Find the coefficient! Answer the following questions with the assistance of the Binomial Theorem
(Theorem 17.8):
a. What is the coefficient of .x 3 in (1 + .x 6?
b. What is the coefficient of .x 3 in (2.x - 3 6 ?
"c. What is the coefficient of .x 3 in (x + 1 20 + (.""\: - I )20 ?"
e. What is the coefficient of .x 3 y 3 in (.x + 1?

The graph of the system of equations is shown below:

The solution of the system is given by the point of intersection of the two lines which is (20/7, -7/2).

The velocity vector and position vector and position vector at t=4 is r(4) = (e₄+2)i+36j - 44k.

a(t) = eti - 6k

Since we know that v(t) = ∫ a(t) dt

= ∫ (eti - 6k) dt

= ∫6ti-6tk+c

where c is the arbitrary vector valued constant

since it is given that

v(0) = 2i + 9j + k

therefore from above

v(0) = e * 0i - 6(0) * k + c

2i + 9j + k =i+c

C= i +9j+k

therefore,

v(t) = eti - 6tk + i + 9j + k

= (et + 1) * i + 9j + (- 6t + 1) * k

Since we know that velocity vector can be found by integration of acceleration vector.

Since, v(t) = (et + 1) * i + 9j + (- 6t + 1) * k

and we know that

R(t) = ∫ v(t)dt

= ∫ of [(a + 1)i + 9j+(-6t + 1)k]dt =(a+t)i+9tj+(-3ta+t)k+C

where C is an arbitrary vector constant.

Now,

Since it given that r(0)=0 therefore

r(0) =(e0+1)+9(0)j)+(-3(0)2+0)x+C

0=2i+ C

C= -2i

therefore

r(t)= (et+t)i+9tj+(-3t+t)k-2i

r(t)=(a+t-2)1+9tj+(-3t+t)k

Since we know that position vector can be found by integration of velocity vector

r(4) = (e4+4-2)i+9(4)j + (-3(4)+4)k

r(4) = (e4+2)1+36j-44k

Now we have found the velocity vector and position vector and position vector at t=4 which are as follows:

v(t) =(et+1)i+9j+(-6t+1)k

r(t) =(et+t-2)i+9tj+(-3t2+t)k

r(4) = (e₄+2)i+36j - 44k

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it is false. 0 is not a natural number. it is a whole number

we can see, the function f(x) = 3x - 5 produces the desired range for the given domain.

The range of numbers that can be plugged into a function is known as its domain. The x values for a function like f make up this collection.(x). A function's range is the collection of values it can take as input. After we enter an x number, the function outputs this set of values.

The function that produces the range of {−11,−5,1,7,13} given a domain of {−2,0,2,4,6} is:

f(x) = 3x - 5

To see why, we can plug in each value from the domain into the equation and see if it produces the corresponding value in the range:

f(-2) = 3(-2) - 5 = -11

f(0) = 3(0) - 5 = -5

f(2) = 3(2) - 5 = 1

f(4) = 3(4) - 5 = 7

f(6) = 3(6) - 5 = 13

As we can see, the function f(x) = 3x - 5 produces the desired range for the given domain.

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Answer:

1.11

2.4

3.5

pls correct me if I'm wrong

Answer:

38. (b) 11

39. (c) 4

40. (c) 5

Step-by-step explanation:

38.)

[tex]\implies \: \sf \sqrt{3xx - 8} = 5 \\ \\ \implies \: \sf 3xx - 8 = {(5)}^{2} \\ \\ \implies \: \sf 3xx - 8 = 25 \\ \\ \implies \: \sf 3xx = 25 + 8 \\ \\ \implies \: \sf 3xx = 33 \\ \\ \implies \: \sf xx = \dfrac{33}{3} \\ \\ \implies \: \sf xx = 11\\ [/tex]

Hence, Required answer is option (b) 11.

39.)

[tex]\implies \: \sf \sqrt{4xx -7 } - 3 = 0 \\ \\ \implies \: \sf \sqrt{4xx - 7} = 3 \\ \\ \implies \: \sf 4xx - 7 = {(3)}^{2} \\ \\ \implies \: \sf 4xx - 7 = 9 \\ \\ \implies \: \sf 4xx = 9 + 7 \\ \\ \implies \: \sf 4xx = 16 \\ \\ \implies \: \sf xx = \dfrac{16}{4} \\ \\ \implies \: \sf xx = 4 \\ [/tex]

Hence, Required answer is option (c) 4.

40.)

[tex]\implies \: \sf \sqrt{6xx + 6} - 6 = 0 \\ \\ \implies \: \sf \sqrt{6xx + 6} = 6 \\ \\ \implies \: \sf 6xx + 6 = {(6)}^{2} \\ \\ \implies \: \sf 6xx + 6 = 36 \\ \\ \implies \: \sf 6xx = 36 - 6 \\ \\ \implies \: \sf 6xx = 30 \\ \\ \implies \: \sf xx = \dfrac{30}{6} \\ \\ \implies \: \sf xx = 5 \\ [/tex]

Hence, Required answer is option (c) 5.

Answer:

m = 2/3

Step-by-step explanation:

Answer:

[tex] \frac{2}{3} [/tex]

Step-by-step explanation:

slope is

[tex] m = \frac{rise}{run} = \frac{y 2 - y1}{x2 - x1} [/tex]

(0,0) & (3,2)

[tex] m = \frac{2 - 0}{3 - 0} = \frac{2}{3} [/tex]

The set is a basis of the space of upper-triangular matrices. The coordinates of with respect to this basis is B⁻¹ × p

In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients that includes only the operations of addition, subtraction, multiplication, and power of variables with a positive integer. Polynomials appear in many areas of mathematics and science. For example, they are used to create polynomial equations that encode a wide variety of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions that appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial circles and algebraic varieties, which are central concepts in algebra and algebraic geometry.

According to the Question:

Converting the polynomials into vectors by taking their coordinate vectors with respect to the standard basis of P³, {1, x, x²}.

Thus B = [-1, 0, -2], [-2, 3, -4], [-2, 9, -8].

And p is [-6, 21, -24].

⇒ [p(x)]B = B⁻¹ × p

Complete Question:

the set B = [tex]\left[\begin{array}{ccc}1&1&\\0&0\end{array}\right][/tex], [tex]\left[\begin{array}{ccc}0&1\\0&-1\end{array}\right][/tex], [tex]\left[\begin{array}{ccc}0&0&\\0&-2\end{array}\right][/tex] is a basis of the space of upper triangular 2 × 2 matrices . Find the coordinates of

M =  [tex]\left[\begin{array}{ccc}-6&-3&\\0&-5&\end{array}\right][/tex] with the respect to this basis.

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The correct answer is:

The equation is [tex]7(c-0.75) = 2.80[/tex], and the regular price of a cookie is [tex]c =\$1.15[/tex].

Explanation:

c is the regular price of a cookie. We know that today they are $0.75 less than the normal price; this is given by the expression [tex]c-0.75[/tex].

We also know if we buy 7 of them, the total is $2.80. This means we multiply our expression, [tex]c-0.75[/tex], by 7 and set it equal to $2.80:

[tex]7(c-0.75) = 2.80[/tex]

To solve, first use the distributive property:

[tex]7 \times c-7\times0.75 = 2.80[/tex]

[tex]7c-5.25 = 2.80[/tex]

Add 5.25 to each side:

[tex]7c-5.25+5.25 = 2.80+5.25[/tex]

[tex]7c = 8.05[/tex]

Divide each side by 7:

[tex]7c\div7 = 8.05\div7[/tex]

[tex]c = \$1.15[/tex].

Answer:

x=12

Step-by-step explanation:

2x-y=15

y=9

2x-9=15

2x=24

x=12

Answer:

21 years old

Step-by-step explanation:

Set Alan's age as x, Bernice's age as y

2x=y

x-4+y-4=55

x+y=63

3y=63

x=21

y=42

Accοrding tο the data, the answers tο Questiοns 1 and 2 are: Harris shοuld anticipate spinning a sum οr less 10 apprοximately 367 times and a tοtal that is 10 οr larger apprοximately 133 times.

Yοur example is an equatiοn since an equatiοn that's any statement with an equal's sign. The usage οf equatiοns in mathematical expressiοns is widespread because mathematicians adοre equal signs. An equatiοn is a cοllectiοn οf guidelines fοr prοducing a specific οutcοme.

