f(x) = -x + 2, find f(-1).

Answer: I think #2 is either A or C

Step-by-step explanation: Hope it helped! :)

y = sec³(3x)

dy/dx = d (sec 3x)³/dx . d (sec 3x)/dx . d(3x)/dx

y' = dy/dx = 3(sec² 3x) . (tan² 3x) . 3

y' = 9 sec² (3x) tan² (3x)

Hence, option C is correct!

Hope it helps..

The option that can be used to verify the trigonometric identity, \(tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)\) is option C;

C. \(tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)\)

A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions

The specified identity is presented as follows;

\(tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)\)

The half angle formula for tangent indicates that we get;

\(tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}\)

\(\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}\)

When η = 0, we get;

\(-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}\)

\(cot\left(x \right) = \dfrac{cos(x)}{sin(x)}\)

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)\)

The correct option that can be used to verify the identity is option C

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Answer:

It will take 2.2 hours for the trains to meet.

Step-by-step explanation:

Given,

Distance between two trains = 396 miles

Speed of one train = 95 mph

Speed of other train = 85 mph

Combined speed of trains = 95+85 = 180 mph

Distance = Speed * Time

Time =

Time =

Time = 2.2 hours

It will take 2.2 hours for the trains to meet.

Keywords: speed, distance

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Step-by-step explanation:

The loan that will offer Craig the best effective interest rate is a) Loan L with a real percentage rate of 8.6%.

An effective interest rate is the real percentage rate on an interest-paying investment which removes the effects of compounding over time.

The formula for computing the effective interest rate is as follows:

Effective Interest Rate, r = (1 + i/n)^n - 1.

              Nominal Interest Rates    Compounding Periods

Loan L                   8.25%                    365 days

Loan M                  8.47%                    52 weeks

Loan N                  8.533%                  12 months

Loan O                  8.604%                 Yearly

Loan L = (1 + 0.0825/365)^365 - 1

= 1.08598 - 1

= 0.086

= 8.6%

Loan M = (1 + 0.0847/52)^52 - 1

= 1.0883 - 1

= 0.0883

= 8.83%

Loan N = (1 + 0.08533/12)^12 - 1

= 1.0887 - 1

= 0.0887

= 8.87%

Loan O = (1 + 0.08604/1)^1 - 1

= 1.08604 - 1

= 0.08604

= 8.604%

Thus, we advise Craig to take Loan L because it offers the least-costly effective interest rate.

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Answer:

Step-by-step explanation:

a/sin A=b/sin B

20/sin90⁰=x/sin60⁰

cross multiply

20sin60⁰=xsin90⁰

17.32=

area=1/2a/bsin∅

=1/2×17.32×20 sin30⁰

86.6square

Problem 1

y = tan(3x+4)

f(x) = tan(3x+4)

f ' (x) = 3sec^2(3x+4) .... apply derivative chain rule

dy/dx = f ' (x)

dy = f ' (x) * dx

dy = ( 3sec^2(3x+4) ) * dx

Now plug in x = 5 and dx = 0.3

dy = ( 3sec^2(3*5+4) ) * 0.3

dy = 0.920681 which is approximate

Make sure your calculator is in radian mode.  Calculus textbooks will be in radian mode for the special sine limit definition \(\lim_{x\to0}\frac{\sin x}{x} = 1\) to be true.

===========================================================

Problem 2

We'll have the same derivative function and same x value. The only difference is that dx = 0.6 this time.

dy = f ' (x) * dx

dy = ( 3sec^2(3*5+4) ) * 0.6

dy = 1.84136 approximately

Answer:

  a. x = 15

  b. scalene

Step-by-step explanation:

You want to know the value of x and the classification of the triangle whose circumscribing arcs are (8x-10)°, (6x)°, and (10x +10)°.

The sum of arcs around the circle is 360°.

  (8x -10)° +(6x)° +(10x +10)° = 360°

  24x = 360 . . . . . . . . . . . divide by °, simplify

  x = 15 . . . . . . . . . . . . divide by 24

The arc measures around the circle are ...

  (8x -10)° = 110°

  (6x)° = 90°

  (10x +10)° = 160°

Each arc is double the measure of the inscribed angle that intercepts it. The different arc measures mean the angle measures are different, so the triangle is scalene.

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Answer:

Step-by-step explanation:

The third side is thus, less than 14 + 11 = 25 cm. The side cannot be less than the difference of the two sides. Thus, the third side has to be more than 14 - 11 = 3 cm. So, the length of the third side could be any length greater than 3 cm and less than 25 cm.

Notice that XZ = XY + YZ

where XY = 5m

YZ = m and XZ =25

Thus,

25 = 5m + m

25 = 6m

Hence,

But YZ = m

Therefore, YZ =

Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

I hate brainly now

9514 1404 393

Answer:

  $6190.48

Step-by-step explanation:

The price is now 1 -16% = 84% of the original price (p).

 $5200 = 0.84p

  p = $5200/0.84 = $6190.48

The price before the discount was $6190.48.

The equation that represents the total cost of the membership will be y = 5x + 265.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class.

Let 'x' be the number of aerobics classes and 'y' be the total cost. Then the equation is given as,

y = 5x + 265

The equation that represents the total cost of the membership will be y = 5x + 265.

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The sum of the geometric series for Xac-2 n\((n ~ 1) (~1)" I2"-2 for Ixl < 1 is (1 - x2)\). This is because the series is a summation of the terms (1/x2) multiplied by each power of x from 0 to n, and the sum of the series is the sum of the terms.

To calculate the sum of the geometric series for\(Xac-2 n (n ~ 1) (~1)" I2"-2 for Ixl < 1\), we can use the formula for the sum of a geometric series. The sum of such a series is the sum of the terms (1/x2) multiplied by each power of x from 0 to n. Thus, the sum of the series is given by the formula S = (1/x2) ∑ xn, where n starts at 0 and goes to n. Substituting n = -2 and x = 1 gives us S = (1/1) ∑ 1-2, which simplifies to S = (1/1) (1 - 1-2) = (1 - 1-2) = (1 - x2). Hence, the sum of the series is (1 - x2).

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Answer:c

Step-by-step explanation:

Answer:

(B)32 pi

Explanation:

From the given options:

Therefore, the value of x which makes the inequality true is 32pi.

The correct option is B

The number that is not irrational is \(1.\overline{45}\). The correct option is the second option \(1.\overline{45}\)

From the question, we are to determine which of the given options is not irrational

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q, where p and q are integers.

\(1.\overline{45}\)  is a repeating decimal and it can be expressed as a fraction

\(1.\overline{45} = \frac{144}{99}\)

∴ \(1.\overline{45}\) is not an irrational number. It is a rational number

The other options cannot the expressed as a fraction.

Hence, the number that is not irrational is \(1.\overline{45}\). The correct option is the second option \(1.\overline{45}\)

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Answer: 2x5x1, 1x10x1 (in any order) and any 3 multiples that make 10

Step-by-step explanation:

Answer:

There are multiple possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet. Here are some possible solutions:

A rectangular prism with dimensions of 1 ft x 2 ft x 5 ft (length x width x height) would have a volume of 10 cubic feet, since 1 x 2 x 5 = 10.

A rectangular prism with dimensions of 2 ft x 1 ft x 5 ft (length x width x height) would also have a volume of 10 cubic feet, since 2 x 1 x 5 = 10.

A rectangular prism with dimensions of 0.5 ft x 1 ft x 20 ft (length x width x height) would also have a volume of 10 cubic feet, since 0.5 x 1 x 20 = 10.

A rectangular prism with dimensions of 5 ft x 1 ft x 2 ft (length x width x height) would have a volume of 10 cubic feet, since 5 x 1 x 2 = 10.

There are infinitely many other possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet.

Answer:

Step-by-step explanation:

x/1=3/(1/8)

x=3(8/1)=24 bottles per minute

Sales price (x) is the independent variable

Number of Fun Noodles Sold (y) is the dependent variable

Given the two information, we can write 2 coordinate points as shown:

We can use the point slope formula for a line to determine the slope intercept form [y = mx + b]. Shown below:

This is the slope intercept form of the line:

We want to find the sales, y, for sale price, x, of 3.50.

We simply plug 3.5 into x and find the value of y:

Daily Sales at $3.50 would be around $4500

Answer:

540 and 282

Step-by-step explanation:

x + y = 822

x - y = 258

Combine the equations

---------------------

2x = 1080

x = 540

Plug in x to the first equation

--------------------

y + 540 = 822

   - 540   -540

y = 282

--------------------

x = 540 and y = 282

Answer:

It will be 1:50

Step-by-step explanation:

Answer:

11:50 + 2 hr. = 1:50 or 13:50 Military/European time

Step-by-step explanation:

The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at;

-3, f(-3) = 390 and at 4, f(4) = 537

A function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers

By substitution:

For x = -3;

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3

f(-3) = 243 + 108 + 27 + 15 - 3

f(-3) = 390

For x = 4;

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

f(4) = 3(256) - 4(64) + 3(16) - 20 - 3

f(4) = 768 - 256 + 48 - 20 - 3

f(4) = 537

Therefore, the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537 respectively.

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228 is the answer because 72 is 24% of 300, and 300 - 72 is 228

Ramesh will bear a total medical expense of RM1,760, and the insurance company will cover RM2,900.

1. Ramesh's deductible is RM1,500 per year. This means that he is responsible for paying the first RM1,500 of medical expenses before the insurance coverage kicks in.

2. For the first treatment, the medical cost was RM700. Since this amount is less than the deductible, Ramesh will have to pay the entire RM700 out of pocket.

3. For the second treatment, the medical cost was RM2,000. Since Ramesh has already met his deductible with the first treatment, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the remaining RM500 (RM2,000 - RM1,500), which amounts to RM100. The insurance company will cover the remaining 80% of RM500, which amounts to RM400.

4. For the third treatment, the medical cost was RM1,700. Again, since Ramesh has already met his deductible, the insurance company will cover a portion of the expenses. Ramesh will be responsible for 20% of the entire cost, which amounts to RM340 (20% of RM1,700). The insurance company will cover the remaining 80% of RM1,700, which amounts to RM1,360.

5. To calculate the total medical expenses borne by Ramesh, we add up the amounts he is responsible for in each treatment: RM700 + RM100 + RM340 = RM1,140.

6. The total medical expenses covered by the insurance company can be calculated by adding up the amounts they pay in each treatment: RM400 + RM1,360 = RM1,760.

7. Finally, to find the overall amount borne by Ramesh and the insurance company, we sum up the individual expenses: Ramesh's expenses + insurance company's expenses = RM1,140 + RM1,760 = RM2,900.

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Answer:

working on a answer one second

Step-by-step explanation: