What is the second derivative of y = 3x5 - 4x4 + 2x2 + 6?

y = $$12x^4$$ - $$4x^3$$ + 2x + 2

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2.

Solve the System of Linear Equations: x + 2y = 9 3x - 4y = - 33

X = 3, y = -6
X = 3, y = 6
X = 2, y = 7
X = -3, y = 6
X = 9, y = 12

Correct Answer

A. X = -3, y = 6

Explanation

The given system of linear equations is:

x + 2y = 9
3x - 4y = -33

To solve this system, we can use the method of substitution or elimination.

Let's use the method of elimination to solve the system:

Multiply the first equation by 3 and the second equation by 1 to make the coefficients of x in both equations equal:

3(x + 2y) = 3(9)
1(3x - 4y) = 1(-33)

This simplifies to:

3x + 6y = 27
3x - 4y = -33

Now, subtract the second equation from the first equation:

(3x + 6y) - (3x - 4y) = 27 - (-33)
3x + 6y - 3x + 4y = 27 + 33
10y = 60
y = 6

Substitute the value of y back into the first equation:

x + 2(6) = 9
x + 12 = 9
x = -3

Therefore, the solution to the system of linear equations is x = -3 and y = 6.

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22

3.

Find the Equation for a line that passes through the two points (3,4) and (1,-10).

Y = 7x - 17
Y = 7x + 17
Y = x/7 - 17
Y = x/7 + 10
Y = x/7 - 10

Correct Answer

A. Y = 7x - 17

Explanation

The equation for a line passing through two points can be found using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the slope is (4 - (-10)) / (3 - 1) = 14 / 2 = 7. Plugging in the slope and one of the points into the slope-intercept form, we get y = 7x - 17.

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12

4.

Find the Exterior Angle of a heptagon

30 degrees
49 degrees
51 degrees
60 degrees
129 degrees

Correct Answer

A. 51 degrees

Explanation

The exterior angle of a regular heptagon (a polygon with 7 sides) can be calculated by dividing 360 degrees (the sum of all exterior angles in any polygon) by the number of sides, which in this case is 7. Therefore, the exterior angle of a heptagon is 360/7 = 51 degrees.

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5

5.

Triangle ABC is similar to DEF. The length of EF is 7 inches, while the length of BC is 5 inches. If the length of AB is 16 inches, what is the length of DE?

22.4 inches
23.0 inches
20.5 inches
25.3 inches
19.5 inches

Correct Answer

A. 22.4 inches

Explanation

Since triangle ABC is similar to DEF, the corresponding sides are proportional. Using the given lengths, we can set up a proportion: AB/DE = BC/EF. Plugging in the values, we have 16/DE = 5/7. Cross-multiplying gives us 7*16 = 5*DE, which simplifies to 112 = 5*DE. Dividing both sides by 5, we get DE = 112/5 = 22.4 inches.

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8

6.

Find the volume of a sphere that has a diameter of 5 meters.

8.3π meters^3
33π meters^3
166π meters^3
83.33π meters^3
6.7π meters^3

Correct Answer

A. 83.33π meters^3

Explanation

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. Given that the diameter of the sphere is 5 meters, the radius would be half of that, which is 2.5 meters. Plugging this value into the formula, we get V = (4/3)π(5/2)^3 = (4/3)π(125/8) = 83.33π meters^3. Therefore, the correct answer is 83.33π meters^3.

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12

7.

Two lines, AB and CD, intersect at point E. If angle AED is 127 degrees, what is angle BED + angle AEC?

127 degrees
26.5 degrees
53 degrees
106 degrees
Not enough information is given to solve the problem.

Correct Answer

A. 106 degrees

Explanation

Angle AED and angle BED are vertical angles, which means they are congruent. Therefore, angle BED is also 127 degrees. Angle AEC and angle BED are adjacent angles that form a straight line, so their sum is 180 degrees. Therefore, angle BED + angle AEC = 127 degrees + 53 degrees = 180 degrees.

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3

8.

Sin(π/3) can be expressed alternatively as

Sin(π/3) cos(π/6)
2 sin(π/3) cos(π/6)
2 sin(π/6) cos(π/6)
2 sin(π/6)
None of the above.

Correct Answer

A. 2 sin(π/6) cos(π/6)

Explanation

The given expression 2 sin(π/6) cos(π/6) is the correct alternative expression for sin(π/3). This is because sin(π/3) can be simplified using the double angle formula for sine: sin(2θ) = 2 sin(θ) cos(θ). In this case, θ is π/6, so sin(π/3) = 2 sin(π/6) cos(π/6). Therefore, the correct answer is 2 sin(π/6) cos(π/6).

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5

9.

Tan(π/2) is equal to

0
Sqrt(2) / 2
3 sqrt(2) / 2
1 / 2
None of the above.

Correct Answer

A. None of the above.

Explanation

The correct answer is "None of the above" because the value of tan(π/2) is undefined. In trigonometry, the tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. When the angle is π/2 (90 degrees), the adjacent side becomes zero, resulting in division by zero, which is undefined. Therefore, none of the given options accurately represent the value of tan(π/2).

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6

10.

What is the limit of the function y = 1 / (x - 4) as x approaches 4?

0
-1/4
+ infinity
- infinity
No limit

Correct Answer

A. No limit

Explanation

As x approaches 4, the denominator of the function becomes 0. When the denominator is 0, the function is undefined. Therefore, the limit of the function does not exist or there is no limit.

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9

11.

What is the slope of the tangent line of y = x³ at x = 2?

M = 4
M = 12
M = -1/12
M = 16
M = -1/16

Correct Answer

A. M = 12

Explanation

The slope of the tangent line to a curve at a specific point can be found by taking the derivative of the equation and evaluating it at that point. In this case, the derivative of y = x^3 is 3x^2. Evaluating this derivative at x = 2 gives us 3(2)^2 = 12. Therefore, the slope of the tangent line to y = x^3 at x = 2 is 12.

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2

12.

What is the second derivative of y = 3x⁵ - 4x⁴ + 2x² + 6?

Y = 20x^3 + 48x^2 + 4
Y = 60x^3 + 48x^2 - 4
Y = 12x^4 - 4x^3 + 2x + 2
Y = 15x^4 - 16x^3 + 4x
Y = 60x^3 - 48x^2 + 4

Correct Answer

A. Y = 60x^3 - 48x^2 + 4

Explanation

The second derivative of a function represents the rate of change of the derivative of that function. In this case, the given function is y = 3x^5 - 4x^4 + 2x^2 + 6. To find the second derivative, we need to take the derivative of the first derivative. The first derivative of y is y' = 15x^4 - 16x^3 + 4x. Taking the derivative of y' gives us the second derivative, which is y'' = 60x^3 - 48x^2 + 4. Therefore, the correct answer is y = 60x^3 - 48x^2 + 4.

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5

13.

What is the derivative of y = sin (2x + 5)?

Cos (2) + 5
Cos (2x + 5)
2 cos (2x + 5)
2 cos (2x) + 5
-2 cos (2x + 5)

Correct Answer

A. 2 cos (2x + 5)

Explanation

The given function is y = sin (2x + 5). To find its derivative, we can use the chain rule. The derivative of sin(u) is cos(u), and the derivative of (2x + 5) with respect to x is 2. Therefore, the derivative of y = sin (2x + 5) is 2 cos (2x + 5).

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4

14.

Integrate (x+4)².

X^3/3 + 4x^2 + 16x + c
4x^3 + 4x^2 + c
X^3 - 4x^2 + x + c
(x + 4)^2 + c
2(x + 4) + c

Correct Answer

A. X^3/3 + 4x^2 + 16x + c

Explanation

The given expression is the integral of (x+4)^2. To integrate this expression, we can use the power rule of integration. According to the power rule, the integral of x^n is (x^(n+1))/(n+1), where n is any real number except -1. Applying this rule to the given expression, we have the integral of (x+4)^2 as (x^3)/3 + 4x^2 + 16x + c, where c is the constant of integration. Therefore, the correct answer is x^3/3 + 4x^2 + 16x + c.

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4

15.

What is the value of sin⁡(2x) if sin⁡(x)=3/5 and x is in the first quadrant?

24/25
7/25
6/5
4/5

Correct Answer

A. 24/25

Are You A True Genius In High School Maths?

Factor 6x2 + 17x + 12.

Solve the System of Linear Equations: x + 2y = 9 3x - 4y = - 33

Find the Equation for a line that passes through the two points (3,4) and (1,-10).

Find the Exterior Angle of a heptagon

Triangle ABC is similar to DEF. The length of EF is 7 inches, while the length of BC is 5 inches. If the length of AB is 16 inches, what is the length of DE?

Find the volume of a sphere that has a diameter of 5 meters.

Two lines, AB and CD, intersect at point E. If angle AED is 127 degrees, what is angle BED + angle AEC?

Sin(π/3) can be expressed alternatively as

Tan(π/2) is equal to

What is the limit of the function y = 1 / (x - 4) as x approaches 4?

What is the slope of the tangent line of y = x3 at x = 2?

What is the second derivative of y = 3x5 - 4x4 + 2x2 + 6?

What is the derivative of y = sin (2x + 5)?

Integrate (x+4)2.

What is the value of sin⁡(2x) if sin⁡(x)=3/5 and x is in the first quadrant?

Factor 6x² + 17x + 12.

What is the slope of the tangent line of y = x³ at x = 2?

What is the second derivative of y = 3x⁵ - 4x⁴ + 2x² + 6?

Integrate (x+4)².