PLEASE HELP!!!!!!!!! ​

Answer:

The equation of the tangent line is given by the following equation:

[tex]\displaystyle y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg)[/tex]

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Rule [Basic Power Rule]:

Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

*Note:

Recall that the definition of the derivative is the slope of the tangent line.

Step 1: Define

Identify given.

[tex]\displaystylef(x) = e^{-x} \\x = -1[/tex]

Step 2: Differentiate

Step 3: Find Tangent Slope

∴ the slope of the tangent line is equal to  [tex]\displaystyle \frac{-1}{e}[/tex].

Step 4: Find Equation

∴ our point is equal to  [tex]\displaystyle \bigg( 1, \frac{1}{e} \bigg)[/tex].

Substituting in our variables we found into the point-slope form general equation, we get our final answer of:

[tex]\displaystyle \boxed{ y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg) }[/tex]

∴ we have our final answer.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

C

Step-by-step explanation:

Answer:

  C.  16π

Step-by-step explanation:

You want to know the area of a circle whose radius is twice the edge of a cube that has a surface area of 24 square units.

The relevant area formulas are ...

  As = 6s² . . . . . . area of cube with edge s

  Ac = πr² . . . . . . area of circle with radius r

Here, we have r = 2s, so the area of the circle is ...

  Ac = π(2s)² = 4πs²

And we have the area of the square as 24, so the value of s² is ...

  As = 24 = 6s²

  24/6 = 4 = s²

Using this in the circle area expression, we have the area of the circle as ...

  Ac = 4π(4) = 16π . . . . . square units

The area of the circle is 16π square units.

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Answer: 2,-2

Step-by-step explanation: 9-7 is 2 and -9 minus -7 is minus 2.

Answer:

The answer is e. (x - 10 * y^2 * z) (x + 10 *y^2 *z)

Step-by-step explanation:

To explain it test all the options by distributing them.

Using an online website that I plugged into the calculator to factory gets answer e.

Answer:

45 degrees      

right angle =90 degrees

remaining :90

angles are equal

so 45 each

Answer:

C

Step-by-step explanation:

The volume is 54,437.52.

Answer:

54,437.52 ( fifty four thousand four hundred thirty seven and fifty two thousanths.)

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Find the cube root of 216

Answer:

See below.

Step-by-step explanation:

1) We know that the circumference of a circle can be found using the formula [tex]c=\pi d[/tex], so for this circle the circumference will be [tex]c=3.14 \times 40=125.6 \text{ yards}[/tex]. The formula for the area of a circle is [tex]A=\frac{1}{4}\pi d^2[/tex], so the area of this circle will be [tex]A=\frac{1}{4} \times 3.14 \times 40^2=1256 \text{ yards}[/tex].

2) First we'll work out the length of the curved side of the shape. That's [tex]\frac{1}{2}\times\pi d =\frac{1}{2} \times 3.14 \times 12=18.84 \text{ mm}[/tex]. Then, we'll add the length of the other two straight sides to get [tex]10.82 \times 2 + 18.84=40.48 \text{ mm}[/tex]. Next: the area of the semi-circle is [tex]\frac{1}{2} \times \frac{1}{4} \pi d^2 = \frac{1}{8} \times 3.14 \times 144 = 56.52 \text{ mm}[/tex]. Adding this to the areas of the two triangles: [tex]56.52+2 \times \frac{1}{2}bh=56.52+(\sqrt{10.82^2-9^2)}\times9 \approx 110.57 \text{ to 2 d.p.}[/tex]

Answer:

x=24

Step-by-step explanation:

you need 300.

10x + 60?

10 x 3 = 300

300 - 60 = 240

300 = (10 x 24) + 60

Answer:

Domain is all real #s

Range is (-∞, 4]  or y < 4

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

[tex]\sqrt{28}[/tex]

Step-by-step explanation:

the point lies between 5 and 6 , that is between

[tex]\sqrt{25}[/tex] and [tex]\sqrt{36}[/tex]

therefore the poi nt approximates to the [tex]\sqrt{28}[/tex]

The total amounts of money which Mrs. Reynolds now has according to the descriptions in the task content is; $68.

It follows from the task content that;

On this note;

Hence, it follows that the amount of money, s she has now is;

Read more on addition and subtraction;

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To determine if you have enough money to buy this product, calculate the sales tax and the final price of the product.

Sales tax is usually expressed as a percentage. Moreover,  this percentage can slighly change depending on the state where you live.

Here is an example:

Final price = 138.12

Learn more about sale tax in: https://brainly.com/question/1811849

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Answer:

See below for answers and explanations (along with a graph for #3)

Step-by-step explanation:

Problem #1

Applying scalar multiplication, [tex]-4w=-4\langle-96,-180\rangle=\langle384,720\rangle[/tex].

