,2 or 3}

Complement of event A will contain all those outcomes in the sample space which are not a part of event A.

So, complement of event A will be: {Rolling a 4,5 or 6}

Thus option A gives the correct answer

what is the difference between the greatest amount and least amount of gasoline used to mow lawns?

1/8 2/8 3/8/4/8 5/8

Answers

Answer:
The difference is 4/8 which is equivalent to 1/2

Explanation:
The given values of gasoline amounts are as follows:
1/8 , 2/8 , 3/8 , 4/8 , 5/8

Since all the values have the same denominator, therefore, we can base our comparison on the numerator. The larger the numerator, the larger the value of the fraction.

Based on this, we can note that:
the least amount of gasoline is 1/8
the greatest amount of gasoline is 5/8

The difference between the two can be computed as follows:
difference = greatest amount - least amount
difference = 5/8 - 1/8
difference = 4/8 which can be simplified to give 1/2

Hope this helps :)

hey can you please help me posted picture of question

Answers

The correct answer is the las option (Option D), which is:

 D. f(x)=(x+4)^4

 The explanation is shown below:

 1. The initial function was G(x)=x^4, whose graph shows that the shape has its vertex at 0,0.
 
 2. If the it was shift 4 units to the left, you only has to add a 4 to the function.

 3. Therefore, you obtain the the equation of the final shape is:

 f(x)=(x+4)^4

 As you can see, the answer is the option D.

A company has a minimum required rate of return of 9% and is considering investing in a project that costs $350,000 and is expected to generate cash inflows of $140,000 at the end of each year for three years. the net present value of this project is

Answers

The net present value of the  project can be calculated as follows:

NPV = - Cost + present value of all cash flows

Cost = $350,000
Present value of all cash flows = C*{[1-(1+r)^-n]/r}
Where C = Yearly cash flows = $140,000, r = discount rate = 9%, n = time of generating cash flows = 3 years.

Therefore,

NPV = -350,000 + 140,000*{[1-(1+0.09)^-3]/0.09} = $4,381.25

Q # 17 please solve the figures

Answers

Answer: First option:
Angle C is congruent with angle X, angle D is congruent with angle Y, angle A is congruent with angle Z

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:

f(t) = −16t2 + 48t + 100

The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____ feet per second.

Answers

Given that a ball which has been thrown up can be modeled by the function:
f(t)=-16t^2+48t+100
the rate of change will be:
f'(t)=-32t+48
thus:
when t=3
f(3)=-32(3)+48=-48

when t=5
f(5)=-32(5)+48=-112
thus the rate of change will be:
[f(5)-f(3)]/(5-3)
=(-112-(-48))/(5-3)
=(-64/2)
=-32 ft/sec

hey can you please help me posted picture of question

Answers

We have the following function:
 C (t) = 6t - 180
 Clearing t we have:
 6t = c + 180
 t = c / 6 + 180/6
 Rewriting:
 t (c) = (c + 180) / 6
 Answer:
 The inverse function for this case is given by:
 t (c) = (c + 180) / 6
 option A

What are the zeros of the polynomial function f(x)=x^2+5x+6

Answers

Find 2 numbers that multiply to 6 and add to 5.

3*2 = 6
3+2 = 5

x^2 + 5x+6 = (x+3)(x+2) = 0

Set each factor equal to zero.
x+3 = 0   ---->  x = -3
x+2 = 0 ----->  x = -2

Answer:
There are two zeros at -2 and -3.

Juan is spinning a wheel with 4 unequal spaces marked with values of $200, $300, $400, and $600. The probability of landing on $200 is 2/9 . The probability of landing on $300 is 4/9 . The probability of landing on $400 is 2/9. The probability of landing on $600 is 1/9 . The expected value of spinning the wheel once is $, and the expected value of spinning the wheel three times is

Answers

a]
The expected value of spinning the wheel is given by:
E(x)=2/9(200)+4/9(300)+2/9(400)+1/9(600)
E(x)=44 4/9+133 1/3+88 8/9+66 2/3
E(x)=333 1/3

b] The expected value of spinning the wheel thrice will be:
(expected value of spinning once)*(number of spins)
=333 1/3*3
=1000/3*3
=1000

Answer:

333 and 1000

Step-by-step explanation:

AB is tangent to circle O at B. Find the length of the radius, r, for AB = 5 and AO = 13.

Answers

ΔABO is a right triangle with AB⊥BO. The radius of the circle is BO. The Pythagorean theorem applies.
AO² = AB² + BO²
13² = 5² + r²
169 -25 = r²
r = √144 = 12

The radius (r) is 12.

the radius is twelve

Assume that the population of the world in 2010 was 6.9 billions and is growing at the rate of 1.1 percent a year. (a) set up a recurrence relation for the population of the world n years after 2010 (b) find an explicit formula for the population of the world n years after 2010. (c) what will the population of the world be in 2030

Answers

a1=6.9
a) an=(an-1)(1.1)
b) an=(6.9)(1.1^n-1)
c) 46.419 billion

Answer:

a 1=6.9

a  an =

(an-1)(1.1)

b  an=

(6.9)

(1.1^n-1)

c

46.419  

billion

Step-by-step explanation:


a customer buys three bottles of water at ninety nine cents each. there is seven percent tax on each bottle. what is the total bill?

Answers

If the tax was 7 cents then each bottle would cost 1.06 each, because tax doesn't mean it's three dollars plus tax which comes to 3.07, it's that if you have a water bottle coming out to 99 cents each and the tax was 7 cents, you add 7 to 99. Which in money, comes out to 1.06 each bottle. So the total bill is 3.18. 
I hope this helped! I don't wanna get your answer wrong! >o<
The total bill of each bottle plus tax would be $5.04

how can you write the expression with a rationalized denominator? √3/√4

Answers

Well √4 = 2

So √3 / √4 would be √3 / 2 so denominator is now rationalized.

Hope this helps.

Using a rain gauge, Gerry determined that 1/2 inch of rain fell during 3/4 of an hour. What is the unit rate of rainfall in inches per hour?

Answers

Your answer was wrong. You flip 3/4 to 4/3
1/2 ÷3/4 =
1/2 ×4/3 =  4/6
4/6 ÷2  = 2/3 is the answer

Final answer:

To calculate the unit rate of rainfall in inches per hour, divide the amount of rainfall (1/2 inch) by the duration (3/4 hour), which gives 2/3 inches per hour.

Explanation:

The student is asking how to find the unit rate of rainfall in inches per hour when given that 1/2 inch of rain fell during 3/4 of an hour. To find the unit rate, divide the total amount of rainfall by the total time to get the amount of rain per one hour.

Step-by-step calculation:

Amount of rainfall: 1/2 inch

Duration of rainfall: 3/4 hour

To find inches per hour, divide the amount of rainfall by the duration:

(1/2 inch) / (3/4 hour) = (1/2) / (3/4) = (1/2) * (4/3) = 4/6 = 2/3 inches per hour.

Therefore, the unit rate of rainfall is 2/3 inches per hour.

What is the volume of a right circular cylinder with a base diameter of 18yd. And a height of 3yd.

Answers

Answer:

[tex]Volume=254[/tex] to the nearest cubic yard.

Step-by-step explanation:

The volume of a right circular cylinder can be calculated using the formula;

[tex]Volume=\pi r^2h[/tex].

The diameter of the base is given to us. We divide it into two to obtain the radius.

[tex]r=\frac{18}{2}=9yd[/tex] and also the height of the cylinder is [tex]h=3yd[/tex].

We substitute these values into the formula to obtain;

[tex]Volume=9^2\times 3\pi yd^3[/tex]

[tex]Volume=243\pi yd^3[/tex]

[tex]Volume=763.4yd^3[/tex]

Answer:

answer= 254

Step-by-step explanation:

a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an intial speed of 130 feet per second. What is the maximum height, in feet, the ball will attain? round to the nearest hundredth

Answers

For this case, the first thing to do is write the equation of moving the ball.
 We have then:
 h (t) = - 16t ^ 2 + 130t + 2
 Deriving we have:
 h '(t) = - 32t + 130
 We match zero:
 -32t + 130 = 0
 We cleared t:
 t = 130/32
 t = 4.0625 s
 We evaluate the value of t = 4.0625 s in the equation of motion:
 h (4.0625) = - 16 * (4.0625) ^ 2 + 130 * (4.0625) + 2
 h (4.0625) = 266.0625 feet
 Answer:
 The maximum height, in feet, the ball will attain is:
 h (4.0625) = 266.0625 feet

Final answer:

Using the kinematic equation for vertical motion, the maximum height a tennis ball will reach when fired at an initial speed of 130 ft/s from a height of 2 feet is approximately 264.91 feet.

Explanation:

Calculating the Maximum Height of a Tennis Ball

The maximum height that a tennis ball will attain when fired vertically can be calculated using the kinematic equations that describe projectile motion. Given that the initial speed of the ball is 130 feet per second and it is launched from a height of 2 feet, we can use the equation for vertical motion:

v^2 = u^2 + 2gh

where v is the final velocity (0 ft/s at the highest point), u is the initial velocity (130 ft/s), g is the acceleration due to gravity (-32.2 ft/s^2, negative because it is directed downwards), and h is the height gained. Rearranging the formula to solve for h we get:

h = (v^2 - u^2) / (2g) = (0 - 130^2) / (2 * -32.2)

After calculating h, we add the initial launch height of 2 feet to find the maximum height above ground:

Maximum Height = h + 2 feet

By plugging in the values, we can find the maximum height to be:

Maximum Height = (0 - 16900) / (-64.4) + 2 ≈ 264.91 feet (rounded to the nearest hundredth).

Therefore, the maximum height attained by the tennis ball is approximately 264.91 feet.

Christina goes to the market with $50. She buys one papaya for $20 and spends the rest of the money on bananas. Each banana cost $6. Write an inequality for the number of bananas purchased

Answers

50 is greater than or equal to 20 + 6x
50 is greater or equal to 20. How you do that is you write a greater than sighn and put a line under it.

please help!! I don't understand

Answers

Answer:

(4, 5)

Step-by-step explanation:

All the medians intersect at the same point. RU and PS are medians so they intersect at the same point that medians QT and PS intersect.

A camera manufacturer spends $2,100 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $14 each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?

Answers

$400 have a nice one!  :) 

Here, first we need to find the number of cameras that can be sold, so that total costs are equal to total revenues.

Let the number of cameras that can be sold be "x".

Total revenue = $ 14x

Total costs will be = $ 2100 + $9x

So, the equation that will be formed ⇒

14 x = 2100 + 9x

5x = 2100

x = 420

Thus, in order to make total costs equal to total revenues, 420 cameras are required to be sold.

If instead of 420, 470 cameras are sold, the daily profit will be calculated as under -

Total revenue = $ 14 × 470 cameras = $ 6,580

Total costs = $ 2100 + ( $ 9 × 470 cameras) = $ 6,330

Daily profit = Total revenue - Total costs = $ 6,580 - $ 6,330 = $ 250


Paige rides her bike around town. She can ride one half of a mile in 1 30 ith of an hour. If she continues to ride at the same pace, how many miles could she travel in 1 hour?

Answers

She could travel 15 miles in an hour

We have been given that Paige can ride one half of a mile in 1/30 th of an hour. And we have to found the distance traveled in 1 hour if she continues to ride at the same pace.

Let d be the distance traveled in 1 hour.

In 1/30 th of an hour distance traveled is 0.5 mile

Hence, in 1 hour the distance traveled is given by

[tex]d=\frac{0.3}{1/30} \\ \\ d=0.5\times 30\\ \\ d=15[/tex]

Therefore, she will travel 15 miles.


