If f(x)=x³-2x², which expression equivalent to f(i)?

The function is undefined for those values of x where the denominator is zero.

The reciprocal identity for sine, cosine, and tangent states that:

sin(x) = 1/csc(x)

cos(x) = 1/sec(x)

tan(x) = 1/cot(x)

It is important to note that csc, sec, and cot are only defined for values of x where the denominator is not equal to zero.

For example, csc(x) is defined as 1/sin(x), so it is undefined for x = kπ where k is any integer and sin(x) = 0.

Similarly, sec(x) is defined as 1/cos(x) and is undefined for x = (k+1/2)π where k is any integer and cos(x) = 0. Finally, cot(x) is defined as 1/tan(x) and is undefined for x = kπ where k is any integer and tan(x) = 0.

Therefore, the reciprocal identity for sine, cosine, and tangent is only defined for certain input values, and it is undefined for those values of x where the denominator is zero.

learn more about reciprocal identity: https://brainly.com/question/24156465

#SPJ1

Answer: D its 50

Step-by-step explanation:

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

For more question equation

https://brainly.com/question/17145398

#SPJ8

Step-by-step explanation:

a probability is always

desired cases / totally possible cases.

now in our case the totally possible area is the area of the triangle XYZ (when D = Z).

the desired case is the area of 20 (which contains also the possibilities of smaller areas).

so, the probability is 20/area.

now, let's find the area of XYZ :

Pythagoras tells us the length of the Hypotenuse :

XZ² = XY² + YZ² = 12² + 6² = 144 + 36 = 180

XZ = sqrt(180)

the area based on all 3 sides we get via Heron's formula

s = (a+b+c)/2

A = sqrt(s(s-a)(s-b)(s-c))

s = (12+6+sqrt(180))/2 = 9 + sqrt(180/4) = 9 + sqrt(45)

sqrt(180) = 2×sqrt(45)

A = sqrt((9+sqrt(45))(-3+sqrt(45))(3+sqrt(45))(9-sqrt(45)))

(a+b)(a-b) = a² - b²

so,

(9+sqrt(45))(9-sqrt(45)) = 81 - 45 = 36

(-3+sqrt(45))(3+sqrt(45)) = 45 - 9 = 36

A = sqrt(36×36) = 6×6 = 36

the probability that the area of XYD is max. 20 is

20/36 = 5/9

Answer:

32

Step-by-step explanation:

Answer: (80.1786, 83.8214)

Step-by-step explanation:

Confidence interval for population mean is given by :-

\(\overline{x}\pm z_c\dfrac{\sigma}{\sqrt{n}}\) , where \(\overline{x}\) = Sample mean , n= sample size , \(\sigma\) = standard deviation, \(z_c\) = critical z-value.

Given: n= 50,  \(\overline{x}= 82\) , \(\sigma=5\)

Critical z-value for 99% confidence level = 2.576

Now, a 99 % confidence interval for the mean:

\(82\pm(2.576)\dfrac{5}{\sqrt{50}}\\\\=82\pm(2.576)(0.70710)\\\\=82\pm1.8215\\\\=(82-1.8214,\ 82+1.8214)\\\\=(80.1786,\ 83.8214)\)

Hence, required 99% confidence interval = (80.1786, 83.8214)

Answer:

P = 0.309

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The common number in 50 is 5. So you just multiply; 50×0.1=5

Answer:

Q= 8

The amount emptied is 8 gallons of water

Step-by-step explanation:

First we need to create the equation for the above statement.

Q is directly proportional to the square of d

Q= kd²

Q= 50

d= 5

50= k5²

50 = k25

K = 50/25

K = 2

K is the constant of proportionality.

Now our equation is

Q= 2d²

Where Q = volume in gallons

d = pipe diameters in inch

For a pipe of diameter 2 inch

The amount of gallons of water emptied assuming the same kinf of flow is

Q= 2d²

Q= 2(2)²

Q= 2(4)

Q= 8

The amount emptied is 8 gallons of water

Answer:

20

Step-by-step explanation:

To find the perimeter you just add all the sides together so 4.1+2.8+2.9+3.5+3.5+3.2=20

Hope this helps! :)

y=5x+4 is the equation for the line that is parallel to y = 5x - 3 and goes through the position (0, 4).

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

The given equation of line,

y=5x-3

slope of line=5

point=(0,4)

y-y1=m(x-x1)

y-4=5(x-0)

y-4=5x

y=5x+4

The equation of line parallel to y = 5x - 3 and passes through the point (0,4) is y=5x+4.

To know more about equation,

https://brainly.com/question/2228446

#SPJ4

Answer:

You distribute first 2 into the parentheses

2x-20 Is your answer

thats all you do

Step-by-step explanation:

The sum of the measures of the interior angles of a 20-sided figure is 3240.

What are Interior angles ?

An interior angle of a polygon is an angle that is created between two of the polygon's adjacent sides. The interior angle of a polygon is also known as the angle measured at the interior of a polygon.

the number of sides of given polygon is 20.

we know that, sum of the measures of the interior angles can be found by using formula : (n-2) × 180

where n= no. of sides of given polygon

So, sum of the measures of the interior angles of 20 sided figure :

     = (n-2) × 180

     = (20-2) × 180

     = 18 × 180

     = 3240 .

To learn more about Interior angles, visit the link :

https://brainly.com/question/24966296

#SPJ1

Answer:

A

Step-by-step explanation:

Banana milk is 6%. So we need to work out 6% of 360 because angles in a circle add up to 360. So we can do this by dividing 360 by 100 then timsing that by 6 to get 21.6 degrees, which is A.

Answer:

21.6

Step-by-step explanation:

6% of 360=21.6

Here

Distance

\(\\ \rm\Rrightarrow \dfrac{|Ax+By+C|}{\sqrt{A^2+B^2}}\)

\(\\ \rm\Rrightarrow \dfrac{|1(2)+1(6)-4|}{\sqrt{1+1}}\)

\(\\ \rm\Rrightarrow \dfrac{8-4}{\sqrt{2}}\)

\(\\ \rm\Rrightarrow \dfrac{4}{\sqrt{2}}\)

\(\\ \rm\Rrightarrow 2\sqrt{2}units\)

True 6. If the obtained sample data (test statistic value) falls inside the critical region, it provides support for the researcher's hypothesis.

True 7.  When the Z-test statistic, obtained from the sample data, falls inside the critical region, it indicates that the observed result is unlikely to have occurred by chance alone under the assumption of the null hypothesis. Therefore, we reject the null hypothesis and accept the alternative hypothesis.

True 8. If the obtained sample data (test statistic value) is not in the critical region, it means that the observed result is likely to have occurred by chance under the assumption of the null hypothesis. hypothesis.

True 9. Failing to reject the null hypothesis means that the data do not provide sufficient evidence to conclude that the treatment or independent variable had a significant effect on the dependent variable.

True 10.  Whenever the statistical decision is to fail to reject the null hypothesis, there is a possibility of making a Type I error.

6. The critical region is determined based on the desired level of significance and contains the extreme values that would lead to rejecting the null hypothesis.

7. When the Z-test statistic, obtained from the sample data, falls inside the critical region, it indicates that the observed result is unlikely to have occurred by chance alone under the assumption of the null hypothesis. Therefore, we reject the null hypothesis and accept the alternative hypothesis.

8. In this case, we do not have sufficient evidence to reject the null hypothesis, and the correct statistical decision is to "fail to reject" the null

9. It does not necessarily mean that the treatment had no effect, but rather that the evidence in the sample is not strong enough to support such a claim.

10. Type I error refers to rejecting the null hypothesis when it is actually true. The probability of committing a Type I error is denoted by the significance level (usually denoted as alpha) and is predetermined before conducting the statistical test.

In summary, the statements are all true. The critical region plays a crucial role in hypothesis testing, and the decisions made based on the test statistic falling inside or outside the critical region determine whether the null hypothesis is rejected or failed to be rejected.

Failing to reject the null hypothesis does not provide sufficient evidence to support the researcher's hypothesis and there is always a possibility of making a Type I error when conducting hypothesis tests.

For more such answers on critical region

https://brainly.com/question/31164533

#SPJ8

Answer:

B (A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units3; therefore, Shannon is correct)

Step-by-step explanation:

I took the test!

The solution is,: A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units^3; therefore, Shannon is correct

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

step 1

Find the area of the base of the rectangular pyramid

we know that:

The volume of the rectangular pyramid is equal to:

V = 1/3 * bh

where

B is the area of the base

H is the height of the pyramid

we have

V= 50

h = 5

substitute and solve for B

we get,

b= 30

step 2

Find the volume of the rectangular prism with the same base area and height

we know that

The volume of the rectangular prism is equal to

V = bh

we have

b = 30

h = 5

substitute

V = 30 * 5 = 150 unit^3

therefore

The rectangular prism has a volume that is three times the size of the given rectangular pyramid. Shannon is correct

To learn more on volume click :

brainly.com/question/1578538

#SPJ2

The velocity or speed is the ratio of distance and time thus the difference between Anna’s walking time and running time for 16km is 32/(3x).

Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.

Average velocity = total distance / total time taken

Units of velocity are given by ⇒ meter/second

Let's say Anna's walking speed is x.

Given that, Anna’s average running speed is 3 times faster than her running speed is 3x

Since,time = distance/speed

The walking time = 16/x

Running time = 16/3x

Difference = 16/x - 16/3x

⇒ (1-1/3)16/x

⇒ (2/3)(16/x)

⇒ 32/(3x).

Hence "The velocity or speed is the ratio of distance and time thus the difference between Anna’s walking time and running time for 16km is 32/(3x)".

To learn more about velocity,

brainly.com/question/18084516

#SPJ1

Answer:

= 6.156 × 105

(scientific notation)

Step-by-step explanation:

= 6.156 × 105

(scientific notation)

= 6.156e5

(scientific e notation)

= 615.6 × 103

(engineering notation)

(thousand; prefix kilo- (k))

= 615600

(real number)

I'm going to assume you're asking where the point is located on a coordinate plane.

We have x = 0 and y = -4.

So, we start at (0, 0) and move down 4 units.

Best of Luck!

Answer:

1 and 2: Parallel; 1 and 3: Neither; 2 and 3: Neither

Step-by-step explanation:

2 lines are parallel if they have the same slope. 2 lines are perpendicular if they have the opposite reciprocal slope.

It is verified that the given vectors x₁ and x₂ are solutions of the given system. Using Wronskian it is shown that they are linearly independent. Then, \(W(t)=7e^{-3t}\). The general solution of the given system is written as \(x(t)=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right]\).

Wronskian analysis helps to determine whether a solution is linearly dependent or independent.

Given the system is \(x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x\).

Let's differentiate x₁ concerning t, and we get,

\(\begin{aligned}x_1'&=\left[\begin{array}{c}\frac{d}{dt}(3e^{2t})&\\\frac{d}{dt}(2e^{2t})&\end{array}\right] \\&=\left[\begin{array}{c}6e^{2t}&\\4e^{2t}&\end{array}\right] \end{aligned}\)

Now,

\(\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_1&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}12e^{2t}-6e^{2t}\\18e^{2t}-14e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}6e^{2t}\\4e^{2t}\end{array}\right]\\&=x_1'\end{aligned}\)

From this, we can write,

\(x_1'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_1\)

Therefore, we conclude that x₁ is a solution to the given system.

Let's differentiate x₂ concerning t, and we get,

\(\begin{aligned}x_2'&=\left[\begin{array}{c}\frac{d}{dt}(e^{-5t})&\\\frac{d}{dt}(3e^{-5t})&\end{array}\right] \\&=\left[\begin{array}{c}-5e^{-5t}&\\-15e^{-5t}&\end{array}\right] \end{aligned}\)

Now,

\(\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_2&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}4e^{-5t}-9e^{-5t}\\6e^{-5t}-21e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}-5e^{-5t}\\-15e^{-5t}\end{array}\right]\\&=x_2'\end{aligned}\)

From this, we can write,

\(x_2'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_2\)

Therefore, we conclude that x₂ is also a solution to the given system.

Now, find the Wronskian of x₁ and x₂, we get,

\(\begin{aligned}W(t)&=\text{det}[x_1\;x_2]\\&=\text{det}\left[\begin{array}{cc}3e^{2t}&e^{-5t}\\2e^{2t}&3e^{-5t}\end{array}\right] \\&=(3e^{2t}\times3e^{-5t})-(e^{-5t}\times2e^{2t})\\&=9e^{2t-5t}-2e^{2t-5t}\\&=9e^{-3t}-2e^{-3t}\\&=7e^{-3t}\\&\neq0\end{aligned}\)

From this, we can conclude that x₁ and x₂ are independent.

Finally, we write the general solution of the system as follows,

\(\begin{aligned}x(t)&=c_1x_1+c_2x_2\\&=c_1 \left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right] +c_2\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right] \\&=\left[\begin{array}{c}3c_1e^{2t}\\2c_1e^{2t}\end{array}\right] +\left[\begin{array}{c}c_2e^{-5t}\\3c_2e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right] \end{aligned}\)

The complete question is -

First, verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system.

\(x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x;\; x_1=\left[\begin{array}{ccc}3e^{2t}\\2e^{2t}\end{array}\right], \;x_2=\left[\begin{array}{cc}e^{-5t}\\3e^{-5t}\end{array}\right]\)

To know more about Wronskian:

https://brainly.com/question/14309076

#SPJ4

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

B

Answer:

C. 5

Step-by-step explanation:

HN = HJ = 11 (tangents drawn from an external point)

KJ = KH - HJ = 16 - 11

KJ = 5

KJ = KL = 5 (tangents drawn from an external point)

KL = x = 5

Answer:

$886.47

Step-by-step explanation:

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

For the given expression, the addition of coefficients is \(5x^2 + 2x - 7\).

In algebra, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression. In other words, it is the number that is being multiplied by the variable.

Addition is a basic mathematical operation that combines two or more numbers or quantities to produce a sum. It is denoted by the plus sign (+). When two or more numbers are added, the result is called the sum or total.

First, we need to combine like terms by adding the coefficients of terms with the same variable(s) raised to the same power.

\((6x^2 + 10x - 7) + (-x^2 - 8x)\)

\(= 6x^2 + (-x^2) + 10x + (-8x) - 7\) (grouping like terms together)

\(= (6x^2 - x^2) + (10x - 8x) - 7\) (rearranging terms)

\(= 5x^2 + 2x - 7\) (combining the coefficients)

Therefore, the final answer for the addition of coefficients is \(5x^2 + 2x - 7.\)

To know more about coefficient visit:

https://brainly.com/question/1038771

#SPJ1

To find the length of AC, we can use the Pythagorean theorem, which states that in a right triangle. the length of AC is approximately  \(29.8 mm\).

the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we can use AC as the hypotenuse, so:

\(AC^2 = AB^2 + BC^2\)

\(AC^2 = (14.7 mm)^2 + (25.9 mm)^2\)

\(AC^2 = 216.09 mm^2 + 671.61 mm^2\)

\(AC^2 = 887.7 mm^2\)

Taking the square root of both sides, we get:

\(AC = \sqrt887.7 mm\)

\(AC \approx 29.8 mm\) (rounded to 1 decimal place)

Therefore, the length of AC is approximately  \(29.8 mm\).

Learn more about hypotenuse here:

https://brainly.com/question/29407794

#SPJ1

The greatest common divisor of 5! and 7! is 840.

To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.

First, let's calculate the prime factorization of 5!:

5! = 5 * 4 * 3 * 2 * 1 = 120.

The prime factorization of 120 is 2^3 * 3 * 5.

Now, let's calculate the prime factorization of 7!:

7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.

The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.

To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.

From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:

GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.

For more such question on divisor

https://brainly.com/question/30126004

#SPJ8