A hiking trail down the side of Mt. Tom drops a vertical distance of 60 meters over a horizontal distance of 300 meters. What is the slope of the trail? Express your answer as a reduced fraction.

Answer:

yes

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer: Im confused?

Step-by-step explanation:

Answer:

[tex]\displaystyle \frac{dy}{dx} = -40x \sin (5x^2) \cos^3 (5x^2)[/tex]

General Formulas and Concepts:

Calculus

Differentiation

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

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:

Step 1: Define

Identify

[tex]\displaystyle y = \cos^4 (5x^2)[/tex]

Step 2: Differentiate

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

Unit: Differentiation

9514 1404 393

Answer:

  a) correct

  b) needs parentheses: -1, (1±i√2)/3

Step-by-step explanation:

a) You can factor by grouping:

  (x³ -2x²) -(5x -10) = x²(x -2) -5(x -2) = (x² -5)(x -2)

Roots are ±√5, 2.

__

b) The sum of odd-degree coefficients is equal to the sum of even-degree coefficients (3-1 = 1+1), so one root is x=-1. Factoring out that leaves the quadratic factor ...

  3x³ +x² -x +1 = (x +1)(3x² -2x +1)

The quadratic formula can be used on the quadratic factor to find its roots:

  x = (-(-2) ±√((-2)²-4(3)(1)))/(2(3)) = (2 ±√-8)/6 = (1 ±√-2)/3

Roots are -1, (1 ±i√2)/3.

Answer:

x(x+1)=6​

Step-by-step explanation:

6= 2 numbers, one after the other, so you have the same number and add 1 to make the second number.

Example:

6=2.5 and 3.5

Answer:

X * (x+1) = 6

Step-by-step explanation:

Answer:

x = 4

QS = 20

Step-by-step explanation:

PS is all the numbers added together.

PQ + QR + RS = PS

(PLUG IN)

8 + 3x - 1 + 9 = 28 (collect like terms)

3x + 16 = 28 (subtract 16 on both sides)

3x = 12 (divide by 3 on both sides)

x = 4

QR + RS = QS

(PLUG IN)

3(4) - 1 + 9 = QS (distribute)

12 - 1 + 9 = QS (collect like terms)

20 = QS

Hope this helps ya!!

Answer:

5,6 meaning the answer is 4

Step-by-step explanation:

Answer:

40 meters

Step-by-step explanation:

Answer:

x = 60°

Step-by-step explanation:

According to the Outside Angles Theorem, the angle formed by the two tangents in the diagram above is equal to half of the difference of the measures of two arcs  that are intercepted.

Therefore:

[tex] x = \frac{1}{2}(360 - 120) - 120) [/tex]

[tex] x = \frac{1}{2}(240 - 120) [/tex]

[tex] x = \frac{1}{2}(120) [/tex]

x = 60°

Answer:

1 pound of grapes cost 3$

Step-by-step explanation:

If 2 pounds of grape cost 6$ then 1 pound of grape cost 3$ Since 1 is half of 2 and 3 is half of 6

Answer:

Step-by-step explanation:

Please see attached a sketch of the television

the size of a television is described by the length of its diagonal in inches.

in this case, the diagonal of the television is 48"

we are told that the aspect ratio is 16:9

hence the dimension of the television as seen from the draft is

length= 16x

height=9x

Applying Pythagoras theorem

(16x)^2+(9x)^2= 48^2

256x^2+81x^2=2304

337x^2=2304

divide both sides by 337 we have

x^2=2304/337

x^2=6.8367

x=√6.8367

x=2.6

What is the height

H=9x

=9(2.6)

=23.5"

Answer:

6th: 2 girl groups of 32 and 2 boy groups of 36

7th: 3 girl groups of 27 and 3 groups of 21

8th: 2 girl groups of 34 and 2 boy groups of 30

Sorry if it's wrong, had a little trouble understanding.

This question is incomplete, the complete question is;

Find the gradient of the function g(x,y)= xy² at the point (5, - 1). Then sketch the gradient together with the level curve that passes through the point.

First find the gradient vector at (5, - 1).

Vg(5,- 1) = [ ]i - [ ]j (Simplify your answers.)

Choose the graph that shows the level curve and the gradient vector at (5, - 1).

options of the sketched graphs are uploaded along this answers

Answer:

Vg(5,- 1) = [ 1 ]i - [ 10 ]j

Option A is the correct graph for this Level

Step-by-step explanation:

Given that;

g(x,y) = xy²

we have to find gradient of this function at ( 5, -1 )

so

Δg(x,y) = dg/dx + dg/dy

d(g)/dx = y² ,       dg/dy = 2gx

therefore

Δg(x,y) = [y²]i + [2yx]j

Δ( 5, -1) = [-1²]i + [2×-1 ×5]j

=Δ(5, -1) = 1i - 10j

[ 1 ]i - [ 10 ]j

Therefore Option A is the correct graph for this Level

Answer:

take any 2 sides and equate it

then u will get the value of x then then take the aside and put the value of x u will get the answer

Answer:

pi/2 and 3pi/2

Step-by-step explanation:

on edge

The required solutions to sin(2x) = 2cos(x) are the following as :  [tex]\:x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n[/tex].

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The equation of trigonometry functions is given in the question:

sin(2x) = 2cos(x)

We have to determine the solution to the given trigonometry equation

As per the question, we have

⇒ sin(2x) = 2cos(x)

Rewrite the above trigonometry equation,

⇒ sin(2x) - 2cos(x) = 0

⇒ 2sin(x)cos(x) - 2cos(x) = 0

Common factor out from the equation,

⇒ 2cos(x)[sin(x) - 1] = 0

Solving each part separately

2cos(x) = 0 and sin(x) - 1 = 0

cos(x) = 0 and sin(x) = 1

[tex]\:x=\frac{\pi }{2}+2\pi n, and \:x=\frac{3\pi }{2}+2\pi n[/tex].

Thus, the required solutions to sin(2x) = 2cos(x) are the following:  [tex]\:x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n[/tex].

Learn more about Trigonometric functions here:

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Answer:

Box 1= 1

Box 2 =-8

Box 3= -2

Step-by-step explanation:

Plug in the numbers that are provided where you see x

-3(x) +8    x=3

Answer:

i dont see it

Step-by-step explanation:

Answer:

Number 7.

since it makes an L shape, and has a 90° angle

Answer:

x + 46

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define expression

4(-8x + 5) - (-33x - 26)

Step 2: Simplify

Answer:

The amount of weight added is 26,729.7 pounds

Step-by-step explanation:

Here, we are told that a gallon of water weighs 8.34 pounds

Now, we want to find the weight of 3,205 gallons of water

Mathematically, that would be;

3,205 * 8.34 = 26,729.7 pounds

Answer:

You buy 10.5 pounds of the $6.50/lb nuts and 4.2 pounds of the $8.60/lb nuts.

Step-by-step explanation:

Let x be the number of pounds of the cheaper nut.

6.5x + 8.6(14.7-x) = 7.1*14.7

6.5x + 126.42 - 8.6x = 104.37

2.1x = 22.05

x = 10.5

Answer:

I got - 6.70820393 i

Step-by-step explanation:

let me know if I am wrong :)

You should first make 7 3/7 and 3 3/5 into improper fractions that would be 52/7 and 18/5 then we can add but we have to make them equivelent in order to do so.  

52/7 = 260/35

18/5 = 126/35

Add 260 and 126 and we will get 386/35 but remember we still have to make it a mixed number so we finally get the answer of 11 1/35

Answer:12x-157-5.2x

Step-by-step explanation:Like this or you want us to solve it lol

The given equation can be written in logarithmic form as  xlog(2) + log(3 × 2ˣ - 5) = log(157).

Logarithm function is defined as the inverse of the exponential function.

If a^(b) = c, then b = log(c) at the base of a.

Logarithm of any number is always positive.

For negative numbers, the logarithm are complex numbers.

The given equation is [tex]3(2^{2x}+3)-5(2^{x} + 2)-156 = 0[/tex]

Suppose 2ˣ be t, then the equation can be rewritten as,

3(t² + 3) - 5(t + 2) - 156 = 0

⇒ 3t² - 5t = 157

⇒ t(3t - 5) = 157

Take logarithm both sides to get,

log(t(3t - 5)) = log(157)

Use the property log(ab) = log(a) + log(b) to get,

log(t) + log(3t - 5) = log(157)

Substitute t = 2ˣ as and apply log(aⁿ) = nlog(a) as,

xlog(2) + log(3 × 2ˣ - 5) = log(157)

Hence, the logarithm form of the given equation is obtained as xlog(2) + log(3 × 2ˣ - 5) = log(157).

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Answer:

y = -7

Step-by-step explanation:

Minus the five from both sides

Answer:

Y = -7

Step-by-step explanation:

subtract 5 from both sides

-7 = y