In a sightseeing boat near the base of the Horseshoe Falls at Niagara Falls, a
passenger estimates the angle of elevation to the top of the falls to be 30°.
If the Horseshoe Falls are 173 feet high, what is the distance from the boat
to the base of the falls?

Answer:

h = 28 inches

Step-by-step explanation:

Let the base of the triangle is b.

the height of the triangle is 4 inches less than four times its  base.

h = 4b-4

The area of the triangle is 112 inch².

The formula for the area of a triangle is given by :

[tex]A=\dfrac{1}{2}bh\\\\112=\dfrac{1}{2}\times b\times (4b-4)[/tex]

It is a quadratic equation, whose solution is as follows :

b = -7 and b = 8 inches

Height, h = 4(8)-4

= 32-4

= 28 inches

Hence, the height of the triangle is 28inches.

Answer:

The one all the way to the left (1 1/9 ft)

Step-by-step explanation:

You have to multiply Height x Width x length together.

Height will be 5/3 or 1.66

length side will have the lenght of 1

Width will be 2/3 or .66

So now you just have all of that. And you get 1.1 ( I multiplied the decimals )

And that was closest to 1 1/9

Answer:

It would take 10 years for the investment to reach 70 dollars.

Step-by-step explanation:

The investment would gain 2 dollars per year. So in 10 years it will gain 20 dollars.

f ( x ) = 3x - 1

g ( x ) = 2x - 3

_____________________

g ( x ) = f ( 2 )

2x - 3 = 3(2) - 1

2x - 3 = 6 - 1

2x - 3 = 5

2x - 3 + 3 = 5 + 3

2x = 8

2x ÷ 2 = 8 ÷ 2

x = 4

Answer:

: let's recall that the average value of a function for an interval of (a,b) is given by formula: k=1b−a∫baf(x)dx where; k:average value k=16−2∫62(x2−2x+5)dx k=14(∣∣∣x33−2x22+5x∣∣∣62) k=14(∣∣∣x33−x2+5x∣∣∣62) k=14[(633−62+5⋅6)−(233−22+5⋅2)] k=14[(2163−36+30)−(83−4+10)] k=14[(2163−6)−(83+6)] k=14[216−183−8+183] k=14[1983−263] k=14[1723] k=17212

QuestionThe average of a function over an interval is computed as (1/width of interval) times the definite integral of the function evaluated over the interval. The indefinite integral of e^2x is (1/2)e^2x. So the answer is found by evaluating:(1/2)*[(1/2)[e^8 - e^4]], or (1/4)[e^8 - e^4]which equals about 731.6.

More

Brainly.com

Question

Find the average value of f(x)=2/x over the interval [1, 3].

Answer · 0 votes

[tex] \bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll}average~rate\of~change\end{array}\\-------------------------------\\f(x)= \cfrac{2}{x} \qquad \begin{cases}x_1=1\x_2=3\end{cases}\implies \cfrac{f(3)-f(1)}{3-1}\implies \cfrac{\quad \frac{2}{3}-\frac{2}{1}\quad }{2}\\\\cfrac{\quad \frac{2-6}{3}\quad }{2}\implies \cfrac{\quad \frac{-4}{3}\quad }{\frac{2}{1}}\implies \cfrac{-4}{3}\cdot \cfrac{1}{2}\implies -\cfrac{2}{3} [/tex]

More

Wyzant

Question

Find the average value of the function f(x)=x^3 over the interval [0,2] and find the value(s) of x at which the function assumes the average values

Answer · 0 votes

The average value of f is defined as: 1/(b-a)∫ f(x) dx (where integral is evaluated from a to b) If we are to integrate f(x) = x3 we get: (1/4)* (x4) Applying formula for average value: [1/(b-a)]*[(1/4)*(x4)]a to b Evaluating this result where a = 0 and b = 2: [1/(2-0)]*[(1/4)*(x4)]a to b =(1/2)*[((1/4)*x4)]a to b =(1/2)*[((1/4)*(2)4) - (2*(0^4))] =(1/2)*[((1/4)*16)-0] =(1/2)*(4) =2

The average rate of change over the interval [a,b], or the secant line between the points a and b on the function f(x), is [f(a) - f(b)]/[a-b]. So, substitute a for 1 and b for 5, and you get [f(1) - f(5)]/[1–5]. The quotient of that is your average rate of change.

the average value of f(x) on [a,b] is ∫[a,b] f(x) dx ----------------------- b-a f' = 3x^2-6x f = x^3-3x^2+4 so, you want ∫[-1,3] x^3-3x^2+4 dx -------------------------- 3 - (-1) which I'm sure you can do.

1/2 e 2 - 1/2 or 3.19 Given: ​f(x)=2x 2 e 2x ​ [0​, 1​] The average value of a function is: Where: a and b -intervals [a,b] f(x) - given function Substitute the values to the formula: In the integration of the function, we will use integration by parts: Let: u = 2x 2 dv = e 2x dx For du, get the derivative of u: du = 2(2x 2-1 ) = 4x dx For v, integrate dv: v = 1/2 e 2x Substitute the values to the integration by parts formula, and plug it in the solution: Get the integration by parts of xe 2x dx and let: u = x dv = e 2x dx for du,get the derivative of x du = dx For v, integrate dv v = 1/2 e 2x Substitute the values to the integration by parts formula, and plug it in the solution: Final answer: The average value of the function is 1/2 e 2 - 1/2 or 3.19

Step-by-step explanation:

plz brian list Oh and the real answer is  k=17212

Answer:

A - 1,4

B -5,8

C -5,4

D -4,2

Step-by-step explanation:

im not shure how to explain

Answer:

A' ( -1, -4 )

B' (-5, -8 )

C' (-5, -4 )

D' ( -4, -2 )

Step-by-step explanation:

I took the test

Answer and Step-by-step explanation:

First, solve for the angle TRS, so that we can find the missing angle.

Subtract the two angles from 180 (because all triangle's angles add up to 180).

180 - 58 - 60 = 62.

By the vertical angles theorem, 62 is equal to the missing angle.

#teamtrees #PAW (Plant And Water)

Answer:

Step-by-step explanation:

31  ,  b/c it's the most common

c 32

Step-by-step explanation:

plz follow me wenelyn andoyo duay sana makatulong ako

Answer:

A

Step-by-step explanation:

Answer:

D. (w-3)/(w-7)

Step-by-step explanation:

(w+3)(w-3)/(w-7)(w+3)

Hence, removing (w+3),

(w-3)/(w-7)

Feel free to mark this as brainliest :D

Answer:

a^2

Step-by-step explanation:

Ia^2I if a<0

Since a^2 is always positive, we can remove the absolute value sign and nothing will change

a^2

Answer:

A. 339.12 cu. in

Step-by-step explanation:

I calculated it logically

Answer: I think your answer is right

Step-by-step explanation:

Answer:

irrational if it's more after this number but if it stops at the last 9 then it's a rational number

hope this helps

have a good day :)

Step-by-step explanation:

This is irrational if it's more after this number but,

If it stops at the last 9 then it's a rational number.

We have given that,

0.949449444944449444449.

An irrational number, any real number that cannot be expressed as the quotient of two integers.

We have to determine rational or irrational.

irrational if it's more after this number but.

If it stops at the last 9 then it's a rational number.

To learn more about the numbers visit:

https://brainly.com/question/251701

Answer:hmmm

Step-by-step explanation:

Answer:

143547

Step-by-step explanation:

1) Multiply the first 2 numbers: 7 x 2 = 14

2) Multiply the first and third numbers: 7 x 5 = 35

3) Now we get 14 and 35. Add both these numbers: 14 + 35 = 49

4) Now subtract the second number that is 2 from 49: 49 - 2 = 47

5) Hence, the answer is 143547

Thanks for giving such an interesting question! Loved it!

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

opposite side sides of a parallelogram are equal.

6x=3x+15

6x-3x=15

3x=15

x=15/3

x=5

y+5=2y-10

5+10=2y-y

15=y

Answer:

6 * m

Step-by-step explanation:

6m is is multiplication so should be the equivalent expression

Written out as words clearly says

six times a number

times meaning multiplication

Meaning any other expression is equivalent as long as it is a form of multiplication

If I'm wrong please tell me if not

Hope this helped :]

Answer:

[tex]f(x) = 2x + 5[/tex]

[tex]g(x) = (x - 6)^2[/tex]

Step-by-step explanation:

Given

(a) to (d)

Required

Which will give:

[tex]f(g(x)) = 2(x - 6)^2 + 5[/tex]

Equate the expression in bracket to g(x)

[tex]g(x) = (x - 6)^2[/tex]

Replace g(x) with x in: [tex]f(g(x)) = 2(x - 6)^2 + 5[/tex]

[tex]f(x) = 2x + 5[/tex]

Answer:

21, 24, 27, 30, 33, 36, 39.

Step-by-step explanation:

Answer:

multiples of 3 : 21, 24, 27, 30, 33, 36, 39.

multiples of 2 : 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40

Step-by-step explanation:

Answer:

[tex]\boxed {\boxed {\sf d=11}}[/tex]

Step-by-step explanation:

Since we want to find the distance between a pair of points, we use the following formula:

[tex]d =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

Where (x₁, y₁) and (x₂, y₂) are the points.

We are given the points E (-5, 4) and F (6,4). If we match the values and corresponding variables, we see that:

Substitute the values into the formula.

[tex]d= \sqrt{(6--5)^2+ (4-4)^2[/tex]

Solve inside the parentheses.

[tex]d= \sqrt{11)^2+(0)^2[/tex]

Solve the exponents.

[tex]d= \sqrt{121+0[/tex]

Add.

[tex]d= \sqrt{121}[/tex]

Solve the square root.

[tex]d= 11[/tex]

The distance between the 2 points is 11.

Answer:

6.9 million

Step-by-step explanation:

the median is the number that is in the middle or centre of a set of observations that is arranged either in an ascending or descending order.

Arrange the land areas in ascending order :

3.3, 3.8, 5.4, 6.9, 9.4, 11.7, 17.3

the number in the middle is the 4th number which is 6.9

Answer:

TRUE

FALSE

FALSE

TRUE

Step-by-step explanation:

yan na po god bless

Answer:

that can't be the right graph because it is not purple and black or has the right information needed to answer this question

Step-by-step explanation:

Is there a graph that goes with this question?

I really want to help but this is not it

Answer:

4

Step-by-step explanation:

To find slope without a graph, you subtract the 2 y-coords and the 2 x-coords, then divide the y-coord by the x-coord.

The formula is (y²-y¹)/(x²-x¹).

So we just plug in the coordinates.

(10-(-2))/(7-4)

(10+2)/(7-4)

12/3

4

So the slope is 4.

---

hope it helps

The slope of the line passing through (4, -2) and (7, 10) is,

⇒ m = 4

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)

We have to given that;

Two points on the line are (4, -2) and (7, 10).

Since, The equation of line passes through the points (4, -2) and (7, 10).

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

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (10 - (-2)) / (7 - 4)

m = 12 / 3

m = 4

Thus, The slope of line = 4

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ2

Answer:

yes both questions the answer are equal

Step-by-step explanation:

(3,5) where 3 is the x coordinate and 5 is the y coordinate

putting it into y=5x-10

5=5(3)-10

5=5

(4,5) where 4 is the x coordinate and 5 is the y coordinate

putting it into y=2x-3

5=2(4)-3

5= 5

Answer:

Step-by-step explanation:

As you can see from the value in the middle of the questions, the domain refers to all the possible x-values (input values) while the range refers to all the possible f(x) values (output values :: y-values). Therefore, for the domain, since the endpoints of the graph are closed circles it means that they are included so the domain would be ...

Domain: -9 ≤ x ≤ 7

The range would be the lowest and highest included y-value on the graph which in this case would be ...

Range: -6 ≤ f(x) ≤ 4

Answer: The equation is 25x + 100

Step-by-step explanation: