Simplify the expression.
sec x/tan x

We want to find all [tex]f(x)[/tex] such that

[tex](D^2-12D-45)[f(x)]=0[/tex]

We have

[tex](D^2-12D-45)[f]=(D-15)(D+3)[f]=0[/tex]

so that either

[tex](D-15)[f]=0\implies f'-15f=0\implies f(x)=e^{15x}[/tex]

or

[tex](D+3)[f]=0\implies f'+3f=0\implies f(x)=e^{-3x}[/tex]

These solutions are linearly independent; we confirm this by computing the Wronskian:

[tex]W=\begin{vmatrix}e^{15x}&e^{-3x}\\15e^{15x}&-3e^{-3x}\end{vmatrix}=-3e^{12x}-15e^{12x}=-18e^{12x}\neq0[/tex]

We can also confirm that these solutions are correct by substituting the solutions for [tex]f(x)[/tex] in the differential equation:

[tex](D^2-12D-45)[e^{15x}]=225e^{15x}-12(15e^{15x})-45e^{15x}=0[/tex]

[tex](D^2-12D-45)[e^{-3x}]=9e^{-3x}-12(-3e^{-3x})-45e^{-3x}=0[/tex]

The linearly independent functions that are annihilated by the differential operator d2 − 12d - 45 are e^{15x} and e^{-3x}, found by solving the quadratic equation associated with the differential equation.

The differential operator given is d2 − 12d - 45. To find out the linearly independent functions that are annihilated by this operator, we have to solve the homogeneous differential equation d2 − 12d - 45 = 0. This is a second order equation, so we expect two linearly independent solutions.

To find the solutions, we seek the roots of the associated quadratic equation m^2 - 12m -45 = 0. This can be factored into (m-15)(m+3), thus giving roots m = 15 and m = -3.

The general forms of the solutions for these roots are e^{15x} and e^{-3x} respectively. Therefore, the functions e^{15x} and e^{-3x} are linearly independent functions that are annihilated by the given differential operator d2 − 12d - 45.

https://brainly.com/question/33987642

#SPJ11

1.5 • 3.142= 4.713 should be the answer

Answer:   4.5π  ≈  14.14 cm²

Step-by-step explanation:

[tex]Area_{\ circle}=\pi \cdot r^2\\\\Area_{\ semicircle}=Area_{\ circle}\div 2\\\\\\A=\dfrac{\pi \cdot 3^2}{2}\\\\\\.\quad =\dfrac{9}{2}\pi\\\\\\.\quad =4.5\pi\\\\\\.\quad =14.14[/tex]

Answer:

Brenda

Step-by-step explanation:

You can divide the number of pages by the number of minutes to find the amount of minutes it takes to read 1 page. For Arnold, 3 pages / 7 minutes = 1 page per approximately 0.43 minutes. For Brenda, 8 pages / 14 minutes = 1 page per approximately 0.57 minutes. Brenda reads slightly faster since 0.57 > 0.43

Answer:

There are 21 luxury vehicles in 3 shipments sent to a dealership . Which of the following expresses the ratio of shipments to luxury vehicles?

A. 21/3

B. 21 to 3

C. 21:3

D. 3:21

Step-by-step explanation:

Answer:

The answer is D. 3:21 Hope this helps!

Answer:

The mean is 5

the median is also 5

and the mode is 1

Step-by-step explanation:

Answer:60,61,73,75,79,81,81,81,92,96,98

Step-by-step explanation: Mean:80

                                             Median:81

                                            Mode:81

Answer:

0.05% means 0.05 per every 100.

Step-by-step explanation:

We find it useful to convert 0.05% to decimal, because if you need to find 0.05% of any number, you can simply multiply that number with 0.0005.

hope this helps!!!!!

The value of 0.05% written as a decimal is 0.0005.

To write 0.05% as a decimal, you need to divide the percentage value by 100.

A decimal number is a number that uses the base-10 numbering system. It is a way of representing numbers using the digits 0-9 and a decimal point. Each digit in a decimal number represents a specific place value, which is a power of 10.

The digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts or decimal fractions.

0.05% divided by 100 is equal to 0.0005.

Therefore, 0.05% written as a decimal is 0.0005.

To know more about decimal numbers follow

https://brainly.com/question/30405685

#SPJ6

the scale factor is 2.

because

if you look at the length AL in the smaller shape, it is 2 squares.

now if you look at the length AL in the enlarged shape, it is 4 squares.

to find the scale factor, do 4 ÷ 2 which is 2.

therefore the scale factor is 2

Answer:

The correct option is 2. The scale factor is 2.

Step-by-step explanation:

The coordinates of preimage are A(1,2), T(0,0), K(4,1) and L(3,2).

The coordinates of image are A'(2,4), T'(0,0), K'(8,2) and L'(6,4).

If a figure dilated by scale factor k with center at origin then the rule of dilation is

[tex](x,y)\rightarrow (kx,ky)[/tex]

[tex]A(1,2)\rightarrow A'(2,4)[/tex]

[tex]k=\frac{\text{x coordinate of image}}{\text{x coordinate of preimage}}[/tex]

[tex]k=\frac{2}{1}[/tex]

[tex]k=2[/tex]

Therefore the scale factor is 2 and the correct option is 2.

Answer:

16.033 min

Step-by-step explanation:

We can write Newton's Law of Cooling as

T = Tₐ + (T₀ - Tₐ)e^(-kt), where

Tₐ = ambient temperature of the surroundings

T₀ = initial temperature of the object

k = the cooling constant

t = the time

(1) Calculate the cooling constant

Data:

T =   110 °F

T₀ = 180 °F

Tₐ =  70 °F

 t =   20 min

Calculation:

110 = 70 + (180 - 70)e^(-k×20)

40 = 110e^(-20k)

0.363 64 = e^(-20k)

-1.0116 = -20k

k = 0.050 580 min⁻¹

(2)After adding cream

(a) Calculate T₀  

2 oz × 40 °F + 12 oz × 180 °F = 14 oz × T₀

80 °F + 2160°F = 14T₀

2240 °F = 14T₀

T₀ = 160 °F

(b) Calculate the time to cool to drinking temperature

110 = 70 + (160 - 70)e^(-0.050 580t)

40 = 90e^(-0.050 580t)

0.444 44 = e^(-0.050 580t)

-0.810 93 = -0.050580t

t = 16.033 min

It will take 16.033 min for the mixture to reach drinking temperature

To determine the time it takes for the mixture to reach drinking temperature, we first calculate the initial temperature of the mixture after adding 2 ounces of 40°F cream to the 180°F coffee, which turns out to be 165°F. Then, according to Newton's Law of Cooling, the time it takes for the mixture to decrease from 165°F to the drinking temperature of 110°F would be the same as the time it took for the original coffee to cool from 235°F to 180°F, given the cooling constant doesn't change when we add the cream. Therefore, the mixture will take approximately 20 minutes to reach drinking temperature.

To determine the time it takes for the mixture to reach drinking temperature, we first need to calculate the initial temperature of the mixture. When you add 2 ounces of 40°F cream to the 180°F coffee, the temperature of the mixture instantly becomes the weighted average of the temperature of the coffee and of the cream. Thus, we have:

(12 * 180 + 2 * 40) / (12 + 2) = 165°F.

Now we need to calculate the time it takes for the mixture to decrease from 165°F to the drinking temperature of 110°F. According to Newton's Law of Cooling, the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature. If we assume that the proportionality constant (or the cooling constant) doesn't change when we add the cream, then the time it takes for the mixture to cool from 165°F to 110°F will be the same as the time it took for the original coffee to cool from 235°F (165 + 70) to 180°F (110 + 70), which is 20 minutes. We can conclude that the mixture will take approximately 20 minutes to reach drinking temperature.

https://brainly.com/question/33399430

#SPJ3

Answer:

sqrt(sqrt(x))

Step-by-step explanation:

A quartic root of is written mathematically as . THe quartic root of 16 is 2 since 2*2*2*2 = 16. However, a quartic root can also be defined as the square root of a square root. For example the √16 = 4 and the √4 = 2. This is the same response as taking the quartic root. This means you can write it as the sqrt(sqrt(x)). In the example, it would be sqrt(sqrt(16)) = sqrt(4) = 2.

The quartic root of a variable x can be calculated using the expression Math.sqrt(Math.sqrt(x)), which calls the square root function twice. This computes the square root of x, then computes the square root of the result, yielding the quartic root.

In order to compute the quartic root of a variable x, we call the Math.sqrt() method twice in a nested manner. The quartic root is essentially the square root of a square root, hence the need for the double call. The appropriate expression in this case would be:

Math.sqrt(Math.sqrt(x))

This expression first computes the square root of x and then computes the square root of the result, which gives us the quartic root of x. As a result, if x is 16.0, the result of this expression would be 2.0, and if x is 81.0, the result would be 3.0.

https://brainly.com/question/32892267

#SPJ3

Answer:

The answer is five.

Step-by-step explanation:

A pyramid with a square base has one square face and there are four triangle faces, so there are five in total.

I hope this helped! :-)

Number of faces of pyramid with a square base is 5.

Hence option A is correct.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Since we know that

A pyramid having square base have,

Number of square face = 1

Number of triangular face = 4

Hence total face in this triangle is,

= 1+4

= 5

Hence total faces = 5.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ7

What is the length of the actual car in feet and inches? 4/5 ft 48/72in

Answer:

280 degrees.

Step-by-step explanation:

To convert radians to degrees we multiply by 180/pi:

angle O = 14pi/ 9 * 180 / pi

=  14*180 / 9

=  280 degrees.

The angle 0=14pi/9 radians can be converted to degrees by using the conversion factor 1 radian = 57.3°. Multiplying the given angle in radians by the conversion factor results in an equivalent angle of 280° in degrees.

To convert the angle from radians to degrees, we use the conversion factor 1 rad = 57.3°. The problem provides the angle 0 = 14pi/9 radians. By using the conversion factor, the process of conversion would be as follows:

Therefore, the angle 0=14pi/9 radians is equal to 280° in degrees.

https://brainly.com/question/32641146

#SPJ3

The first month has the equation raised to 11 which is the number of months left in the period.

So each month the equation would be the same except it would be raised to 1 less than the previous month.

Month 2 = 50(1.003)^10

Month 3 = 50(1.003)^9

Month 4 = 50(1.003)^8

Month 5 = 50(1.003)^7

Month 6 = 50(1.003)^6

Month 7 = 50(1.003)^5

Month 8 = 50(1.003)^4

Month 9 = 50(1.003)^3

Month 10 = 50(1.003)^2

Month 11 = 50(1.003)^1

Month 12 = 50(1.003) ( the last month would not be raised to anything)

Answer:

600

Step-by-step explanation:

its 50 X 12

thats how you would solve that

1+y (greater than or equal to symbol) 6

Answer:

Step-by-step explanation:

0.3. x + 18.3

The data for tree 1 is an illustration of a linear equation.

The linear equation that fits the data for tree 1 is: [tex]\mathbf{y = 0.3x + 18.3}[/tex]

From the complete question, we have the following points

[tex]\mathbf{(x_1,y_1) = (1,18.6)}[/tex]

[tex]\mathbf{(x_2,y_2) = (3,19.2)}[/tex]

First, we calculate the slope (m)

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{19.2 - 18.6}{3 -1}}[/tex]

[tex]\mathbf{m = \frac{0.6}{2}}[/tex]

[tex]\mathbf{m = 0.3}[/tex]

The equation is then calculated as:

[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]

So, we have:

[tex]\mathbf{y = 0.3(x - 1) + 18.6}[/tex]

[tex]\mathbf{y = 0.3x - 0.3+ 18.6}[/tex]

[tex]\mathbf{y = 0.3x + 18.3}[/tex]

Hence, the linear equation that fits the data for tree 1 is: [tex]\mathbf{y = 0.3x + 18.3}[/tex]

Read more about linear equations at:

https://brainly.com/question/21088228

Answer:

12

Step-by-step explanation:

subtract 25 minus 13 and you get 12 which means 12 students come in cars

Destructimous had 6 ultra power blasts.

