1.
What are the solutions to the equation 0 = x2-x-6?

Answer:

y=3x+7

Step-by-step explanation:

subtract 7 from 10 to get answer

To solve this, we can make a substitution. Let u = 2 − 3x^2. Then, we differentiate both sides with respect to x to find du/dx = -6x.

Solving for dx, we have dx = du / (-6x). Substituting these expressions back into the integral, we get:

∫(x^2 − 3x^2) dx = ∫(x^2 − 3x^2) (du / (-6x))

Next, we simplify the integrand:

= ∫((-2x^2 + 3x^2) du / (6x))

= ∫(x^2 du / 6x)

= (1/6) ∫(x du)

= (1/6) ∫u du

Integrating u with respect to u, we get:

= (1/6) * (u^2 / 2) + C

= (1/12) * u^2 + C

Finally, substituting back u = 2 − 3x^2, we have:

= (1/12) * (2 − 3x^2)^2 + C

= (1/12) * (4 − 12x^2 + 9x^4) + C

Simplifying further, we get the final solution:

= (1/12) * (9x^4 − 12x^2 + 4) + C

This is the integral of x^2 − 3x^2 dx in terms of x.

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a) f is positive on the intervals (-∞, 1/3) and (3, ∞).

b) f is negative on the intervals (-1, 2) and (4, ∞).

c) f is decreasing on the interval (1/3, 3) for a given polynomial function.

d) f is increasing on the intervals (-∞, -1) and (2, 4).

Polynomial functions are functions that are defined by polynomial expressions. A polynomial expression is a finite sum of terms that are each monomial expression, which means they consist of a constant coefficient multiplied by a variable raised to a non-negative integer power.

The general form of a polynomial function is:

f(x) = \(a_n\) \(x^{n\) + \(a_{n-1}\)\(x^{{n-1}}\) + ... + \(a_1 x\) + a_0

where n is a non-negative integer, \(a_n\), \(a_{n-1}\), ..., \(a_1,\) \(a_0\) are constants (called the coefficients), and x is the variable.

Using the graph of the polynomial function f(x) = -\(x^{3}\) + 5\(x^{2}\) - 2x - 8, we can complete the sentences as follows:

a) f is positive on the intervals (-∞, 1/3) and (3, ∞). This is because the graph of the function is above the x-axis on these intervals.

b) f is negative on the intervals (-1, 2) and (4, ∞). This is because the graph of the function is below the x-axis on these intervals.

c) f is decreasing on the interval (1/3, 3). This is because the graph of the function is sloping downward from left to right on this interval.

d) f is increasing on the intervals (-∞, -1) and (2, 4). This is because the graph of the function is sloping upward from left to right at these intervals.

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The formula for the area of a trapezoid is given as, a = 1/2 h (a + b) Where, a and b are the measures of two bases of the trapezoid and h is the height of the trapezoid. The area of the trapezoid is given as 24 square inches and the two bases of the trapezoid measure 4 inches and 6 inches.

We need to find the height of the trapezoid. Using the given formula, we can find the height of the trapezoid as below: 24 = 1/2 h (4 + 6)

Simplifying the above expression, we get: 24 = 5h

Hence, the height of the trapezoid is 24/5 or 4.8 inches.

Trapezoid is a quadrilateral with only one pair of parallel sides. The bases of the trapezoid are those parallel sides and the height of the trapezoid is the perpendicular distance between the two bases. In this question, the area of the trapezoid is given as 24 square inches and the two bases of the trapezoid measure 4 inches and 6 inches. We need to find the height of the trapezoid.

Simplifying the above expression, we get:24 = 5h

Hence, the height of the trapezoid is 24/5 or 4.8 inches.

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Answer:

4(x+y)

Step-by-step explanation:

x+y is one side length and there are 4 side lengths.

Answer:

       \(\huge\boxed{\sf 10x^2-13x-3}\)

Step-by-step explanation:

\(=(2x-3)(5x+1)\\\\=2x(5x+1)-3(5x+1)\\\\Distribute\\\\= 10x^2+2x-15x-3\\\\= 10x^2-13x-3\\\\\rule[225]{225}{2}\)

Answer:

B

Step-by-step explanation:

I am assuming that this ball is a perfect sphere.

The volume of a sphere is \(\frac{4}{3} *\pi *r^3\)

We have the diameter, and in order to find the radius, we just have to divide by 2. 6/2=3. Now, we have to plug in the 3 to the equation.

\(\frac{4}{3} *\pi *3^3\)

3 cubed is 27, so now we have \(\frac{4}{3} *\pi *27\)

27*4/3*pi=36pi

Answer:

−(x+11−  square root of 121+c )(x+11+ square root of 121+c)

Step-by-step explanation: hoped I helped

To find the derivative of the function f(x, y, z) = xy + xz + yz at point P(1, -2, 2) in the direction of 10i + 11j - 2k, we use the directional derivative formula. The derivative of f(x, y, z) in the given direction is 39.

The directional derivative of a function f(x, y, z) in the direction of a unit vector v = ai + bj + ck is given by the dot product of the gradient of f(x, y, z) and the unit vector v.

First, we calculate the gradient of f(x, y, z):

∇f(x, y, z) = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k = yi + xi + xj + yk + zk + yj = (y + z)i + (x + z)j + (x + y)k.

Next, we find the unit vector in the given direction:

v = 10i + 11j - 2k.

Then, we take the dot product of the gradient and the unit vector:

∇f(x, y, z) · v = ((y + z)i + (x + z)j + (x + y)k) · (10i + 11j - 2k) = (y + z)(10) + (x + z)(11) + (x + y)(-2) = 10y + 10z + 11x + 11z - 2x - 2y.

Finally, we substitute the values of x, y, and z from point P(1, -2, 2):

∇f(1, -2, 2) · v = 10(-2) + 10(2) + 11(1) + 11(2) - 2(1) - 2(-2) = 39.

Therefore, the derivative of f(x, y, z) at point P(1, -2, 2) in the direction of 10i + 11j - 2k is 39.

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The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

Answer:

Step-by-step explanation:

That would be Tobey Maguire an American Actor best known from Spider Man. Recently made a comeback in no way home.

Answer:

Toby Miguire that is!

Step-by-step explanation:

Answer:

your answer would be -18

The period of the function f(x) = cos(2.22x+0.19) is 2.8323 and the period of the function f(x) = sin(1.05x)  is 5.9834

The period of a trigonometric function, we use the formula:
Period = 2π/|B|
where B is the coefficient of x in the function.

For the first function, f(x) = cos(2.22x+0.19), the coefficient of x is 2.22. Therefore, the period is:
Period = 2π/|2.22| ≈ 2.8323

For the second function, f(x) = sin(1.05x), the coefficient of x is 1.05. Therefore, the period is:
Period = 2π/|1.05| ≈ 5.9834

So, the period of the first function is 2.83 and the period of the second function is 5.98. Both answers are rounded to four decimal places.

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Answer:

\(x=2\\y=-3\)

Step-by-step explanation:

We have:

\(-9x-10y=12\\-3x+3=y\)

Since we already have a variable value (\(y\)) in the second equation, it would be easiest to substitute the value for \(y\) in the first equation:

\(-9x-10(-3x+3)=12\)

Distribute \(-10\) into \((-3x+3)\):

\(-9x+30x-30=12\)

Combine like terms:

\(21x-30=12\)

Add \(30\) to both sides of the equation:

\(21x=42\)

Divide by the coefficient of \(x\), which is \(21\):

\(x=2\)

_

Now that we have our \(x\) value, we can substitute that in to the second equation to find our \(y\) value:

\(-3(2)+3=y\)

Multiply:

\(-6+3=y\)

Combine like terms:

\(-3=y\)

Answer: The correct answers are B, D, and F.

Step-by-step explanation: B is correct because 8 x 5 is 40, and 40-5 is less than or equal to 36. C is correct because if you plug in 41/8, the answer is 36. Anything higher than 41/8 is greater than 36.  F is correct because 5 is a solution and 5 is less than 41/8. Therefore, the correct answers are B, D, and F.

The standard form of the given numbers is 207360 × 10¹⁷.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given the numbers is  (5 x 1,000,000) (6 x 100,000) (4 x 10,000) (8 x 1,000) (3 x 100) (2 x 10) (4 x 0.1) (9 x 0.001)

Now standard form means we need to write the exponents form.

So,

5 x 6 x 4 x 8 x 3 x 2 x 4 x 9 = 207360

And

1,000,000 x  100000 x 10000 x 1000 x 100 x 10 x 0.1 x 0.001 = 10¹⁷

So, combine 207360 x  10¹⁷

Hence "The standard form of the given numbers is 207360 × 10¹⁷".

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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9514 1404 393

Answer:

  16.4

Step-by-step explanation:

The law of cosines is useful here. It tells you ...

  b^2 = a^2 + c^2 -2ac·cos(B)

  b^2 = 22^2 +10^2 -2·22·10·cos(44°)

  b^2 ≈ 267.49

  b ≈ √267.49 ≈ 16.35514

  b ≈ 16.4

Answer:

thx for points

Answer:

A= 12

B = -4

Step-by-step explanation:

( -3,0) & (0,9) should satisfy the equation Ax + By = -36

when ( -3,0)

-3A+ 0 = -36

A = 12

when (0,9)

0 + 9B = -36

B = -4

The value of A and B is 12 and -4.

Given that,

Based on the above information, the calculation is as follows:

Ax + By = -36

When (-3,0)

So,

-3A+ 0 = -36

A = 12

Now  

when (0,9)

So,  

0 + 9B = -36

B = -4

Therefore we can conclude that the value of A and B is 12 and -4.

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The perimeter of the region swept out by the circle during translation is 2π units.

When a circle is translated, its shape remains the same, but its position in space changes. The perimeter of the region swept out by the circle during translation will be the same as the perimeter of the circle itself.

Given:

Diameter of the circle = 2 units

Translation distance = 5 units

Calculate the radius of the circle.

Radius (r) = Diameter / 2

r = 2 / 2

r = 1 unit

Calculate the perimeter of the circle.

Perimeter of a circle (P) = 2 x π x r

P = 2 x π x 1

P = 2π units

Therefore, the perimeter of the region swept out by the circle during translation is 2π units.

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Answer:

1. 6   2. 8  3. 4     4.40 5 . 4                                                                                                 Step-by-step explanation:

Answer:

Step-by-step explanation:

7

3 = 7 - 4

-1 = 3 - 4

-5 = -1 - 4

so the 5th:  -5 - 4 = -9

     the 6th:   -9 - 4 = -13

and the 7th:   -13 - 4 = -17

the outlier may also affect the median, as the median value corresponds to the midpoint of the data set.

An outlier is an observation that differs significantly from other observations in a data set. The range of a data set measures the difference between the highest and lowest values in the set. When an outlier is included as the minimum value of the data set, the range of the data set increases due to the large difference between the outlier and the other data points. Therefore, the outlier had the most effect on the range of the data set.

The outlier had an impact on other measures of variability as well. For example, the inclusion of the outlier may increase the variance of the data set. This is because the outlier increases the difference between all the observations and the mean, thus increasing the variability of the data set. The outlier also affects the interquartile range, as it increases the difference between the upper and lower quartiles. In addition, the outlier may also affect the median, as the median value corresponds to the midpoint of the data set.

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Step-by-step explanation:

1. Amplitude = 1.  g(x) = 1 sin(6x).  The coefficient 1 is the amplitude.  The range of the function is \(-1 \le g(x) \le 1\)  or, in interval notation, [-1, 1]

2. The period is  \(\frac{2\pi}{6}=\frac{\pi}{3}\).

x-intercepts (at the beginning, middle, and end of the period) \(0,\,\frac{\pi}{6},\,\frac{\pi}{3}\)

Maximum (1/4 of way through period)  \(\left(\frac{\pi}{12},\,1 \right)\)

Minimum (3/4 of way through period)  \(\left( \frac{\pi}{4}, \, -1 \right)\)

Answer: Balloon is 27.5 ft high.

Step-by-step explanation:

As per the give , we made a diagram (in attachment).

To find the vertical distance from the growth we consider entire triangle as right triangle , where height is making right angle with ground.

in right triangle,

\(\sin \theta=\dfrac{Hypoteuse}{height}\\\\\Rightarrow\ \sin 79^{\circ}=\dfrac{28}{height}\\\\\Rightarrow\ 0.98162718344=\dfrac{28}{height}\\\\\Rightarrow\ height = 0.98162718344\times28\\\\\Rightarrow\ height = 0.98162718344\times28\approx27.5\)

hence, balloon is 27.5 ft high.

Answer:

6 litres

Step-by-step explanation:

.80 * 6 = 4.80

Mark can buy 6 litres of milk for 80p per.

leaving 20p left, of his £5

hope this helps:)

Answer:

this is simple math.

Step-by-step explanation:

easy, mark does have a 5 dollar note, and a litre of milk that costs 80p

he can buy as many as he can, so he buys around;

mark buys over; you divide. By dividing this answer you will get your result. I apologize if this answer didn't help out.

Answer: h+8

Step-by-step explanation:

It’s simple h MORE than 8

Answer: h+8

Step-by-step explanation: