If a function is always positive, then what must be true about its derivative? (a) the derivative is increasing (b) the derivative is decreasing (c) the derivative is always positive (d) the derivative is never negative (e) you can't conclude anything about the derivative

Answers

Answer 1

Consider the function [tex]f(x)=x^2+1[/tex], which is always positive. The derivative is

[tex]f'(x)=2x[/tex]

which is negative for [tex]x<0[/tex] and positive for [tex]x>0[/tex]. This example alone tells you that you can't generally describe the sign of the derivative of a strictly positive function, so the answer is E.

Answer 2

Final answer:

Though a function is always positive, it doesn't provide specific information about its derivative. The derivative can be positive, negative, or zero, depending on whether the function is increasing, decreasing, or constant. Hence, we can't definitively conclude anything about the derivative if we only know the function is always positive.

Explanation:

If a function is always positive, it means that its graph lies entirely above the x-axis. However, this fact provides no definitive information about the derivative of the function.

The derivative of a function tells us the rate at which the function is changing. It can be positive, negative, or zero, depending on whether the function is increasing, decreasing, or constant, respectively. However, for a function to be always positive, does not necessarily dictate whether it is constantly increasing, decreasing, or constant.

For instance, consider the function y = x2. This function is always positive for x ≥ 0, but its derivative, which is 2x, is not always positive. It is zero when x = 0 and positive for x > 0. Similarly, think of an undulating curve-like sine function which stays above the x-axis. Its derivative oscillates between positive and negative as the function goes through its crest and trough points.

Therefore, the answer to your question is (e) you can't conclude anything about the derivative just because the function is positive.

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Related Questions

The area of the parallelogram is 65 square miles. Find its base and height.

Answers

(base 13) (height 5)

(base 5) (height 13)

Area of parallelogram = base × height

Base = 13
Height = 5

Or:

Base = 5
Height = 13

Hope this helped☺☺

hello can you please help me posted picture of question

Answers

Total number of people = 10

Number of women = 6

Probability of selecting 1st women = 6/10
Probability of selecting 2nd women = 5/9
Probability of selecting 3rd women = 4/8

Probability that are 3 selected candidates are women = 6/10 x 5/9 x 4/8 = 1/6

So, the correct answer is option A

what is the solution to the equation 3sqrt(5x-4)=3sqrt(7x+8)

Answers

x = -6

However this is an extraneous solution since it would make the number under the sqrt a negative number.

Answer:

The answer is: 'no solution'

Step-by-step explanation:

The given equation is: [tex]3\sqrt{5x-4}=3\sqrt{7x+8}[/tex]

Dividing both sides of the equation by 3, we will get.....

[tex]\sqrt{5x-4}=\sqrt{7x+8}[/tex]

Taking square on both sides.....

[tex](\sqrt{5x-4})^2=(\sqrt{7x+8})^2\\ \\ 5x-4=7x+8\\ \\ 5x-7x=8+4\\ \\ -2x=12\\ \\ x=\frac{12}{-2}=-6[/tex]

Plugging this [tex]x=-6[/tex] back to the given equation......

[tex]3\sqrt{5(-6)-4}=3\sqrt{7(-6)+8}\\ \\ 3\sqrt{-34}=3\sqrt{-34}[/tex]

As we are getting a negative number inside the square root, so the equation becomes imaginary. Thus [tex]x=-6[/tex] is a restricted value.

Hence, there is 'no solution' for this equation.

What is the value of x in the equation –6 + x = –2?
8
4
–4
–8

Answers

the answer is 4.... -6+4=-2

a cube with side length s has a volume of 216 cubic centimeters. the equation s^3 = 216 shows the volume of a cube. what is the side length of the cube in centimeters

Answers

I would say 44 is the answer

s³ = 216 ⇒ s = ∛( 216 )

So you just need to take cubic root of 216.

Since 6³ = 216, then ∛( 216 ) = 6

So the side length of the cube would be 6 cm.

Hope this helps.

