how to solve tangent​

1. The velocity at time t , v(t) = (18t² + 3 ) m/s

2. The velocity at time t = 3 seconds = 165 m/s

3. The acceleration at time t, a(t) =( 36t )m/s²

4. The acceleration at time t = 3 seconds = 108 m/s²

The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity.

Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.

1. s(t) = 6t³ + 3t +9

to find the velocity at time t, we differentiate s(t)

= 18t² + 3

2. at t = 3s

= 18(3)² +3

= 165 m/s²

3. v(t) = 18t² + 3

to get the acceleration at time t, we differentiate v(t)

= 36t

4. when t = 3

a = 36 × 3

= 108 m/s²

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espero que sea de tu agrado la tarea que te estoy enviando

soy de peru

brillith2022

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

the answer is c

Step-by-step explanation:

Answer:

1)  m = negative StartFraction 10 over 4 EndFraction

2) m = negative five-halves

3) m = \(-\frac{7}{4} - \frac{3}{4}\)

Step-by-step explanation:

The given equation is:

=> \(\frac{3}{4} +m = -\frac{7}{4}\)

Subtracting 3/4 to both sides

=> m = \(-\frac{7}{4} - \frac{3}{4}\)

=> m = \(\frac{-10}{4}\)

=> m = \(-\frac{5}{2}\)

Answer:

-5/2 ye

cause ya do the math

Step-by-step explanation:

The period of the function f(t) = 2.3cos(0.25t) is 8π. Hence, the correct answer is d) period 8π.

To determine the period of the function f(t) = 2.3cos(0.25t), we need to consider the coefficient of t inside the cosine function.

In this case, the coefficient is 0.25, which represents the frequency of the cosine function. The period of a cosine function is given by the formula T = 2π/frequency.

Using this formula, we can calculate the period of the function f(t) as follows

T = 2π / 0.25

T = 8π

Therefore, the period of the function f(t) = 2.3cos(0.25t) is 8π.

Hence, the correct answer is d) period 8π.

The period of a function represents the length of one complete cycle or the distance between two consecutive identical points on the graph of the function. In this case, the function is a cosine function, and the period determines how long it takes for the function to repeat its values

The coefficient 0.25 in the function f(t) = 2.3cos(0.25t) affects the frequency of the cosine function. A smaller coefficient results in a slower oscillation, while a larger coefficient leads to a faster oscillation. In this case, since the coefficient is 0.25, it means that the function completes one full cycle within 8π units of time.

Understanding the period of a function is crucial for analyzing its behavior, identifying the frequency of oscillation, and studying its repetitive patterns.

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Answer:

Its 1 because you are moving the digits 1 place to the right

Step-by-step explanation:

Given :

Janelle is viewing an image of a sculpture. She enlarges it using a scale of 0.2 cm to 1/8 ft.

To Find :

How many centimetres in the image are used to show 1 foot of the sculpture.

Solution :

Ratio of enlargement is :

\(R=\dfrac{\text{Size in feet}}{\text{Size in cm}}\\\\R=\dfrac{\dfrac{1}{8}}{0.2}\\\\R=\dfrac{5}{8}\ ft/cm\)

Let, enlarged size of 1 foot required x cm of image.

\(\dfrac{1}{x}=\dfrac{5}{8}\\\\x=\dfrac{8}{5}\\\\x=1.6\ cm\)

Therefore, 1.6 cm of image is required.

Hence, this is the required solution.

Answer:

1.6

Step-by-step explanation:

Answer:

8.06

Step-by-step explanation:

I used my brain and paper. I don't want to have to explain it anymore sorry but yes I think that is the right answer.

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The given expression is :

so, the number line where, value of x is plotted as +8 and -8 is the Correct one.

that is :

The second number line ~

Answer: y=3x+0

Step-by-step explanation: rise (y) over run (x) would be 3/1, which is 3. The line passes through the origin (0,0) so its 0.

No, the trapezoids are not similar because their corresponding angles do not have the same measures.

The given trapezoids ABCD and EFGH can be analyzed to determine if they are similar. Similarity in geometric figures implies that their corresponding angles are congruent, and their corresponding sides are proportional.

Let's examine the angles of the trapezoids:

In trapezoid ABCD:

Angle A = 137 degrees

Angle B = 90 degrees

Angle C = 90 degrees

Angle D = 43 degrees

In trapezoid EFGH:

Angle E = 136 degrees

Angle F = 90 degrees

Angle G = 90 degrees

Angle H = 44 degrees

By comparing the angles, we can observe that angles B and F are both right angles (90 degrees) in both trapezoids. Additionally, angles C and G are also right angles (90 degrees) in both trapezoids.

However, angles A and E, as well as angles D and H, do not have the same measures. Angle A measures 137 degrees in trapezoid ABCD, while angle E measures 136 degrees in trapezoid EFGH. Similarly, angle D measures 43 degrees in trapezoid ABCD, while angle H measures 44 degrees in trapezoid EFGH.

Since the corresponding angles in the two trapezoids do not have the same measures, we can conclude that trapezoids ABCD and EFGH are not similar.

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Answer:

Step-by-step explanation:

A. The null hypothesis is most of the time always the default hypothesis.

In this case study, the null hypothesis is people who regularly listen to radio talk shows vote in national elections as people in general.

While the alternative claim would be: people who regularly listen to radio talk shows are more or less likely to vote in national elections than people in general.

B. Since there are two options in the alternative claim: more or less, the researcher would use a two tailed hypothesis Z test. But if there is only one option, either more or less, then the researcher can use a one tailed Z test.

Answer:

30 square millimeters

Step-by-step explanation:

3 x 3 = 9

3 x 1 = 3

there are two sides with the area 9 therefore...

9 x 2 = 18

There are four sides with the area 3 therefore...

3 x 4 = 12

Therefore the suface area is

12 + 18 = 30

Answer:

16

Step-by-step explanation:

12+1=13

13+1=14
14+1=15
15+1=16

1+1=2
2+1=3
3+1=4

---------
4+6=10

10+6=16

(6+6=12)

Answer:

0.02 is the smaller number

Step-by-step explanation:

Answer:

multiply ur options, so 9x10= 90

Step-by-step explanation:

Answer:

9x + 8

Step-by-step explanation:

2(3x + 1) + 5x + 9 - 2x - 3

⇒ 6x + 2 + 5x + 9 - 2x - 3

⇒ 9x + 8

Algebra

2(3x+1)=6x+2

Then combine like terms.

6x+2+5x+9-2x-3

9x+8

Answer:

The 95 % confidence interval of the mean of the time playing video games. is

        \(15.67< \mu <17.52\)

Step-by-step explanation:

From the question we are told that

      The sample size is \(n = 35\)

        The sample mean is \(\= x = 16.6\)

       The standard deviation is  \(\sigma = 2.8\)

The confidence level is  95%  hence the level of significance is mathematically represented as

     \(\alpha = 100 - 95\)

     \(\alpha = 5\)%

      \(\alpha = 0.05\)

Now the critical value of half of this level of significance obtained from the normal distribution table is  

       \(Z_{\frac{\alpha }{2} } = 1.96\)

The  reason for the half is that we are considering the two tails of the normal distribution curve which we use to obtain the interval

Now the standard error of the mean is mathematically evaluated as

       \(\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }\)

substituting values  

     \(\sigma _{\= x} = \frac{2.8 }{\sqrt{35} }\)

      \(\sigma _{\= x} = 0.473\)

the 95 % confidence interval of the mean of the time playing video games.

is mathematically evaluated as

    \(\= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x }) < \mu < \= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x })\)

substituting values

    \(16.6 - (1.96 * 0.473) < \mu < 16.6 + (1.96 * 0.473)\)

     \(15.67< \mu <17.52\)

A point on the line is (0, 3).

Given equation of the line:y + 3 = 3/2 (x + 4)

It can be rewritten in slope-intercept form as: y = 3/2x + 6 - 3

Slope of the line can be determined by comparing with y = mx + b, where m is the slope and b is the y-intercept.

Therefore, comparing given equation with y = mx + b, we get Slope (m) = 3/2

To find a point on the line, we can substitute any arbitrary value of x or y and solve for the other variable.

Let's take x = 0:y + 3 = 3/2 (0 + 4)y + 3 = 6y = 3

Therefore, a point on the line is (0, 3).

Now, to graph the line, we need to plot this point and use the slope to find other points. We know that slope is rise over run, which means for every increase of 2 units in x, there is an increase of 3 units in y.

So, we can use this to find other points as follows:Starting from (0, 3), move 2 units to the right and 3 units up to get another point, say (2, 6).Then, move 2 units to the left and 3 units down to get another point, say (-2, 0).

Join all the points on the graph to get the line.

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Given,

The polygon ABCD if AB = 15, BC = 15,

CD = 15.

AB is perpendicular to BC.

BC perpendicular to CD.

CD perpendicular to DA.

DA perpendicular to AB.

Required

The shape of the polygon.

Here, all sides are equal and all sides are perpendicular to each other.

Hence, the shape of the polygon is square, rectangle .

Substituting x= 3 -7y/3​ into y= 9/7 -3x/7, we have

Therefore,

This implies that,

So the number of solutions is infinite.

We can set x = 1, then

Hence, (1, 6/7) is a solution

We can also set y = 3, then

Hence, (3, -4) is another solution

The sheet decreased by 1.5 meters and is now at 2.5 meters.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, s=−0.25t + 4 represents the thickness of the ice over t weeks. To find the thickness at 6 weeks, substitute t=6.

s = -0.25(6)+4

s = 2.5 meters

It started at t= 0 at 4 meters. So it decreased by (4 - 2.5) = 1.5 meters.

The start of spring has 4 meters because when t= 0, s= -0.25(0)+4 = 4

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During the cold winter months, a sheet of ice covers a lake near the Arctic Circle. At the beginning of spring, the ice starts to melt.

The variable s models the ice sheet's thickness (in meters) t

weeks after the beginning of spring.

s=−0.25t+4s=-0.25t+4

s=−0.25t+4

By how much does the ice sheet's thickness decrease every 6 weeks?

Answer:

Step-by-step explanation:

30 dollars to spend she wants to buy at least ten which mean's since 2 times 5 is 10 and 4 times 5 is 20 and 10 plus 20 equals thirty which means she can buy 5 small coffee's and 5 large coffee's

hdhduxhx, this is the solution to the exercise:

Multiplying by -1 the second equation, we have:

y = -3x - 3

-y = 4x + 5

____________

0 = x + 2

x = -2

_____________

Now we can solve for y in the first equation, this way:

y = - 3x - 3

y = -3 (-2) - 3

y = 6 - 3

y = 3

____________

Finally, let's prove that x = -2 and y = 3 is correct for the second equation, as follows:

y = -4x - 5

3 = -4 (-2) - 5

3 = 8 - 5

3 = 3

___________

We proved that x = -2 and y = 3 is correct.

Answer:

please set me in star

The value of f(1) by using the attached graph is f(1) = -2.

A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.

Given:

The graph shown in the question is representing the function value,

To find f(1) = ?

The value of f(1) will be equal to the value of x as the graph is linear so,

f(1) = value of y at x = 1

value of y at x = 1 = -2  (From the graph)

Thus, f(1) = -2.

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