The total number of blasts Destructimous has is:

Total blasts = Sonic blasts + Heat rays

Total blasts = 7 + 13

Total blasts = 20

Now, we know that Destructimous has a 2/7 chance of using its ultra power blast. To find out how many ultra power blasts it fires, we calculate 2/7 of the total blasts:

Ultra power blasts = (2/7) * Total blasts

Ultra power blasts = (2/7) * 20

Ultra power blasts = 40/7

Now, since we can't have a fraction of a blast, we need to round this number to the nearest whole number. In this case, 40/7 is approximately 5.71, so when rounded, it's 6.

So, Destructimous had 6 ultra power blasts.

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

distributive property because u need to mulptiply the number outside with the parentheses

Answer:

A)Distributive property

Step-by-step explanation:

This is because you need to multiply

right isosceles

rs:34&rs=rt+st

rt:17

st:17

ab=[(x(a)-x(b))+(y(a)+y(b))]

Answer:

Isosceles.

Step-by-step explanation:

We are going to check it with the distance formula

d(R,T) = [tex]\sqrt[2]{(3-4)^{2}+(-3-1)^{2}}[/tex]

= [tex]\sqrt[2]{(-1)^{2}+(-4)^{2}}[/tex]

= [tex]\sqrt[2]{1+16}[/tex]

=  [tex]\sqrt[2]{17}[/tex].

d(T,S) = [tex]\sqrt[2]{(4-8)^{2}+(1-0)^{2}}[/tex]

= [tex]\sqrt[2]{(-4)^{2}+(1)^{2}}[/tex]

= [tex]\sqrt[2]{16+1}[/tex]

=  [tex]\sqrt[2]{17}[/tex].

d(S,R) = [tex]\sqrt[2]{(8-3)^{2}+(0-(-3))^{2}}[/tex]

= [tex]\sqrt[2]{(5)^{2}+(3)^{2}}[/tex]

= [tex]\sqrt[2]{25+9}[/tex]

=  [tex]\sqrt[2]{34}[/tex].

Then, as the triangle has two sides with the same length, the triangle is isosceles.

Moving the decimal point left or right works in the metric systems because; The metric system is based on powers of 10.

It follows from the task content that the reason for moving the decimal point left or right in metric system conversions be identified.

It follows from metric system conversions that;

Based on the aforementioned, it can be concluded that the measurements conversion in the metric system is such that the decimal point is moved left or right.

Read more on metric system conversions;

https://brainly.com/question/976935

#SPJ1

Answer:

x = ±√2

Step-by-step explanation:

         x - 1 =     1/(x + 1)

(x -1)(x + 1) =     1     Multiplied each side by x + 1

       x² - 1 =     1     Difference of two squares

           x² =     2     Add 1 to each side

           x  = ±√2

x-1 is the reciprocal of x+1 when x = -√2 or x = √2.

Check:

(a) x = -√2

  -√2 - 1 = 1/(-√2 + 1)

-(√2 + 1) = (√2 +1)/[(-√2 +1)(√2 + 1)]

-(√2 + 1) = (√2 +1)/(-2 +1)

-(√2 + 1) = (√2 +1)/(-1)

-(√2 + 1) = -(√2 +1)

(b) x = √2

√2 - 1 = 1/(√2 + 1

√2 - 1 = (√2 - 1)/[(√2 + 1)(√2 - 1) ]

√2 - 1 = (√2 - 1)/(2 - 1)

√2 - 1 = (√2 - 1)/1

√2 - 1 = √2 - 1

OK.

Answer:x = ±√2

Step-by-step explanation: this is because reciprocal means the numerator and denominator switches

So the equation is x-1=1/(x+1)

And you solve for it thats how u get the answer

Answer:

P(n) = 0.5

Step-by-step explanation:

For two events which are independent, we use the multiplication rule which states P (A and B) = P(A) * P(B). Substitute P(m) = 0.4 and P(m and n) = 0.2 into this formula.

P (m and n) = P(m) * P(n)

0.2 = 0.4*P(n)

Divide by 0.4 on both sides.

0.2 / 0.4 = P(n)

0.5 = P(n)

Answer:

no simplify. answer is:

b. log(1/7)

ANSWER

d.

[tex] \frac{1}{7} [/tex]

EXPLANATION

We want to simplify

[tex] {10}^{ log( \frac{1}{7} ) } [/tex]

Recall that the common logarithm has a base of 10.

This implies that,

[tex] {10}^{ log( \frac{1}{7} ) } = {10}^{ log_{10}( \frac{1}{7} ) } [/tex]

Recall again that:

[tex] {p}^{ log_{p}(q) } = q[/tex]

Therefore,

[tex] {10}^{ log( \frac{1}{7} ) } = {10}^{ log_{10}( \frac{1}{7} ) } = \frac{1}{7} [/tex]

Answer:

option a

[tex]log\frac{x^{5} }{(x-8)^{6} }[/tex]

Step-by-step explanation:

Given in the question an expression

5logx - 6log(x-6)

To solve this question we will apply two of the logarithm property

1) power rule

alogx = log[tex]x^{n}[/tex]

log[tex]x^{5}[/tex] - log[tex](x-8)^{6}[/tex]

2) substraction rule

The log of a quotient is the difference of the logs

loga (x/y) = loga x - loga y

[tex]logx^{5}- log(x-8)^{6}[/tex]

log[tex]\frac{x^{5} }{(x-8)^{6} }[/tex]

Answer:

a edge

Step-by-step explanation:

Answer:

28π and 196π

10π and 25π

2500π

A = C/4π

Step-by-step explanation:

The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. The area of the circle is the amount inside the circle and is found using A = πr². Substitute the relevant values in each situation into the formulas to find the circumference and area.

if the radius of a circle is 14 units, what is its circumference? what is its area?

Substitute r = 14.

C = 2πr = 2π(14) = 28π

A = πr² = π(14)² = 196π

if a circle has diameter 10 units, what is its circumference? what is its area?

Substitute r = 5.

C = 2πr = 2π(5) = 10π

A = πr² = π(5)² = 25π

if a circle has circumference 100π units, what is its area?

Substitute C = 100π to find the radius. Then substitute the radius into the are formula.

C = 2πr

100π=2πr

100 = 2r

50 = r

A = πr² = π(50)² = 2500π

if a circle has circumference c, what is its area in terms of c?

Cole the circumference formula for r. Then substitute the expression into the area formula.

C = 2πr

r = C / 2π

A = πr² = π(C/2π)² = πC/4π² = C/4π

1. Circumference: [tex]\(28\pi\)[/tex]units, Area: [tex]\(196\pi\)[/tex] square units.

2. Circumference: [tex]\(10\pi\)[/tex]units, Area: [tex]\(25\pi\)[/tex]square units.

3. Area: [tex]\(2500\pi\)[/tex]square units.

4. Area: [tex]\(\frac{C^2}{4\pi}\)[/tex]  square units.

Let's go through each question one by one, using the formulas for the circumference and area of a circle.

1. If the radius of a circle is 14 units, what is its circumference? What is its area?

  - The circumference [tex]\( C \)[/tex] of a circle is given by the formula:

[tex]\[ C = 2\pi r \][/tex]

    where [tex]\( r \)[/tex] is the radius.