I suck at math lol. Could someone give me the answers in detail? Picture attached! Thanks

Answers

11] Volume of cylinder is given by:
Volume=πr²h
r=1.7m, h=15 m
plugging in the values in our formula we get:
V=π(1.7)²×15
V=43.35π

Answer: 43.35π m³

12]
Volume of the oblique cylinder will be:
V=πr²h
r=4 in, h=8
thus
V=π×4²×8
V=128π in²

Answer: 128π in²

N a class, 20% of the students are male and 80% female. among male students, 40% wears eyeglasses; among female students, 30% wear eye glasses. if we select a student from the class at random, what is the probability that the student wears eyeglasses

Answers

[tex]|\Omega|=100\%=1\\ |A|=40\%\cdot20\%+30\%\cdot80\%=0.4\cdot0.2+0.3\cdot0.8=0.08+0.24=0.32\\\\ P(A)=\dfrac{0.32}{1}=0.32=32\%[/tex]

2.
Find the annual percentage rate, using the annual percentage rate table.
Amount Financed: $8,900

Finance Charge: $1,030.62

Number of Payments: 24

Answers

Amount Financed: $8,900
Finance Charge: $1,030.62
Number of Payments: 24

(Finance Charge)/(Amount Financed)*100$=($1,030.62)/($8,900)*100$
(Finance Charge)/(Amount Financed)*100$=(0.1158)*100$
(Finance Charge)/(Amount Financed)*100$=$11.58

In the row of number of Payments 24, we look for:
(Finance Charge)/(Amount Financed)*100$=$11.58, and we to which annual porcentage rate it corresponds in the first row

Answer: The annual percentage rate is 10.75%

Someone please help.

Answers

In the given geometric series, each next term is obtained by multiplying the previous term by a fixed number known as common ratio.

In this case the common ratio is -3.

As,

- 3.49 x -3 = 10.47
10.47 x - 3 = -31.41
and so on...

So, the next number of the series will be:

94.23 x - 3= -282.69

Thus, the answer to this question is - 282.69

Can anyone find the Surface Area of E?

Answers

The surface area is 26 units squared. I simply counted the number of sides!

Q9 Q3.) Solve the matrix equation 4X + 5A = B

Answers

Hi there!

See pictures below for the answer! My handwriting isn't that good. Let me know if you can't read it :)

solve the system using substitution method
3x+y=6
2x-4y=10

Answers

[tex]\left\{\begin{array}{ccc}3x+y=6&|-3x\\2x-4y=10\end{array}\right\\\\\left\{\begin{array}{ccc}y=6-3x\\2x-4y=10\end{array}\right\\\\substitute\ y=6-3x\ to\ the\ second\ equation\\\\2x-4(6-3x)=10\\\\2x-4\cdot6-4\cdot(-3x)=10\\\\2x-24+12x=10\\\\14x-24=10\ \ \ |+24\\\\14x=34\ \ \ \ |:14\\\\x=\dfrac{34}{14}\to x=\dfrac{17}{7}\\\\substitute\ the\ value\ of\ x\ to\ first\ equation\\\\y=6-3\cdot\dfrac{17}{7}=6-\dfrac{51}{7}=\dfrac{42}{7}-\dfrac{51}{7}=-\dfrac{9}{7}[/tex]

[tex]\boxed{\left\{\begin{array}{ccc}x=\dfrac{17}{7}\\\\y=-\dfrac{9}{7}\end{array}\right}[/tex]

[tex]\begin{cases}&3x + y = 6 \\&2x - 4y = 10\end{cases}[/tex]

Multiply 4 to the first equation:
[tex]\begin{cases}&12x + 4y = 24 \\&2x - 4y = 10\end{cases}[/tex]

ADD Equation 1 to Equation 2 and find x:
[tex]\begin{aligned}&14x =34 \\&x= 34/14 \\& x = 17/7\end{aligned} [/tex]

Substitute x = 17/7 and find y:
[tex]\begin{aligned}&3x + y = 6 \\&3 (17/7) + y = 6 \\& 51/7 + y = 6 \\&y = -9/7\end{aligned} [/tex]

Answer: x = 17/7, y = -9/7

if an object is propelled upward from a height of s feet at an initial velocity of v feet per second h=-16t^2+96t+8 after how many seconds is the height 116 feet?

Answers

654 is the answer for this question

5u exponent 7 - 21u exponent 7

Simply

Answers

Assuming the given is: 5u^7 - 21u^7
Since both algebraic terms are identical (both are using u^7), we can subtract the coefficients directly, as in: 5 - 21 = -16
Therefore, 5u^7 - 21u^7 = -16u^7

Which values of x would make a polynomial equal to zero if the factors of the polynomial were (x-2) and (x-11)?

Answers

if the factors of the polynomial were (x-2) and (x-11), then if anyone of them is equal "0", a polynomial will be equal zero.
x-2=0
x=2
x-11=0
x=11

A polynomial will be equal 0 if x=2, or x=11.