Part A: Tο calculate the likelihοοd that Harris will spinning a sum οr less 10, multiply the οverall number οf spins by the chance οf οbtaining a sum οr less 10. The οutcοmes οf the first spinner's spin are 1, 2, and 3, while the results οf the secοnd spinner's spin are 4, 5, 6, 7, and 8. Hence, the amοunts οr less 10 are:

1 + 4 = 5

1 + 5 = 6

1 + 6 = 7

1 + 7 = 8

1 + 8 = 9

2 + 4 = 6

2 + 5 = 7

2 + 6 = 8

2 + 7 = 9

3 + 4 = 7

3 + 5 = 8

3 + 6 = 9

There are 11 amοunts that cοuld be less than ten. The number οf successful results divided by the entire number οf pοssibilities, which is 11/15, represents the likelihοοd οf receiving a payοut οf less than 10 in a single spin. Harris will therefοre spin a tοtal less than 10 times, and the equatiοn tο estimate this is:

11/15 = x/500

After finding x, we οbtain:

x = (11/15) x 500

x = 366.67, which rοunds up tο 367

Sο, Harris shοuld expect tο spin a sum less than 10 abοut 367 times.

Part B: Tο determine hοw frequently Harris shοuld anticipate spinning a sum οf ten οr mοre, we can deduct the times that he shοuld anticipate spinning a sum lοwer than ten frοm the οverall number οf spins:

500 - 367 = 133

Therefοre, Harris shοuld expect tο spin a sum that is 10 οr greater abοut 133 times.

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Answer:

hope it helps

Step-by-step explanation:

based on the given condition formulate

Answer:8

Step-by-step explanation:8x1=8

If cotθ = 3/4 then cosθ = -3/5 is the right option according to the rules of trigonometry.

Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It is primarily concerned with the study of the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent, and their applications in various fields such as engineering, physics, and navigation.

A triangle is a three-sided polygon, and its angles are the angles formed by the intersection of its sides. The sum of the angles in a triangle is always 180 degrees.

First, we know that cot(0) = adjacent / opposite = 3/4.

In quadrant 3, the adjacent side is negative and the opposite side is positive, so we can draw a right triangle in quadrant 3 with adjacent side -3 and opposite side 4.

The hypotenuse can be found using the Pythagorean theorem.

h² = adjacent²+ opposite²

h² = (-3)^2 + 4^2

h²= 9 + 16

h² = 25

h = 5

So we have a right triangle in quadrant 3 with adjacent side -3, opposite side 4, and hypotenuse 5.

Using the definitions of the trigonometric functions, we can find the values of the other functions:

sin(0) = opposite / hypotenuse = 4/5

cos(0) = adjacent / hypotenuse = -3/5

tan(0) = opposite / adjacent = -4/3

csc(0) = hypotenuse / opposite = 5/4

sec(0) = hypotenuse / adjacent = -5/3

cot(0) = adjacent / opposite = 3/4 (given)

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The transversal angle of 45 is angle6.

Two lines intersect at a location, creating an angle.

An "angle" is the term used to describe the width of the "opening" between these two rays. The character is used to represent it.

Angles are frequently expressed in degrees and radians, a unit of circularity or rotation.

In geometry, an angle is created by joining two rays at their ends. These rays are referred to as the angle's sides or arms.

An angle has two primary components: the arms and the vertex. T

he two rays' shared vertex serves as their common terminal.

Hence, The transversal angle of 45 is angle6.

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Answer: MN || VT

Step-by-step explanation:

We can see that MN is vertical, and the only angle that is vertical, is VT. And we can see that they don't obstruct their lines (meaning that they don't intersect), and keep going for infinity. So, VT would be the only parallel line to the one given.

Hope this helps

Answer:

680 ways

Step-by-step explanation:

C(17, 3) gives 17! / (14! 3!), or (17*16*15)/6 = 680 ways to select the 3 individuals.

Hope this helped!

find the velocity function from the derivative of s

v=s'=-32t+vo

set that equal to 64, solve for time t.

In your average velocity, you should have had a negative distance, which would have made a negative velocity (meaning downward). see the original equation for the negative sign.

Mark me brainiest!

Answer: Consider the expression (2x − 3) − (-3x + 4).

First, distribute the negative sign and rewrite the expression:

2x − 3 + 3x – 4.

Then, model the polynomial.

There are no zero pairs, so the difference is 5x − 7.

Step-by-step explanation:

PLATO

The bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.

Trigοnοmetry is οne οf the mοst impοrtant branches in mathematics that finds huge applicatiοn in diverse fields. The branch called “Trigοnοmetry” basically deals with the study οf the relatiοnship between the sides and angles οf the right-angle triangle.

Hence, it helps tο find the missing οr unknοwn angles οr sides οf a right triangle using the trigοnοmetric fοrmulas, functiοns οr trigοnοmetric identities. In trigοnοmetry, the angles can be either measured in degrees οr radians. Sοme οf the mοst cοmmοnly used trigοnοmetric angles fοr calculatiοns are 0°, 30°, 45°, 60° and 90°.

We can use trigοnοmetry tο sοlve fοr the hοrizοntal distance. Let x be the hοrizοntal distance frοm the bοat tο the lighthοuse.

Then, tan(5°) = οppοsite/adjacent = 139/x

Sοlving fοr x, we get:

x = 139/tan(5°) ≈ 1592.53 feet

Therefοre, the bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.

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The marginal probability function E(Y1) = 2/3, variance of a binomial distribution is V(Y1) = 4/9, and E(Y1-Y2) = 0, using the joint probability function for Y1 and Y2 and the fact that they have binomial distributions with n=2 and p=1/3.

The marginal probability function of Y1 is binomial with n=2 and p=1/3, as given in Exercise 5.19. Therefore, we have:

E(Y1) = np = 2(1/3) = 2/3.

The variance of a binomial distribution with parameters n and p is given by np(1-p), so we have:

V(Y1) = np(1-p) = 2(1/3)(2/3) = 4/9.

We can use the linearity of expectation to find E(Y1-Y2):

E(Y1 - Y2) = E(Y1) - E(Y2)

We know that E(Y1) = 2/3 from part (a), but we need to find E(Y2). Using the same reasoning as in part (a), we find that the marginal probability function of Y2 is also binomial with n=2 and p=1/3. Therefore, we have:

E(Y2) = np = 2(1/3) = 2/3.

Substituting these values into the expression for E(Y1-Y2), we get:

E(Y1 - Y2) = 2/3 - 2/3 = 0.

Therefore, E(Y1-Y2) is equal to 0.

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As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

A circle is a closed object made up of all points in a plane that are separated from the center by a predetermined distance, known as the radius. The diameter is the distance across the circle that passes through its center, while the circumference is the distance around the circle. The ratio of a circle's circumference to its diameter is always pi (), or roughly 3.14. Pi is also known as the proportionality constant. Circles are significant geometric forms that are used frequently in mathematics, science, and daily life.

given

AC and BC are both the circle's radii since A and B are points of tangency. Hence, AC = BC = 5.

We can apply the Pythagorean theorem to segment AB as follows:

[tex]AB^2 = 52 + 52 \\AB^2 = AC^2 + BC^2[/tex]

AB² = 50

AB = √50 = 5√2

As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

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The number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E is 3600.

The word PROBLEM has 7 letters, which can be arranged in 7! (factorial) ways, i.e. [tex]7*6*5*4*3*2*1 = 5040.[/tex]

Now to calculate the number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E, we can first calculate the number of words which start with O or end with E.

For words starting with O, there are 6 letters left and these can be arranged in 6! ways, i.e.[tex]6*5*4*3*2*1 = 720.[/tex]

For words ending with E, there are again 6 letters left and these can be arranged in 6! ways, i.e. [tex]6*5*4*3*2*1 = 720[/tex].

Now the total number of words which start with O or end with E will be the sum of two, i.e. 720 + 720 = 1440.

Therefore, the number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E will be the total number of words minus the total number of words which start with O or end with E, i.e. 5040 - 1440 = 3600.

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To determine whether a transformation is one-to-one or onto, one must analyze its behavior and properties, such as passing the horizontal line test for one-to-one or checking if the range equals the codomain for onto.

In mathematical terms, a transformation refers to a function that maps elements from one set, called the domain, to another set, called the range. A transformation is said to be one-to-one if no two distinct elements in the domain are mapped to the same element in the range. This means that each element in the range is associated with a unique element in the domain.

On the other hand, a transformation is onto if every element in the range is mapped to by at least one element in the domain. In other words, for each element in the range, there exists at least one element in the domain that maps to it.

To determine whether a transformation is one-to-one or onto, one can analyze its properties and behavior. For example, a transformation is one-to-one if and only if it passes the horizontal line test. This means that no two points in the domain map to the same point on a horizontal line. To determine if a transformation is onto, one can check if the range of the transformation equals the codomain.

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The given question is incomplete, the complete question is:

How to determine the transformation is one to one and/or onto?

The area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6 is 1/10( ln(4) - 1/10 ln(t+8))

To find the area under the curve y = 1/ (x^2 + 6x -16) from x = t to x = 6, where t > 2, we need to evaluate the definite integral:

∫[t,6] 1/ (x^2 + 6x -16) dx

To solve this integral, we can use partial fraction decomposition. First, we factor the denominator:

x^2 + 6x -16 = (x+8)(x-2)

Then, we can write:

1/ (x^2 + 6x -16) = A/(x+8) + B/(x-2)

Multiplying both sides by (x+8)(x-2), we get:

1 = A(x-2) + B(x+8)

Setting x = -8, we get:

1 = A(-10)

So, A = -1/10.

Setting x = 2, we get:

1 = B(10)

So, B = 1/10.

Therefore, we can write:

1/ (x^2 + 6x -16) = -1/10(x+8) + 1/10(x-2)

Substituting this into the integral, we get:

∫[t,6] 1/ (x^2 + 6x -16) dx = ∫[t,6] (-1/10(x+8) + 1/10(x-2)) dx

Integrating, we get:

= [-1/10 ln|x+8| + 1/10 ln|x-2|] from t to 6

= 1/10 ln|6-2| - 1/10 ln|t+8|

= 1/10 ln(4) - 1/10 ln(t+8)

Therefore, the area is: 1/10( ln(4) - 1/10 ln(t+8))

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_____The given question is incomplete, the complete question is given below:

begin by finding the area under the curve from to y = 1/ (x^2 + 6x -16) from x = t to x = 6, t>2 this area can be written as the definite integral

a) Drawing of the situation is shown in below figure.

b) 0.75 radians

c) 42.97 degrees

Conversion is the process of changing a value from one unit or system of measurement to another.

a) The situation of the drawing: The center of the Ferris wheel is labeled "O", and its radius is 59 feet. Angela boards the Ferris wheel at point A and travels a distance of 44.3 feet along the arc to point B. The angle that she sweeps out along the arc is labeled θ.

(Drawing of the situation is shown in below figure)

b) The length of an arc of a circle by the formula:  s = rθ

Given, the radius of the circle is 59 feet and the length of the arc that Angela travels is 44.3 feet. So,

θ = s / r

θ = 44.3 / 59

θ ≈ 0.75 radians

Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 0.75 radians.

c) To convert radians to degrees, we use the formula:

θ (in degrees) = θ (in radians) × 180 / π

θ (in degrees) = 0.75 × 180 / π

θ (in degrees) ≈ 42.97 degrees

Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 42.97 degrees.

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a) Drawing of the situation is shown in below figure.
b) 0.75 radians
c) 42.97 degrees

Conversion is the process of changing a value from one unit or system of measurement to another.

a) The situation of the drawing: The center of the Ferris wheel is labeled "O", and its radius is 59 feet. Angela boards the Ferris wheel at point A and travels a distance of 44.3 feet along the arc to point B. The angle that she sweeps out along the arc is labeled θ.
(Drawing of the situation is shown in below figure)
b) The length of an arc of a circle by the formula:  s = rθ
Given, the radius of the circle is 59 feet and the length of the arc that Angela travels is 44.3 feet. So,
θ = s / r
θ = 44.3 / 59
θ ≈ 0.75 radians
Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 0.75 radians.
c) To convert radians to degrees, we use the formula:
θ (in degrees) = θ (in radians) × 180 / π
θ (in degrees) = 0.75 × 180 / π
θ (in degrees) ≈ 42.97 degrees
Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 42.97 degrees.

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The values are [tex]\lim_{x \to {\(-2}^{-}[/tex] [tex]f(x) = \frac{1}{h}[/tex]

[tex]\lim_{x \to {\(-2}^{+}[/tex] [tex]f(x) = 3[/tex] and [tex]\lim_{x \to {\(2}[/tex] [tex]f(x) =[/tex] 3

The concept of limits is used to describe the behavior of a function as its input approaches a certain value.

[tex]\lim_{x \to {\(-2}^{-}[/tex] [tex]f(x) = \lim_{h \to \o[/tex] [tex]f(-2-h)[/tex] = [tex]\lim_{h \to \o[/tex] [tex]\frac{1}{(-2-h)+2}[/tex]

[tex]\lim_{h \to \o[/tex]  [tex]\frac{1}{h}[/tex]  

(So, Does not exist)

[tex]\lim_{x \to {\(-2}^{+}[/tex] [tex]f(x)[/tex] = [tex]\lim_{h \to \o[/tex] [tex]f(-2+h)[/tex]

[tex]\lim_{h \to \o[/tex] [tex]3(-2+h)+9[/tex] = 3

(So, Does not exist)

[tex]\lim_{x \to {\(-2}[/tex] [tex]f(x)[/tex] = 3×(-2) +9 = -6+9= 3

(So, Does not exist)

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The answer is A, rhombus.