For Exercises 1 and 2, use the figure at the rights
1. What is m 24 ifm 28 = 40°?
1.
A. 500
B. 180°
C. 70°
D. 40°

The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).

To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:

\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)

Let's calculate the first four terms:

Starting with the first term, we substitute

\(\(f(a) = f(1) = 2(1) = 2x\)\)

For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).

\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)

\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)

Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)

Since the second derivative is zero, the third term is zero.

Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)

Similarly, the fourth term is also zero.

Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:

(2x + 2x - 2)

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Answer:

answers are below

Step-by-step explanation:

1. k = -12

2. x = 14

3. y = -18

4. x = 34/3 or 11.3333333

5. x = -10

6. b = 17

7. x = 1/7

8. y = -2

Hope this heps!! Tell me if you need any explanations :)

Answer:

1. -12

2. 14

3. -18

4. 11 1/3

5. -1 3/5

6. -17

7. 1/7

8. 7 1/3

Step-by-step explanation:

Most of them should be right but sorry if wrong

The least volume to greatest volume will be sphere B, sphere C, sphere A and sphere D.

The volume of the sphere is calculated as:

= 4/3 πr³

where r = radius

The volume of sphere A will be:

= 4/3 πr³

= 4/3 × π × 4³

= 85.3π

The volume for sphere B will be:

= 4/3 πr³

= 4/3 × π × (6/2)³

= 4/3 × π × 3³

= 36π

The volume for C is given as 64π.

The volume for D has a radius double that of B. This will be Radius = 3 × 2 = 6

= 4/3 πr³

= 4/3 × π × 6³

= 288π

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Answer:

She forgot about the negative sign in front of the 3.7, therefore, she added 3.7 to -3.3 which is equals to 0.4

Answer:

2x-y+2= 0

Step-by-step explanation:

(-5,-2)=(x1, y1)

(3, 14) =(x2, y2)

now,

slope(m)= y2-y1 / x2-x1

=14+2 / 3+5

= 16 /8

=2 units

passing point = (-5,-2) = x1,y1

now,

eqn of the line can be represented as,

y -y1 = m (x-x1)

y +2 = 2 (x +5)

y+2 = 2x +10

y = 2x+10-8

0 = 2x+2-y

2x-y+2 =0 is the required eqn

Answer:

licker 90000000000000000

Answer:

y is for genius factor

a is for angles

b are absoulutely for divides and multiply from the sides of heptagon

X are like EQUAL to 7 tables for example D% 72*(09 1/2 its just like this!!

and Deciamals are apart like 22 . 27 its just like that!!

Step-by-step explanation:

Does this help? let me know!!

The angle amount of m is 128⁰

Angle can also refer to the length of a rotation or an angle. The Greek word , which means "crooked, curled," and the English word "ankle," are related words. Both stem from the Proto-Indo-European root  which means "to bend" or "bow," in some way.

A plane angle, according to Euclid, is the inclination to each other of two intersecting lines in a plane that are not perpendicular to one another. Proclus asserts that an angle must be either a quality, a number, or a connection. Eudemus used the first idea, viewing an angle as a departure from a straight line; Carpus of Antioch used the second idea, viewing an angle as the distance or space between intersecting lines; and Euclid used the third idea. Vertical angles, opposing angles, or vertically opposite angles refer to a pair of angles that are directly across from one another and are created by two straight lines meeting to form a "X". Vert is the shorthand for them. opp.

The vertical angle theorem states that angles that are vertically opposing are equal. The assertion shown that since both of a pair of vertical angles are supplementary to both of the neighboring angles, the vertical angles are equal in measure, according to Eudemus of Rhodes' attribution of the proof to Thales of Miletus. When Thales visited Egypt, it is recorded in history[9] that he noticed the Egyptians measuring the vertical angles whenever two intersecting lines were drawn to ensure that they were equal. Thales came to the conclusion that one might establish

4x+6=7x-21

3x=27

x=9

x+x+42+42=360

2x+84=360

x=128⁰

Therefore, the angle amount of m is 128⁰

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Let's suppose that the number of students that paid the regular price is x, then the number of students that got a discount would be 314-x. Let's assume the number of students that paid the regular price is x, then the number of students that got a discount would be 314-x. So, the number of students that paid the regular price is 202, and the number of students that got a discount is 112.

Now let's set up an equation based on the given data: The cost of each student that paid the regular price is PHP 50, so the total cost for them is 50x. The cost of each student that got a discount is PHP 30, so the total cost for them is 30(314-x). The total cost of the trip is PHP 10,080.

So: 50x + 30(314 - x) = 10080

Simplifying, we get: 50x + 9420 - 30x = 10080
20x = 6660
x = 333. Therefore, the number of students that paid the regular price is 333. The number of students that got a discount is 314 - 333 = -19. However, this doesn't make sense since the number of students can't be negative. Therefore, we made an error somewhere, and we need to go back and check our work.

The problem is that the number of students that paid the regular price plus the number of students that got a discount should equal the total number of students, which is 314. But our calculation of x is greater than the total number of students. This is not possible, so we need to revise our equation.

One possible way to do this is to define a new variable, y, to represent the number of students that got a discount. Then we have: x + y = 314 and 50x + 30y = 10080

Solving this system of equations gives: x = 202y = 112. Therefore, the number of students that paid the regular price is 202, and the number of students that got a discount is 112.

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Answer:

a) The ratio of used books to new books is of \(\frac{9}{4}\).

b) The ratio of all books on the shelf to used books is of \(\frac{13}{9}\)

Step-by-step explanation:

Ratio of a to b:

The ratio of a to b is given by:

\(\frac{a}{b}\)

Ratio of b to a:

The ratio of b to a is given by:

\(\frac{b}{a}\)

In this question:

13 books, 9 used, 4 new.

(a) What is the ratio of used books to new books?

9 used, 4 new. So

The ratio of used books to new books is of \(\frac{9}{4}\).

(b) What is the ratio of all books on the shelf to used books?

13 books on the shelf, 9 used. So

The ratio of all books on the shelf to used books is of \(\frac{13}{9}\)

Answer: B

Step-by-step explanation:

To get no solution you need to have 2 sides of the equations that don't match. If you go through B you will end up getting 3x- (11/7)=3x-2 which is not true.

Nolan stops reading at time 2:05 am.

To calculate this,  first, calculate the amount of time elapsed since he began reading. Since he started reading at a quarter to 11, then subtract 11:45 pm (a quarter to 12) from the time he began reading, which was 11:45 pm. This gave me an elapsed time of 0 hours and 15 minutes.  then added this elapsed time to the total time Nolan read, which was 3 hours and 5 minutes. This gave us a total elapsed time of 3 hours and 20 minutes. Finally, then added this total elapsed time to the start time of 11:45 pm. This gave me the result of 2:05 am as the time Nolan stopped reading.

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Answer:

m=8/3

Step-by-step explanation:

x1    y1      x2   y2

(1, 3)         (-2, -5)

m= y2-y1/x2-x1= -5-3/-2-1= -8/-3=8/3

ml = 0 is valid so the sets of quantum numbers are validated or not validated as mentioned above.

Here are the given sets of quantum numbers for the hydrogen atom which need to be validated.

Set 1 (n=3, l=3, ml=0, ms=+1/2) - Valid or Not valid

Set 2 (n=2, l=1, ml=1, ms=-1/2) - Valid or Not valid

Set 3 (n=4, l=1, ml=0, ms=-1/2) - Valid or Not valid

The first step is to understand the set of quantum numbers. Each electron in an atom is assigned a set of four quantum numbers.

The four quantum numbers are: n, l, ml, and ms. The principal quantum number n, the angular momentum quantum number l, the magnetic quantum number ml, and the spin quantum number ms are the four quantum numbers that define the electron's state.

Set 1 (n=3, l=3, ml=0, ms=+1/2)

It is not valid because ml can be from -l to +l, and when l is 3, ml can be -3,-2,-1,0,1,2,3. So, the value of ml should be from -3 to +3.

Set 2 (n=2, l=1, ml=1, ms=-1/2)

It is valid because l = 1, so ml can be -1,0,1. Therefore, ml = 1 is valid.

Set 3 (n=4, l=1, ml=0, ms=-1/2)

It is valid because l = 1, so ml can be -1,0,1. Therefore, ml = 0 is valid.

Thus, the sets of quantum numbers are validated or not validated as mentioned above.

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The curved surface area of a cylinder with radius of 7 cm and height of 15 cm is 259.7 cm²

An equation is an expression that shows how two numbers and variables are related using mathematical operations such as addition, subtraction, exponent, division and multiplication.

The curved surface area of a cylinder is:

Curved surface area = 2π * radius * height

From the image:

Radius = 7 cm, height = 15 cm, therefore:

Curved surface area = 2π * 7 cm * 15 cm = 259.7 cm²

The curved surface area is 259.7 cm²

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to solve this first we need to find out the value of the inside function and then of the outside:

f(g(-7))

first, we need to know g(-7), and from the bottom table we can see is 21

now we replace it:

f(g(-7)) = f(21) and on the top table we see it's -3

so the answer of a is -3

and the same for the others:

b. f(g(-5))

g(-5)= 11

f(g(-5))=f(11)= 6

so b. 6

c. g(f(8)) here we need to see the top table first

f(8)=9

g(f(8))=g(9)= 8

so c. 8

d. g(f(14))

f(14)=3

g(f(14))=g(3)= 15

so d.15

Answer:

Explanation:

Quotient rule in differentiation

Answer:

\({ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ { \tt{ \sin(55 \degree) = \frac{x}{15} }} \\ x = 15 \sin(55 \degree) \\{ \boxed{ \bf{ x = 12.29 \: }}} \: feet\)

Recall that sine is the ratio of opposite over hypotenuse, so we say

sin(theta) = opposite/hypotenuse

If we have a triangle labeled as such in the diagram below, then we can use symbols to write sin(theta) = A/C

Similarly, cos(theta) = B/C since cosine is the ratio of adjacent over hypotenuse.