Answer:

[tex]x=2\text{ (or) }x=11[/tex]

Step-by-step explanation:

We have been given factors of a polynomial as [tex](x-2)[/tex] and [tex](x-11)[/tex]. We are asked to find the values of x that would make the polynomial equal to zero.

We will use zero product property of polynomials to solve our given problem. The zero product property of polynomials states that if any of two factors of a polynomial is zero, then their product will be equal to zero.

Upon equating our given factors to zero, we will get:

[tex](x-2)(x-11)=0[/tex]

[tex](x-2)=0\text{ (or) }(x-11)=0[/tex]

[tex]x-2=0\text{ (or) }x-11=0[/tex]

[tex]x-2+2=0+2\text{ (or) }x-11+11=0+11[/tex]

[tex]x=2\text{ (or) }x=11[/tex]

Therefore, [tex]x=2\text{ (or) }x=11[/tex] will make the polynomial equal to zero.

Can someone help with this math question

Answers

This is a problem of region. As shown in the figure, we have straight lines. We know that the equation for non-vertical lines is often given in the slope-intercept form by:
[tex]y=mx+b[/tex]

being m the slope of the line and b the y-intercept of it.

On the other hand, if x = 0 then y = b.

We will order the equations above without inequalities like this:

[tex]y=-x-6[/tex]

So, the G and J are straight lines with negative slope. We need to find the one that matches the inequality. Taking a point, for example (0, 0), we will analyze Figure J, so in the inequality:

[tex]0+0\ \textless \ -6[/tex]

This is false, so this statement doesn't match the Figure J. Therefore, the answer is G.

What is the y-intercept of the quadratic y=-2x^2-4x-5 ?
(-5,0)
(0,-2)
(-1,3)
(0,-5)

Answers

y - intercept is f(0) then (0; m)

We have: [tex]y=-2x^2-4x-5\to f(0)=-2(0)^2-4(0)-5=-5[/tex]

Answer: (0; -5)

hello can you please help me posted picture of question

Answers

1/25, since there are 25 square in total and there is only one center square.

your answer would be 1/25 since there are 25 squares in all. The 1 as a denominator would come from the probability.

What situation should be used to rewrite 16(x^3+1)^2 -22(x^3+1)-3=0 as a quadratic equation

Answers

[tex]16(x^3+1)^2-22(x^3+1)-3=0[/tex]

Use substitution: [tex]x^3+1=t[/tex]

[tex]16t^2-22t-3=0\\\\16t^2-24t+2t-3=0\\\\8t(2t-3)+1(2t-3)=0\\\\(2t-3)(8t+1)=0\iff2t-3=0\ \vee\ 8t+1=0[/tex]

[tex]2t-3=0\ \ \ |+3\\\\2t=3\ \ \ |:2\\\\t=\dfrac{3}{2}\\..............................\\8t+1=0\ \ \ \ |-1\\\\8t=-1\ \ \ \ |:8\\\\t=-\dfrac{1}{8}[/tex]

we're going back to substitution:

[tex]x^3+1=\dfrac{3}{2}\ \vee\ x^3+1=-\dfrac{1}{8}\ \ \ \ |subtract\ 1\ from\ both\ sides\ of\ the\ equations\\\\x^3=\dfrac{1}{2}\ \vee\ x^3=-\dfrac{9}{8}\\\\x=\sqrt[3]{\dfrac{1}{2}}\ \vee\ x=\sqrt[3]{-\dfrac{9}{8}}[/tex]

[tex]x=\dfrac{1}{\sqrt[3]2}\ \vee\ x=-\dfrac{\sqrt[3]9}{2}\\\\\boxed{x=\dfrac{\sqrt[3]4}{2}\ \vee\ x=-\dfrac{\sqrt[3]9}{2}}[/tex]

A triangle has side lengths of 10 centimeters, 2 centimeters, and c centimeters.

Enter a value to complete the inequality that describes the possible values for c, the length of the third side of the triangle.

HELP ASAP I COULD GET A PRESIDENTIAL AWARD FOR THIS!!!

Answers

Answer:

Step-by-step explanation:

The possible values of the third side of the triangle can be written as, 8 < c < 12.

What is Triangle?

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given a triangle.

Side lengths of the triangle are 10 centimeters, 2 centimeters, and c centimeters.

We have to find the possible values of c.

By the triangle Inequality Theorem,

10 - 2 < c < 10 + 2

8 < c < 12

Hence the possible values of c are 9, 10 and 11.

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Suppose you have an isosceles triangle, and each of the equal sides has a length of 1 foot. suppose the angle formed by those two sides is 45^\circ. then the area of the triangle is

Answers

The triangle has a 45-deg angle.
The base angles are congruent and measure 67.5 deg.
The congruent sides measure 1 ft.
Use law of sines to find the length of the base.

[tex] \dfrac{\sin 67.5^\circ}{1~ft} = \dfrac{\sin 45^\circ}{b} [/tex]

[tex] b = \dfrac{\sin 45^\circ}{\sin 67.5^\circ}~ft [/tex]

[tex] b = 0.765~ft [/tex]

Draw a height from the vertex of the 45-deg angle to the base.
Half of the base is 0.765 ft/2 = 0.383 ft

We can find the height of the triangle using the small triangles.

0.383^2 + h^2 = 1^2

h = 0.9239 ft

A = bh/2 = 0.765 * 0.9239/2 ft^2

A = 0.354 ft^2

Final answer:

The area of a given isosceles triangle with sides of 1 foot in length and a 45-degree angle between these sides is 0.5 square feet.

Explanation:

The area of an isosceles triangle can be calculated using the formula 1/2 base times height. But since we know that the triangle is isosceles and the angle between the equal sides is 45 degrees, this forms a 45-45-90 degree triangle which is a special kind of triangle. In a 45-45-90 degree triangle, the lengths of the sides are in the ratio 1:1:√2. Therefore, the length of the base (which also serves as the height in this case) will be the same length as the equal sides, 1 foot. Substituting these into the formula for area, we get Area = 1/2 * 1 ft * 1 ft = 0.5 square feet.

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If the radius of a cone is doubled and the height is tripled, what happens to the volume?

Answers

This is the answer . Have a nice day

A die is continuously rolled until the total sum of all rolls exceeds 375. what is the probability that at least 90 rolls are necessary?

Answers

Final answer:

To find the probability of at least 90 rolls being necessary for the total sum of all rolls to exceed 375, we need to consider the probabilities associated with each roll.

Explanation:

To find the probability of at least 90 rolls being necessary for the total sum of all rolls to exceed 375, we need to consider the probabilities associated with each roll.

The maximum possible sum from a single roll of a six-sided die is 6, so after 90 rolls, the maximum possible sum is 90 * 6 = 540. If the total sum exceeds 375, it means that at least one roll resulted in a value greater than 2.

To calculate the probability, we need to find the complement of the event that the total sum is less than or equal to 375, which is the event of the total sum being greater than 375. Let's assume that the probability of rolling a value greater than 2 is p. The probability of at least 90 rolls being necessary is 1 - (1 - p)^90.

If the volume is 56 1/4 cubic feet and the length is 7 1/2ft and the width is 3 3/4ft what is the height?

Answers

The height is 2. Multiply 7.5 by 3.75 and you should get 28.125. Divide 56.25 by 28.125 and you will get 2. If you want to check, multiply 2 by 7.5 by 3.75 and you will get 56.25.

The foci of the hyperbola are ( 13 , 0) and (− 13 , 0), and the asymptotes are y = 12 x and y = − 12 x. find an equation of the conic section with the given properties. use x and y as the variables in your answer.

Answers

y=k+- a/b(x-h)

y=-+12x

12=a/b

a=12b

c²=a²+b²

(13,0) and (-13,0)

13²=(12b)²+b²

169=145b²

b= 13/12

169=a²+169/145

a²= 24336/145

x²/a²-y²/b²=1

145x²/24336 + 145y²/169=1

The equation of the conic section is [tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

The foci of the hyperbola are given as: (13,0) and (-13,0)

The asymptote is given as [tex]y =\pm 12x[/tex]

Divide both sides of [tex]y =\pm 12x[/tex] by x.

[tex]\frac yx = \pm 12[/tex]

Where y/x = a/b.

So, we have:

[tex]\frac ab = \pm 12[/tex]

Make a the subject

[tex]a = \pm 12b[/tex]

Recall that

[tex]c\²=a\²+b\²[/tex]

Where:

[tex]c = \pm13[/tex]

[tex]c\²=a\²+b\²[/tex] becomes

[tex](\pm 13)^2 = (\pm 12b)^2 +b^2[/tex]

[tex]169 = 144b^2 +b^2[/tex]

Evaluate like terms

[tex]169 = 145b^2[/tex]

Make b^2 the subject

[tex]b^2 = \frac{169}{145}[/tex]

Recall that [tex]a = \pm 12b[/tex]

Square both sides

[tex]a^2 = 144b^2[/tex]

Substitute [tex]b^2 = \frac{169}{145}[/tex]

[tex]a^2 = 144 \times \frac{169}{145}[/tex]

[tex]a^2 = \frac{24336}{145}[/tex]

The equation of the conic section is represented as:

[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

Substitute known values

[tex]\frac{x^2}{24336/145} - \frac{y^2}{169/145} = 1[/tex]

Rewrite as:

[tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

Hence, the equation of the conic section is [tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

Answers

Since the base is a regular quadrilateral, each of its 4 sides must have length
s = P/4
s = (60 cm)/4 = 15 cm

The area of one lateral face is the product of side length and height.
A = s×h
105 cm² = (15 cm)×h
Then the height of the prism is
h = (105 cm²)/(15 cm) = 7 cm

The area of the base is then
B = s²
B = (15 cm)² = 225 cm²

The volume of the prism is the product of its base area and height.
V = Bh
V = (225 cm²)×(7 cm) = 1575 cm³

The volume is 1575 cm³.

Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 4

Answers

Final answer:

Given the lengths of the major and minor axes of an ellipse, one can derive the standard form equation of the ellipse. In this example, the lengths were 16 and 4, yielding a standard form equation of x²/4 + y²/64 = 1.

Explanation:

The subject of this question is about finding the standard form equation for an ellipse given the lengths of the major and minor axes. To find the equation of the ellipse, we need to identify the semi-major axis (a) which is half the length of the major axis, and the semi-minor axis (b), which is half the length of the minor axis.

In this case, the lengths of the major and minor axes are 16 and 4 respectively, which gives us a semi-major axis of 8 and a semi-minor axis of 2. The standard form equation of an ellipse with a vertical major axis is given by:

(x-h)²/b² + (y-k)²/a² = 1

Where (h, k) is the center of the ellipse. In this case, since the center of the ellipse is at the origin (0,0), the equation becomes:

x²/4 + y²/64 = 1

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What is is the equation of the line perpendicular to y = 3x-7 that contains the point (6,8)?

A. 1/3x - 7
B. 1/3x + 6
C. -1/3x - 7
D. -1/3x + 10

Answers

The slope of the perpendicular line will be the negative reciprocal of 3, the slope of the given line.
m = -1/(3) = -1/3

Only choices C and D have this slope. Only choice D goes through the given point. (-1/3)*6 +10 = -2 +10 = 8.

The appropriate selection is ...
D. (-1/3)x + 10

The equation of the line perpendicular to y = 3x -7 that passes through the point (6, 8) is Option D. y = -1/3x + 10. The slope of the perpendicular line is -1/3. Using point-slope form, we determine the final equation.

To find the equation of a line perpendicular to y = 3x - 7 that passes through the point (6, 8), we must determine the slope of the perpendicular line first.

The slope of the given line is 3. The slope of a line perpendicular to this one is the negative reciprocal of 3, which is -1/3.

We now use the point-slope form of the linear equation, which is:

y - y₁ = m(x - x₁)

Substitute m = -1/3 and the point (6, 8):

y - 8 = -1/3(x - 6)

Distribute -1/3:

y - 8 = -1/3x + 2

Add 8 to both sides:

y = -1/3x + 10

Thus, the equation is Option D. -1/3x + 10.

What is the slope of the line? A) -3 B) - 1/3 C) 1/3 D) 3

Answers

(1,1) and (2,4)

slope = (y2 - y1)/(x2 - x1)
slope = (4 - 1)/(2 - 1) = 3/1 = 3

answer
D) 3

C. 1/3 if I'm not mistaken should be the answer. You already could eliminate A. -3 and B. -1/3 since both are negatives. The line of this is pointing straight forward therefore D. 3 and C. 1/3 is left to choose from now it doesn't have a point on 3 that's how you know right away D can't be the solution. Hope I helped

Hey can you please help me posted picture of question

Answers

Shifting left can be expressed as addition of a number to x.

So,

F(x) shifted to left will be F(x + c), where c is any constant

So,

G(x) will be of the form F(x+c) or (x + c)²

From the given options, only option B lists such an expression.

So the answer is option B

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