    Given [tex]\( r = 14 \)[/tex] units, we have:

[tex]\[ C = 2\pi \times 14 = 28\pi \text{ units} \][/tex]

  - The area [tex]\( A \)[/tex]of a circle is given by the formula:

[tex]\[ A = \pi r^2 \][/tex]

    Given [tex]\( r = 14 \)[/tex] units, we have:

[tex]\[ A = \pi \times 14^2 = \pi \times 196 = 196\pi \text{ square units} \][/tex]

2. If a circle has diameter 10 units, what is its circumference? What is its area?

  - The diameter [tex]\( d \)[/tex] is related to the radius by [tex]\( d = 2r \)[/tex]. Therefore, the radius [tex]\( r \)[/tex] is:

[tex]\[ r = \frac{d}{2} = \frac{10}{2} = 5 \text{ units} \][/tex]

  - Using the circumference formula [tex]\( C = 2\pi r \):[/tex]

[tex]\[ C = 2\pi \times 5 = 10\pi \text{ units} \][/tex]

  - Using the area formula [tex]\( A = \pi r^2 \):[/tex]

[tex]\[ A = \pi \times 5^2 = \pi \times 25 = 25\pi \text{ square units} \][/tex]

3. If a circle has circumference [tex]\( 100\pi \)[/tex] units, what is its area?

  - Given the circumference [tex]\( C = 100\pi \),[/tex] we can find the radius [tex]\( r \)[/tex] using the formula [tex]\( C = 2\pi r \):[/tex]

[tex]\[ 100\pi = 2\pi r \][/tex]

    Dividing both sides by [tex]\( 2\pi \):[/tex]

[tex]\[ r = \frac{100\pi}{2\pi} = 50 \text{ units} \][/tex]

  - Using the area formula [tex]\( A = \pi r^2 \):[/tex]

[tex]\[ A = \pi \times 50^2 = \pi \times 2500 = 2500\pi \text{ square units} \][/tex]

4. If a circle has circumference [tex]\( C \),[/tex] what is its area in terms of [tex]\( C \)[/tex]

  - Given the circumference [tex]\( C \),[/tex] we can express the radius [tex]\( r \)[/tex] in terms of [tex]\( C \)[/tex] using the formula [tex]\( C = 2\pi r \):[/tex]

[tex]\[ r = \frac{C}{2\pi} \][/tex]

  - Using the area formula [tex]\( A = \pi r^2 \)[/tex] and substituting [tex]\( r = \frac{C}{2\pi} \):[/tex]

[tex]\[ A = \pi \left( \frac{C}{2\pi} \right)^2 = \pi \left( \frac{C^2}{4\pi^2} \right) = \frac{\pi C^2}{4\pi^2} = \frac{C^2}{4\pi} \][/tex]

To assess the evidence of Hypothesis testing, the students need to determine the likelihood of the proportion of Millennial students at their campus that live at home with their parents being 36% or higher.

The question here is regarding the testing of a population proportion using statistical hypothesis testing, specifically a one-sample z-test. The null hypothesis (H0) is that the population proportion is equal to a specified value, in this case, 36%). The alternative hypothesis (Ha) is that the population proportion is greater than the specified value (more than 36%).

The question we need to answer is 'If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be more than 36%?'

The scenario suggests an indication towards a right-tailed z-test as we're looking to see if the data indicates a proportion >36%. However, as with all statistical tests, one should be cautious about drawing definitive conclusions without additional context and understanding the potential for sampling variability and error.

https://brainly.com/question/34171008

#SPJ12

Answer:

I dont really know the answer.. but ill try; if its wrong I am so sorry;

Step-by-step explanation:

First you must get the area of a circle, which is; A= pi r squared

and all you have to do is fill it in like this;

A= 3.14 x 2.0

           ^

    A= 6.28

1/8 chance since there are 8 numbers from 5 to 12 and 1 is only one number so 1/8