Using what you know about angles and triangles, what is the measure of angle 6?

Answers

∠4 = 90  (verticallyopposite)
∠2 = 68 (verticallyopposite)

∠6 = ∠2 + ∠4 (exterior angles = sum of opposite angles)

∠6 = 68 + 90 = 158°

Answer: 158°

Answer:158

Step-by-step explanation:∠6 = 68 + 90 = 158°

which statement describes the ratio of weight to mass and the value of x in the table?

Answers

To find the ratio, pick any pair of corresponding table values.
  weight/mass = (196 N)/(20 kg) = 98/10 N/kg

You can find x from ...
  (98/10)x = 1078
  x = 1078*10/98 = 110

The appropriate choice is ...
  B   The ratio is 98/10; x = 110
Other Questions
The New Deal's support for organized labor was best shown by A: bolstering the nation's banking system B: setting up a national retirement system C: establishing the Tennessee Valley Authority D: establishing the right of collective bargaining asmine works at the public library after school. She makes $7.00 per hour. She cannot work more than 15 hours per week. If y = 7x represents Jasmine's earning, what are the values in the domain? Which person is most likely to cause a pandemic? one who had a cold and stayed at home one who was sick with the flu and flew to multiple countries one who had diabetes and continued to eat fatty foods one who washed hands frequently and got vaccinations50 point plzzzzzzzzzzzz Kieshas quality-control manager told her she must have 97% of her clocks functioning properly. She found a report that said 6 out of 300 clocks tested were not working properly. Kiesha predicts that she will have enough working clocks to please the manager. Which statements are true about Kieshas prediction? Check all that apply.Kieshas experimental probability is 1/30Kiesha will have more than 97% of the products working.Kiesha will not meet 97% because more than 3% of her clocks will be broken.Kieshas experimental probability is 1/50When the inventory is 4000 clocks, the prediction is that 3920 clocks will work. Which calculation helps determine which producer has the absolute advantage? Resources used multiplied by amount produced Amount produced divided by resources used Amount produced minus resources used Resources used divided by amount produced Describe the two-state solution with respect to Israel and Palestine what are the prospects for success You wish to invest $500. You are going to earn 5% simple interest. How much interest will you earn? which of the following is the correct notation for the complex number [tex] \sqrt{ - 81 - 14} [/tex] The first European colony in the New World to declare independence was __________. how many neutrons does the most common isotope of hydrogen have? Most migrants to the u.s. during the latter part of the 1800's came from which part of europe Characteristics of carbon monoxide include all of the following EXCEPT:It is a colorless gas.It is very dangerous and inhaling too much can be fatal.It is a potent gas.It is found in tobacco smoke. Enzo sits with a small group of friends at lunch. Occasionally, he drinks alcohol from his parents liquor cabinet and stays home, even though his friends invite him to go places. He likes to play video games in his free time and is slightly overweight. Which behaviors are signs that Enzo may need professional mental health treatment? Check all that apply. drinking alcohol being overweight playing video games withdrawing from activities having a small group of friends Properly observing xenia requires which of the following? Select all that apply.A.) offering food and shelter to the travelerB.) treating the host with respectC.) offering a parting gift to the travelerD.) offering a parting gift to the hostE.) introducing yourself as soon as you meet the host Simplify 11/12 - 6/4 who is the 38 president of the U.S. (07.06)Number line with open circle on 9 and shading to the left. Which of the following inequalities best represents the graph above? x < 9 x > 9 x 9 x 9 Home of the impressionists options: 1) Colleville-sur-mer 2) Honfleur 3) Nantes 4) Carnac Which is not true of radioactive half-life? radioactive half-life is increased by heating the isotope. independent of the physical or chemical form of the isotope. the time required for the level of radioactivity in a sample to be cut in half. independent of the amount of radioactive material present? All dialogue should?A. Be easy to memorize.B. Should like real conversation and have a purpose.C. Sound like educated people are speaking.D. Be difficult to memorize.