Its magnitude would be [tex]||-4w||=\sqrt{384^2+720^2}=816[/tex].

Its direction would be [tex]\displaystyle\theta=tan^{-1}\biggr(\frac{720}{384}\biggr)\approx61.927^\circ\approx62^\circ[/tex].

Thus, B) 816; 62° is the correct answer

Problem #2

Find the time it takes for the ball to cover 13ft:

[tex]x=(24\cos48^\circ)t\\13=(24\cos48^\circ)t\\t\approx0.8095[/tex]

Find the height of the ball at the time it takes for the ball to cover 13ft:

[tex]y=6.1+(24\sin48^\circ)t-16t^2\\y=6.1+(24\sin48^\circ)(0.8095)-16(0.8095)^2\\y\approx10.053[/tex]

Thus, A) 10.053 is the correct answer

Problem #3

We have [tex]u=\langle0,-8\rangle[/tex] and [tex]v=\langle6,0\rangle[/tex] as our vectors. Thus, [tex]u+v=\langle0+6,-8+0\rangle=\langle6,-8\rangle[/tex]. Attached below is the correct graph. You can also solve the problem visually by using the parallelogram method where the resultant vector is the diagonal of the parallelogram.

Problem 4 (#7)

[tex]\displaystyle t \cdot v=(7)(-10)+(-3)(-8)=-70+24=-46[/tex]

Thus, C) -46 is the correct answer

Problem 5 (#8)

Find [tex]r[/tex] and [tex]\theta[/tex]:

[tex]r=\sqrt{x^2+y^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}=2\sqrt{17}\approx8.246[/tex]

[tex]\displaystyle\theta=tan^{-1}\biggr(\frac{y}{x}\biggr)=tan^{-1}\biggr(\frac{-8}{2}\biggr)\approx-75.964^\circ[/tex]

Find the true direction angle accounting for Quadrant IV:

[tex]\theta=360^\circ-75.964^\circ=284.036^\circ[/tex]

Write the complex number in polar/trigonometric form:

[tex]z=8.246(\cos284.036^\circ+i\sin284.036^\circ)[/tex]

Thus, C) 8.246(cos 284.036° + i sin 284.036°) is the correct answer

Problem 6 (#12)

Eliminate the parameter and find the rectangular equation:

[tex]x=3t\\\frac{x}{3}=t\\ \\y=t^2+5\\y=(\frac{x}{3})^2+5\\y=\frac{x^2}{9}+5\\9y=x^2+45\\0=x^2-9y+45\\x^2-9y+45=0[/tex]

Thus, D) x^2-9y+45=0 is the correct answer

Problem 7 (#13)

Find the magnitude of the vector:

[tex]||v||=\sqrt{(-77)^2+36^2}=85[/tex]

Find the true direction of the vector accounting for Quadrant II:

[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{36}{-77}\biggr)\approx-25^\circ=180^\circ-25^\circ=155^\circ[/tex]

Write the vector in trigonometric form:

[tex]w=85\cos155^\circ i+85\sin155^\circ j[/tex]

Thus, D) w=85cos155°i+85sin155°j is the corrwect answer

Problem 8 (#15)

[tex]\frac{z_1+z_2}{2}=\frac{(3-7i)+(-9-19i)}{2}=\frac{-6-26i}{2}=-3-13i=(-3,-13)[/tex]

Thus, C) (-3,-13) is the correct answer

Problem 9 (#16)

Treat the golf ball and wind as vectors:

[tex]u=\langle1.3\cos140^\circ,1.3\sin140^\circ\rangle[/tex] <-- Golf Ball

[tex]v=\langle1.2\cos50^\circ,1.2\sin50^\circ\rangle[/tex] <-- Wind

Add the vectors:

[tex]u+v=\langle1.3\cos140^\circ+1.2\cos50^\circ,1.3\sin140^\circ+1.2\sin50^\circ\rangle\approx\langle-0.225,1.755\rangle[/tex]

Find the magnitude of the resultant vector:

[tex]||u+v||=\sqrt{(-0.225)^2+1.755^2}\approx1.769[/tex]

Find the true direction of the resultant vector accounting for Quadrant II:

[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{1.755}{-0.225}\biggr)\approx-82.694^\circ\approx-83^\circ=180^\circ-83^\circ=97^\circ[/tex]

Thus, B) 1.769 m/s; 97° is the correct answer

Problem 10 (#17)

Identify the vectors and add them:

[tex]u+v+w=\langle50\cos20^\circ,50\sin20^\circ\rangle+\langle13\cos90^\circ,13\sin90^\circ\rangle+\langle35\cos280^\circ,35\sin280^\circ\rangle=\langle50\cos20^\circ+13\cos90^\circ+35\cos280^\circ,50\sin20^\circ+13\sin90^\circ+35\sin280^\circ\rangle=\langle53.062,-4.367\rangle[/tex]

Find the magnitude of the resultant vector:

[tex]||u+v+w||=\sqrt{53.062^2+(-4.367)^2}\approx53.241[/tex]

Find the true direction of the resultant vector accounting for Quadrant IV:

[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{-4.367}{53.062}\biggr)\approx-4.705^\circ\approx-5^\circ=360^\circ-5^\circ=355^\circ[/tex]

Thus, A) 53.241, 355° is the correct answer

Problem 11 (#18)

We observe that [tex]z_1=-8-6i[/tex] and [tex]z_2=4-4i[/tex], hence, [tex]z_1+z_2=(-8-6i)+(4-4i)=-4-10i[/tex]

Thus, Q is the correct answer

Problem 12 (#19)

Find the dot product of the vectors:

[tex]F_1\cdot F_2=(12000*14500)+(7000*-5000)=174000000+(-35000000)=139000000[/tex]

Find the magnitude of each vector:

[tex]||F_1||=\sqrt{12000^2+7000^2}=1000\sqrt{193}\\||F_2||=\sqrt{14500^2+(-5000)^2}=500\sqrt{941}[/tex]

Find the angle between the two vectors:

[tex]\displaystyle \theta=\cos^{-1}\biggr(\frac{F_1\cdot F_2}{||F_1||||F_2||}\biggr)\\ \theta=\cos^{-1}\biggr(\frac{139000000}{(1000\sqrt{193})(500\sqrt{941})}\biggr)\\\theta\approx49.282^\circ\approx49^\circ[/tex]

Thus, C) 49° is the correct answer

Problem 13 (#20)

Using scalar multiplication, [tex]7v-2w=7\langle8,-3\rangle-2\langle-12,4\rangle=\langle56,-21\rangle-\langle-24,8\rangle=\langle56-(-24),-21-8\rangle=\langle80,-29\rangle=80i-29j[/tex]

Thus, A) -80i - 29j is the correct answer

Answer:

4/50

Step-by-step explanation:

12,24,36,48 are multiples of 12

Answer:

51

Step-by-step explanation:

5x^2 - x + 9

5(3^2) - 3 + 9

5(9) + 6

45 + 6

= 51

Answer:

4:9

Step-by-step explanation:

Find the area in inch first:

20 inch × 10 inch = 200 inch

Area in feet:

(20×15) + (10×15) = 450 inch

Area of the drawing : Area of the actual playground

200:450

Simplify it by dividing by 5

Last answer =4:9

Answer:

6.3

Step-by-step explanation:

151.2/24 in order to find out how many miles he drove per day

the answer is 6.3 miles per day

Answer:

6.3 Miles

Step-by-step explanation:

just divide 151.2 by 24.

Answer:

6825 in^3

Step-by-step explanation:

First break the shape into two shapes a square prism and triangular prism

the volume of a square prism is equal to s^2 * h

and the volume of a triangular prism is 1/2 b * l *h

square prism:

v = s^2 * h

v = 13^2 * 30

v = 5070 in^3

triangular prism:

v = 1/2 b * l * h

v = 1/2 * 9 * 30 * 13

v = 1755 in^3

then you add the two volumes to get the total volume

5070 + 1755 = 6825 in^3

Answer:

97.2 ft

Step-by-step explanation:

4 1/2*3*7 1/5=13.5*7.2=

97.2

Answer: 6 feet describes the center, and 9 feet describes the spread

Step-by-step explanation:

The center of a data set is mostly considered as the median or the mean

Here mean is 6 (given). And median is also 6. As 6 is exactly at the middle of the data set. (When arranged in ascending order)

Now, one of the way of calculating the spread is calculating the range, here it's given that the range is 9.

Therefore, 6 feet describes the center, and 9 feet describes the spread is correct.

Answer:

The length of the hypotenuse ≈ 39.7 cm

Explanation:

Since the given triangle is a right-angled triangle, this means that we can apply the Pythagorean theorem.

The equation for Pythagorean calculation is:

(hypotenuse)² = (first leg)² + (second leg)²

In the given, we have:

first leg = 30 cm

second leg = 26 cm

Substitute with the givens in the above equation to get the hypotenuse as follows:

(hypotenuse)² = (30)² + (26)²

(hypotenuse)² = 1576

This means that:

either hypotenuse = √1576 = 39.69 ≈ 39.7 cm ..........> accepted

or hypotenuse = -√1576 = -39.69 ......> rejected as length can't be negative

Hope this helps :)

The maximum amount, in dollars, the customer could have spent for the mounting kit after purchasing the television is $125.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the customer spend $x on television, and $y on mounting kit.

x + y = 500

x = 300 + 75 = 375

y = 500 - 375 = $125

Thus, the maximum amount, in dollars, the customer could have spent for the mounting kit after purchasing the television is $125.

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