Then from here we use a bit of algebra to compute the left hand side of the given equation. The goal is to see if we can simplify it to 1.

\(\sin^2\left(\theta\right)+\cos^2\left(\theta\right)\\\\\left(\sin\left(\theta\right)\right)^2+\left(\cos\left(\theta\right)\right)^2\\\\\left(\frac{A}{C}\right)^2+\left(\frac{B}{C}\right)^2\\\\\frac{A^2}{C^2}+\frac{B^2}{C^2}\\\\\frac{A^2+B^2}{C^2}\\\\\frac{C^2}{C^2}\\\\1\)

So this shows that the left hand side is identically the same as the right hand side (both sides are 1), and it doesn't matter what you replace theta with. Theta can be any real number and the equation will always be true.

Note: if you're wondering how A^2+B^2 became C^2, it's because of the pythagorean theorem. So that's why this trig identity is often referred to as the pythagorean trig identity.

Using the graph of g we get (a) value of function g at x=0 is 5

(b) \(\lim_{x \to \00} g(x)\) or limit of g(x) at x=0 does not exist

(c) value of function g at x=1 is 4

(d) \(\lim_{x \to \11} g(x)\)  or  limit of g(x) at x=1 is 4

What is limit of a function how can limit be interpreted using graph of that function?

Limit : Limit is the value that a function output approaches as the input  approaches to a certain value.

For any function g(x) ,\(\lim_{x \to \22} g(x)\) means that the value g(x) approaches as the x approaches to 2 .

From any graph we can easily see that to what value g(x)=y  on the curve is approaching when the x  is approaching to some value on x axis and if the graph is breaking on the value where x is approaching then the limit does not exist for that value of x.

For given graph

We can see value of value of function g at x=0 is 5 and value of function g at x=1 is 4

As the graph is breaking on x=0 into two functions then \(\lim_{x \to \00} g(x)\) or limit of g(x) at x=0 does not exist

As the graph is not breaking at x=1 or we can say that graph of g(x)is approaching to 4 as x approaches to 1 then   \(\lim_{x \to \11} g(x)\)  or  limit of g(x) at x=1 is equal to g(1) that is  4

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When two angles sum up to 90° they are called complementary angles.

Since the sum of angle 1 and angle 2 = 90°, they will be called each other's complements.

Thus, the angle pair is called complementary angles.

▪︎Therefore, the correct option is (C) complementary

Answer:

B

Step-by-step explanation:

:)

Answer:

540

Step-by-step explanation:

This is a linear equation y=18x. I got this equation by dividing all of the y values by the x value and finding that 18 was the common answer. Then I plugged in 30 for x and solve for y.

Answer:

Explanation BELOW:

Step-by-step explanation:

To figure this out, do the following:

Take the X values and multiply them by 3, then add 2 to get your Y values.

EXAMPLE: X=3.

y=2+3x

y=3x3=9

y=9+2

y=11

The combined cost of the notebooks and the pens will be; $5.5

We have been Given that Kendall bought 6 notebooks and 3 pens for a total of $27. The cost of one notebook is $1.50 more than the cost of one pen.

The two equations can be written;

6N + 3 P = 27

n = 1.5 +P

Solve the above equations by substitution method;

6(1.5 + P) + 3P = 27

9 +6p +3p = 27

9p = 18

p (pen): $2

N (notebook): $3.5

The combined cost will be;

Cost = 2 + 3.5

Cost = $5.5

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Tangent ratios can be greater than or equal to 1 because acute angle is between 45 degrees and 90 degrees.

If the opposite side is longer than the adjacent side, then the tangent ratio will be greater than 1.

Similarly, if the opposite side is equal in length to the adjacent side, then the tangent ratio will be equal to 1.

In general, the tangent ratio can be greater than or equal to 1 when the opposite side is longer or equal in length to the adjacent side. This occurs when the acute angle is between 45 degrees and 90 degrees.

It is important to note that when the acute angle is less than 45 degrees, the tangent ratio will always be less than 1. Conversely, when the acute angle is greater than 90 degrees, the tangent ratio will be negative and less than 1.

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The graph of a proportional relationship is a line through the origin or a ray whose endpoint is the origin

3. No because it's a line that doesn't go through the origin

4. Yes because it's a line through the origin

5. Yes because 1/3 = 2/6 = 3/9 = 4/12

6. No because 4/2 isn't equal to 8/5

7. Draw a graph just like 4., but change the y-axis

8. a. Let the equation be y = ax. 27 = 3a. a = 9. Therefore the equation is y = 9x.

8. b. 9

8. c. 9 * 5 = 45

9. a. The car travels 25 (> 18) miles per gallon of gasoline.

9. b. 25 * 8 - 18 * 8 = 7 * 8 = 56