if r(t) = 3t, 2t2, 4t3 , find r'(t), t(1), r''(t), and r'(t) × r ''(t).

Answer:

x^2-10x-9+9/x-6

quotient:x^2-10x-9

remainder:9

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

the three vectors are linearly dependent and they cant generate a 3 dimensional vector subspace.

Lets take v1 = (1,0,0), v2 = (1,1,0) and v3 = (0,1,0). Neither of the vectors are a multiple of the other, however they dont generate R³ because for example the vector (0,0,1) is not a linear combination of v1, v2 and v3.

Not that, despite not being a multiple of v1 or v3, v2 is a linear combination of v1 and v3, because it is the sum of both of them. Therefore, the three vectors are linearly dependent and they cant generate a 3 dimensional vector subspace.

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Answer:

125

Step-by-step explanation:

alternate interior

The range is ( 290, 230).

In statistics, the standard deviation is a measure of the amount of variation. The low standard deviation indicates that the values tend to be close to the expected value of the set, while a high standard deviation indicates that the values are spread out over a wide range.

According to the question,

The middle 50% of the pregnancies are within two standard deviations of the mean: 260 ± 2*15

               = ( 260 + 2*15 , 260 - 2*15)

               = ( 260 + 30, 260-30)

               = ( 290, 230)

Hence the range is ( 290, 230).

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To make x the subject of the equation q^2 = x - m^2, we can start by adding m^2 to both sides of the equation:

q^2 + m^2 = x

We can then rearrange the terms to get x on the left side:

x = q^2 + m^2

This is the equation with x as the subject.

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The function in f(t) form that describes the amount of fuel in the plane at time t will be;

⇒ f (t) = 112.25t + 31.425.75

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.

Now,

Since, After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.

Hence, The equation of line passes through the points (13, 32882) and (31, 34902.5)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (32882 - 34902.5) / ((31 - 13)

m = 2020.5 / 18

m = 112.25

Thus, The equation of line with slope 112.25 is,

⇒ y - 32885 = 112.25 (x - 13)

⇒ y - 32885 = 112.25x - 1459.25

⇒ y = 112.25x - 1459.25 + 32885

⇒ y = 112.25x + 31.425.75

Therefore, The function in f(t) form that describes the amount of fuel in the plane at time t will be;

⇒ f (t) = 112.25t + 31.425.75

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Answer:

[tex]x {}^{ \frac{19}{15} } [/tex]

Step-by-step explanation:

Hope that's helps

When use the graphs of f and g to graph then, we find that

Now, h(x) = (f + g)(x)

As you know that different x values that must be taken into consideration so that the graph h (x).

At first, h (0) = f (0) + g (0) = 2 - 1 = 1

Now,

If h (1) = f (1) + g (1) =

3 + 0 = 3

Then, after proper calculation, now

Later as we know, hence

finally the answer is h (3) = f (3) + g (3)

= 2 + 0 = 2

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Since the function increases; stops; and decreases x= -2 has to be a maximum. Similarly, x=0 is a minimum and x=2 is an inflection point. (They are "relative" max/mins as opposed to absolute.

"Critical Points" (maximums, minimum and inflection points) occur when the first derivative of the function is zero. Here f(x) is neither increasing nor decreasing at that exact point. When f '(x) is positive, f(x) is increasing; when f '(x)is negative f(x) is decreasing. In this case, the critical points are x= -2, 0, 2. For x<-2 the derivative is positive so the function is increasing, for x>-2 the derivative is negative so the function is decreasing.

b) When f '(x) is positive, f(x) is increasing; when f '(x) is negative f(x) is decreasing. In this case, the critical points are x= -2, 0, 2. For x<-2 the derivative is positive so the function is increasing, for x>-2 the derivative is negative so the function is decreasing.

Concavity is determined by the second derivative, which is easy to sketch from the first. Where f '(x) is decreasing, f ''(x)is negative; where f '(x) is increasing f ''(x) is positive. Where f '(x) is zero, f ''(x) has critical points. Now from this graph, where f ''(x) is positive, f(x) is concave up, where f ''(x)is negative, f(x) is concave down. I get that f(x) is concave up on(-1,1) and (2,3).

c) Now it should be easy to graph f from the maxs mins and critical points. There is my attempt.

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The product of the monomial and the polynomial given is 12x⁶y³-28x⁴y⁵+8x⁴y⁴-4x³y⁴

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations.

Given that, a polynomial and a monomial 4x³y³ and (3x³-7xy²+2xy-y)

To find the product of the monomial and the polynomial, we will multiply them,

4x³y³×(3x³-7xy²+2xy-y)

= 12x⁶y³-28x⁴y⁵+8x⁴y⁴-4x³y⁴

Hence, The product of the monomial and the polynomial given is 12x⁶y³-28x⁴y⁵+8x⁴y⁴-4x³y⁴

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The excretion  Superscript one-eighth Beeline is

[tex]\left(x^{\frac{1}{8}}\right)\left(x^{\frac{3}{8}}\right)=12[/tex]

What is exponential identity?

An example of an exponential function is the growth of bacteria. Some bacteria double every hour. If you start with 1 bacterium and it doubles every hour, you will have 2x bacteria after x hours. This can be written as f(x) = 2x.

To find, the possible value of x = ?

[tex]\begin{aligned}& \therefore\left(x^{\frac{1}{8}}\right)\left(x^{\frac{3}{8}}\right)=12 \\& \Rightarrow x^{\frac{1}{8}}+\frac{3}{8}=12\end{aligned}[/tex]

Using the exponential identity

,[tex]\begin{aligned}& a^m a^n=a^{m+n} \\& \Rightarrow x^{\frac{1+3}{8}}=12 \\& \Rightarrow x^{\frac{4}{8}}=12 \\& \Rightarrow x^{\frac{1}{2}}=12\end{aligned}[/tex]

Squaring both sides, we get

[tex]\begin{aligned}& \left(x^{\frac{1}{2}}\right)^2=(12)^2 \\& \Rightarrow x^{\frac{1}{2} \times 2}=144 \\& \Rightarrow x=144\end{aligned}\therefore The possible value of x=144[/tex]

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If a lawyer charges 120 an hour then the bill for 3 hours and 20 minutes will be 400

Bill: A bill is the printed or written statement of the money owed for goods or services.In later Latin, bulla became billa, and in English billa became bill. The word can still refer to various official documents, such as a proposed law that is brought before parliament, although it is now most commonly used for documents that request payment of money.

One hour = 60 minutes

3 hours and 20 minutes = 3×60 +20

                                        = 180+20=200

Here, one hour=60 minutes charges 120

1 minute charges = 120/60

                             = 2

200 minute charges = 2×200=400

Therefore If a lawyer charges 120 an hour then the bill for 3 hours and 20 minutes will be 400.

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The length, b, of the longest side of the triangle is 13.17 cm

From the question, we are to determine the length, b, of the longest side of the triangle

From the given information,

Area of the triangle = 22.4 cm²

Then, we can write that

22.4 = 1/2 × a × 3.7 sin97

44.8 = a × 3.7 sin97

44.8 = a × 3.6724

a = 44.8/3.6724

a = 12.199

a = 12.2

Given that the sides of the triangle are a, b, and c,

Then,

From the law of cosines, we can write that

b² = c² + a² - 2ac cosB

b² = 3.7² + a² - 2×a×3.7 cos97°

b² = 3.7² + 12.2² - 2×12.2×3.7 cos97°

b² = 3.7² + 12.2² - 2×12.2×3.7 cos97°

b² = 173.53

b = √173.53

b = 13.17 cm

The length of b is 13.17 cm

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The measure of the first angle is 70° and the measure of the second angle is 100°.

The measure of complementary angles is the sum of their angles equal to 180°. Thus, if one angle has a measure of 70°, then the other angle must have a measure of 180° - 70° = 110°. Since the difference between the two angles is 14°, the first angle must have a measure of 70°, and the second angle must have a measure of 100°. This is because if the first angle has a measure of 70°, then the second angle must have a measure of 110°. Since the difference between the two angles is 14°, the second angle must have a measure of 100° in order to meet this difference. Therefore, the measure of the first angle is 70° and the measure of the second angle is 100°.

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Using logical reasoning, we know that Aha's current body temperature after taking the medicine is 34°C.

Deductive reasoning, often known as logical reasoning, is the process of drawing conclusions from a body of facts or evidence.

It involves putting specific premises in front of conclusions.

Induction and abduction are two additional categories of logical reasoning that are typically distinguished in addition to the formal deduction.

If one has a premise or precondition, a conclusion or logical consequence, and a rule or material conditional that signals the conclusion given the premise, one can explain the following.

So, we know that:

The normal body temperature of the body is 37°C.

Aha current body temperature is 3 more than normal body temperature, then it is: 37 + 3 = 40°C (Current body temperature)

After taking medicine,

Temperature is 6° less than current body temperature, that is:

40 - 6 = 34°C

Temperature is 3° less than the normal body temperature, that is:
37 - 3 = 34°C

Then, the current temperature after taking medicine: 34°C

Therefore, using logical reasoning, we know that Aha's current body temperature after taking the medicine is 34°C.

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The Corner Points are (-6.529, -10.235), (0, -2.4), (2, 0), (-2.143, 0), (0, 5)

What is Linear Inequality?

A linear inequality is a mathematical inequality that incorporates a linear function. A linear inequality contains one of the inequality symbols. It displays data that is not equal in graph form.

Solution:

Please refer to the Graph

So, we plotted the graph using the basic point method in which we found two point of the equation to draw a straight line.

And once we drawn the lines for the Inequalities we shaded the respective region

The Corner Points are (-6.529, -10.235), (0, -2.4), (2, 0), (-2.143, 0), (0, 5)

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The value of the function given as (f . g)(2) is D. (f.g)(2) = 44, the number of boats

It's important to note that functions are the expressions that are separated by an equal sign. It should be noted that that they've dependent as well as independent variables.

In this case, the function f(x)=2x²+3 represents the rate of a boat traveling with the current in miles per hour and the function g(x)=x+ 2 represents the time the boat traveled in hours. This will be illustrated as:

f(x) = 2x² + 3.

g(x) = x + 2

Therefore, we will evaluate the product

(f . g)(x) = (2x² + 3(x + 2)

(f . g)(x) = (2 × 2² + 3)(2 + 2)

(f . g)(2) = 44

The correct option is D.

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The correct option is; 4: this contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3.

The function being used is;

f(x) = (x - 3)⁻²

If we separate this function according to x, we obtain;

f'(x) = -2/(x - 3)³

Finding all c values f(7) − f(1) = f '(c)(7 − 1).is our goal.

This suggests that;

0.06 - 0.25 = -2/(c - 3)³ x 6

-0.19 =  -12/(c - 3)³

(c - 3)³ = 63.157

c = 6.98

If the Mean Value Theorem holds for this function, then f must be continuous on [1,7] and differentiable on (1,7).

But when x = 3, f is not continuous, hence the Mean Value Theorem's prediction is false.

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The complete question is-

Let f(x) = (x − 3)−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about the Mean Value Theorem?

Answer:

  30 feet

Step-by-step explanation:

You want to know the distance between the first and last of 10 stakes evenly spaced, such that the first and fourth are 10 feet apart.

Between stakes 1 and 4 are 3 gaps. Between stakes 1 and 10 are 9 gaps, which is 3 times as many.

The distance from the 1st to 10th stakes will be 3 times the 10 ft distance from the 1st to 4th stakes.

  3 · 10 ft = 30 ft

The first and tenth stakes are 30 feet apart.

Answer:

$43

Step-by-step explanation:

substitute x = 2.75 into f(x)

f(2.75) = 12(2.75) + 10 = 33 + 10 = 43

that is he earns $43

Answer: 1 knife costes £5.52

Step-by-step explanation:

Let a knife costes £x and a spoon costes £y

Hence, we obtain a system of equations:

x=3y                         (1)

12x+9y=82.80         (2)

Divide both parts of the equation (2) by 3:

x=3y                    

4x+3y=27.6        (3)

We substitute the value of x=3u into equation (3):

4(3y)+3y=27.6

12y+3y=27.6

15y=27.6

Divide both parts of the equation by 15:

y=£1.84

x=3y

x=3(1.84)

x=£5.52

Only answers A, C, and D are in standard form, so we can rule B out immediately.

If you throw (5,1) into A, you get:

   5(5) - 2(1) = 23

        25 - 2 = 23

This checks, so A *might* be the answer.

If you throw (5,1) into C, you get:

  2(5)-3(1) = 9

      10 - 3 ≠ 9

This doesn't check, so it's not C.

If you throw (5,1) into D, you get:

  5(5)+2(1) = 23

     25 + 2 ≠ 23

This doesn't check, so it's not D.

The only standard form equation that (5,1) is a solution for is A.

Your answer is A.

The population means may be the same

So, option D is correct.

What is meant by confidence interval?

In statistics, the probability that a population parameter will fall between a set of values a predefined percentage of the time is known as the confidence interval. Analysts typically use confidence intervals that cover 95% or 99% of the expected observations while assessing data. In frequentist statistics, an estimation range for an unknown parameter is referred to as a confidence interval. The most common confidence level for computing confidence intervals is 95%, however other levels, such 90% or 99%, are also occasionally employed. The conclusion is reached that the result is statistically significant if the confidence interval eliminates the value of zero effect.

If (μ₁- μ₂=0) is included in the confidence interval, that means this two means have the same difference that is zero.

Therefore, they may be nearly same,

So, The population means may be the same

Hence, option D is correct.

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Answer:

  y = (4 -x)e^-2

Step-by-step explanation:

You want an equation of the tangent line to the graph of f(x) = xe^−x at its inflection point.

The inflection point on a curve is the point where the second derivative is zero, where the curve changes from being concave downward to concave upward, or vice versa.

We can use the product rule to differentiate f(x):

  (uv)' = u'v +uv'

  f'(x) = 1·e^-x +x·(-1)(e^-x) = (e^-x)(1 -x)

Then the second derivative is ...

  f''(x) = (-e^-x)(1 -x) +(e^-x)(-1) = (e^-x)(x -2)

The second derivative is zero where one of its factors is zero. e^-x is never zero, so we have ...

  (x -2) = 0   ⇒   x = 2

The point of inflection occurs at x = 2.

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

For this problem, we have ...

  m = f'(2) = (e^-2)(1 -(2)) = -e^-2

  (h, k) = (2, f(2)) = (2, 2e^-2)

So, the equation of the tangent line is ...

  y -2e^-2 = -e^-2(x -2)

In slope-intercept form, this is ...

  y = (-e^-2)x +4e^-2

__

Additional comment

We can rearrange the equation to ...

  y = (4 -x)e^-2

Usually a tangent line touches the graph, but does not cross it. The tangent at the point of inflection necessarily crosses the graph.

Answer:

t=180-2x46=88 degrees

u=1/2(180-114)=33 degrees

Answer:

b) The stock is 5.5 less than the original value, and the absolute value is 5.5.

Step-by-step explanation:

First of all, let's make our number line. The question says you need it to start at -9, so we can assume that it will go until 10. It also wants us to make half-tick marks. (There is an image attached of the number line.)

It says that -5.5 is labeled, so do that on your number line.

Next, it explains that 0 is the original price. 0 is where the stock is starting at. This does not mean that the value of the stock is 0!!! (It means that NO MATTER what the price of the stock is, that is now considered 0.)  

Now for the multiple choice, here's why all the answers are incorrect/correct.

a) If something is -5.5 less, it's the same as subtracting a negative number- which makes it positive!! SO this would mean that it added value.

b) Correct! Since it value is lower by 5.5, it's 5.5 less than the og value.

c) Since it's -5.5 greater, that's like adding a negative number: it's the same as subtracting. I suppose this is technically correct, but it's weird.

d) This one says's it's 5.5 greater, which is totally wrong. The value is decreasing, not increasing!

All of them say the absolute value is 5.5. This is correct. Absolute value is the distance from 0, and -5.5 is 5.5 units away from 0. (put simply, absolute value is just making the number positive.

hopefully this makes sense and helps you!!

Answer:

x-intercept is (10,0)

y-intercept is (0, -8)

Step-by-step explanation:

Our equation is 4x - 5y = 40

Let's find x-intercepts first

X-intercepts is when the y = 0

So we put 0 in for the y, and we have the equation

4x =40

x =10

So our x-intercept located at (10,0)

Now find the y-intercepts

Y-intercepts is when the x = 10

So we put 0 in for the x, and we have the equation

-5y = 40

y= -8

So our y-intercept is located at (0,-8)

Answer:

Step-by-step explanation:

Y-int: (0, -8)

X-Int: (10, 0)

To find the y and x intercepts you have to plug in the 0 for the variable. You'd get 4(0)-5y=40 you get this by plugging in the 0 for x and then you solve. 4 x 0 is 0 so you'd get -5y=40 divide -5 on both sides and get y=-8 meaning that is the y-intercept.

You'd do the same when you look for the x-int. Just that you'd plug in a 0 for y instead of x. Which is 4x-5(0)=40. -5 x 0 is 0. So you'd have 4x=40 divide both sides by 4 and you'd get x=10 meaning that is the x intercept.

Remember that when looking for the y- intercept there should always be a zero in front meaning the x-value, and when looking for the x-intercept there should always be a  zero in the back meaning the y-value.

(Hopefully you were able to understand how I got the x and y intercepts for this equation)