Please help! I’m struggling!

Answer:

[tex]30^{\circ}[/tex].

Step-by-step explanation:

Let [tex]\theta[/tex] denote the unknown angle of elevation. Let [tex]h[/tex] denote the height of the tower.

Refer to the diagram attached. In this diagram, [tex]{\sf A}[/tex] denotes the top of the tower while [tex]{\sf B}[/tex] denote the base of the tower; [tex]{\sf BC}[/tex] and [tex]{\sf BD}[/tex] denote the shadows of the tower when the angle of elevation of the sun is [tex]60^{\circ}[/tex] and [tex]\theta[/tex], respectively. The length of segment [tex]{\sf AB}[/tex] is [tex]h[/tex]; [tex]\angle {\sf ACB} = 60^{\circ}[/tex], [tex]\angle {\sf ADB} = \theta[/tex], and [tex]{\sf BD} = 3\, {\sf BC}[/tex]..

Note that in right triangle [tex]\triangle {\sf ABC}[/tex], segment [tex]{\sf AB}[/tex] (the tower) is opposite to [tex]\angle {\sf ACB}[/tex]. At the same time, segment [tex]{\sf BC}[/tex] (shadow of the tower when the angle of elevation of the sun is [tex]60^{\circ}[/tex]) is adjacent to [tex]\angle {\sf ACB}[/tex].

Thus, the ratio between the length of these two segments could be described with the tangent of [tex]m\angle {\sf ACB} = 60^{\circ}[/tex]:

[tex]\begin{aligned}\tan(\angle {\sf ACB}) &= \frac{\text{opposite}}{\text{adjacent}} = \frac{{\sf AB}}{{\sf BC}}\end{aligned}[/tex].

[tex]\begin{aligned}\frac{{\sf AB}}{{\sf BC}} = \tan(60^{\circ}) = \sqrt{3}\end{aligned}[/tex].

The length of segment [tex]{\sf AB}[/tex] is [tex]h[/tex]. Rearrange this equation to find the length of segment [tex]{\sf BC}[/tex]:

[tex]\begin{aligned} {\sf BC} &= \frac{{\sf AB}}{\tan(\angle ACB)} \\ &= \frac{h}{\tan(60^{\circ})}\\ &= \frac{h}{\sqrt{3}} \\ &\end{aligned}[/tex].

Therefore:

[tex]\begin{aligned}{\sf BD} &= 3\, {\sf BC} \\ &= \frac{3\, h}{\sqrt{3}} \\ &= (\sqrt{3})\, h\end{aligned}[/tex].

Similarly, in right triangle [tex]{\sf ABD}[/tex], segment [tex]{\sf AB}[/tex] (the tower) is opposite to [tex]\angle {\sf ADB}[/tex]. Segment [tex]{\sf BD}[/tex] (shadow of the tower, with [tex]\theta[/tex] as the angle of elevation of the sun) is adjacent to [tex]\angle {\sf ADB}[/tex].

[tex]\begin{aligned}\tan(\angle {\sf ADB}) &= \frac{\text{opposite}}{\text{adjacent}} = \frac{{\sf AD}}{{\sf BD}}\end{aligned}[/tex].

[tex]\begin{aligned}\frac{{\sf AB}}{{\sf BD}} = \tan(\theta) \end{aligned}[/tex].

Since [tex]{\sf AB} = h[/tex] while [tex]{\sf BD} = (\sqrt{3})\, h[/tex]:

[tex]\begin{aligned}\tan(\theta) &= \frac{{\sf AB}}{{\sf BD}} \\ &= \frac{h}{(\sqrt{3})\, h} \\ &= \frac{1}{\sqrt{3}}\end{aligned}[/tex].

Therefore:

[tex]\begin{aligned}\theta &= \arctan\left(\frac{1}{\sqrt{3}}\right) \\ &= 30^{\circ}\end{aligned}[/tex].

In other words, the angle of elevation of the sun at the time of the longer shadow would be [tex]30^{\circ}[/tex].

Answer:

x=

1

3

y+

17

3

Step-by-step explanation:

This is all i can get so far, if can improve opon this let me know

All four sides of a square are congruent and they all equal 90 degrees

The sum of slip is 9 small coffee order, then sum is 11 medium coffee order, and when the sum is 6 or 14 large coffee is ordered.

Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.

A hat contains 4 slips of paper labeled as 3,3,6 and 8. One slip is selected randomly and without replacing, another one is selected. The number on the slips are added together.

The probability of getting a sum of 6 (3+3) is,

[tex]P_(3,3)=\dfrac{1}{4}\times\dfrac{1}{3}+\dfrac{1}{3}\times\dfrac{1}{4}\\P_(3,3)=\dfrac{1}{12}+\dfrac{1}{12}\\P_(3,3)=\dfrac{2}{12}\\P_(3,3)=\dfrac{1}{6}[/tex]

The probability of getting the sum of 9 (6+3) or (3+6) is,

[tex]P_(3,6)=\dfrac{1}{4}\times\dfrac{2}{3}+\dfrac{2}{4}\times\dfrac{1}{3}\\P_(3,6)=\dfrac{2}{12}+\dfrac{2}{12}\\P_(3,6)=\dfrac{4}{12}\\P_(3,6)=\dfrac{1}{3}[/tex]

The probability of getting the sum of 9 (6+3) or (3+6) is,

[tex]P_(3,8)=\dfrac{1}{4}\times\dfrac{2}{3}+\dfrac{2}{4}\times\dfrac{1}{3}\\P_(3,8)=\dfrac{2}{12}+\dfrac{2}{12}\\P_(3,8)=\dfrac{4}{12}\\P_(3,8)=\dfrac{1}{3}[/tex]

The probability of getting a sum of 6 (3+3) is,

[tex]P_(6,8)=\dfrac{1}{4}\times\dfrac{1}{3}+\dfrac{1}{3}\times\dfrac{1}{4}\\P_(6,8)=\dfrac{1}{12}+\dfrac{1}{12}\\P_(6,8)=\dfrac{2}{12}\\P_(6,8)=\dfrac{1}{6}[/tex]

There are three size of coffee to order:

Thus, when the sum of slip is 9 small coffee order, if sum is 11 medium coffee order, and when the sum is 6 or 14 large coffee is ordered.

Learn more about the arrangement here;

https://brainly.com/question/6032811

#SPJ1

Answer:

(-4,2)

Step-by-step explanation:

Kindly check the attatched image to see the system graphed

The two equations intersect at (-4,2) so the solution is (-4,2)

Answer:

D. 8x - 3

Step-by-step explanation:

Simply add all the sides up - 2x+3x+3x - 1+1+1 = 8x - 3

Step-by-step explanation:

Simplify the expression by using the Distributive Property.

For this expression, we'll be distributing. In simpler terms, multiplying 3 into the values inside the parentheses.

Think of the expression as;

[tex]3(3a-6)=(3 \times3a)+(3 \times -6)[/tex]

Multiply;

[tex]3 \times 3a=9a[/tex] (Multiply the whole number.)

[tex]3 \times -6=-18[/tex]

Your simplified expression is [tex]9a-18.[/tex]

Answer:

The answer is 3.2

Step-by-step explanation:

Answer:

260m

Step-by-step explanation:

the length and the width of a football field is 80m and 50 meters.

perimeter- (80+50)×2= 260m

hope it helps

Answer:

E and F.

Step-by-step explanation:

This can be written in quadratic formula.

x = -b +- √b² - 4ac/2a

The equation to solve is written as ax² + bx + c = 0.

a = 2, b = 7, c = 3

x = -7 +- √49 (7²) - 24 (4*2*3, or 4ac).

x = -7 +- √25

x = -7 +- 5

divide by 2a (4)

-7/4 = -1.75

5/4 = 1.25

now we do -1.75 +- 1.25

x = -1/2 (F.)

x = -3 (E.)
Sorry for the late response, I had made an error and had to fix it.

Answer: G

Step-by-step explanation:

1 pound equals =16 ounces

12.5 * 16=200

so 200 ounces.

Answer:

48

Step-by-step explanation:

Straight line=180 degrees

we already know one angle and thats 132

so we're trying to find the other angle demention so we do 180-132 and end up with 48

Hope that helps :)

Answer:

0.06

Step-by-step explanation:

Answer:

.06

Step-by-step explanation:

If 1 is 100%, then .06 is 6%.

Hope this helps!

Answer:

Question 1

F

T

T

The volume of figure A can be found by multiplying (5 · 7)(2).

Question 2

T

T

F

The total volume of the figure is 442 mm³

Question 3

T

F

T

The volume of the triangular prism is 108 in³

Step-by-step explanation:

Formula used

Volume of a prism = base area × height

Area of a rectangle = width × length

Area of a triangle = 1/2 × base × height

Volume of a cube = s³  (where s is the side length)

---------------------------------------------------------------------------------------------------

⇒ Volume of Figure A = (5 · 7)(2)

                                     = 70 cm³

⇒ Volume of Figure B = (13 · 7)(2)

                                     = 182 cm³

⇒ Total Volume = Volume of Figure A + Volume of Figure B

                           = 70 + 182

                           = 252 cm³

The first statement is false.

Rewritten statement:

The volume of figure A can be found by multiplying (5 · 7)(2).

---------------------------------------------------------------------------------------------------

⇒ Volume of rectangular prism = (15 · 15)(2)

                                                    = 450 mm³

⇒ Volume of central cube = 2³

                                            = (2 · 2 · 2)

                                            = 8 mm³

⇒ Total Volume = Volume of rectangular prism - Volume of cube

                           = 450 - 8

                           = 442 mm³

The third statement is false.

Rewritten statement:

The total volume of the figure is 442 mm³

---------------------------------------------------------------------------------------------------

⇒ Volume of rectangular prism = (12 · 3)(8)

                                                    = 288 in³

⇒ Volume of triangular prism = (1/2 · 12 · 6)(3)

                                                 = 108 in³

⇒ Total Volume = Volume of rectangular prism + Volume of triangular prism

                           = 288 + 108

                           = 396 in³

The second statement is false.

Rewritten statement:

The volume of the triangular prism is 108 in³

Answer:

Step-by-step explanation:

21   22    23   23   23   24   24   24   27   29

(23 + 24)/2= 47/2= 23.5 is the median temperature

Since the unit rate of Tito is greater than that of Jonah, hence Tito is running at a faster rate

The ratio of distance covered by an object to tme taken is unit rate.

Calculate the unit rate for both Jonah and Tito

For Jonah

Unit rate = 5laps/9minutes

Unit rate = 0.56 laps per minute

For Tito

Unit rate = 7laps/11.2minutes

Unit rate = 0.625laps per minute

Since the unit rate of Tito is greater than that of Jonah, hence Tito is running at a faster rate

Learn more on rate here: https://brainly.com/question/24304697

#SPJ1

Answer:

1125 m

Step-by-step explanation:

Given equation:

[tex]h=-5t^2+150t[/tex]

where:

Method 1

Rewrite the equation in vertex form by completing the square:

[tex]h=-5t^2+150t[/tex]

[tex]\implies h=-5t^2+150t-1125+1125[/tex]

[tex]\implies h=-5(t^2-30t+225)+1125[/tex]

[tex]\implies h=-5(t-15)^2+1125[/tex]

The vertex (15, 1125) is the turning point of the parabola (minimum or maximum point).  As the leading coefficient of the given equation is negative, the parabola opens downward, and so vertex is the maximum point.  Therefore, the maximum height is the y-value of the vertex: 1125 metres.

Method 2

Differentiate the function:

[tex]\implies \dfrac{dh}{dt}=-10t+150[/tex]

Set it to zero and solve for t:

[tex]\implies -10t+150=0[/tex]

[tex]\implies 10t=150[/tex]

[tex]\implies t=15[/tex]

Input found value of t into the original function and solve for h:

[tex]\implies -5(15)^2+150(15)=1125[/tex]

Therefore, the maximum height is 1125 metres.

Convert to vertex form y=a(x-h)²+k

Vertex at (15,1125)

As a is negative parabola is opening downwards hence vertex is maximum

Answer: $26

Step-by-step explanation:

   If $19.50 is 3/4, we need to find 4/4.

3/4 -> 0.75

4/4 -> 1

    We will set up a proportion and solve.

[tex]\frac{19.5}{0.75} =\frac{x}{1}[/tex]

19.5 = 0.75x

26 = x

         The professional ball is $26.

Answer:

$26

Step-by-step explanation:

19.50 = 3/4

so

to find 1/4, we do 19.50 / 3 = 6.5

6.5 = 1/4

so the price of a professional ball would be 4/4 (1 whole)

6.5 x 4 = 26

Hope this makes sense.

- profparis

The true statement about the two functions is:

"Both f(x) and g(x) increase on the interval of (–4 , ∞)."

Here we have the functions:

f(x) = log₂(4x)

g(x) = 4x - 3

That can be seen in the graph at the end. In the graph the green one is the logarithmic function.

As you can see there, both of these have similar ranges that go from (-∞, ∞) and both are increasing functions.

Then the correct statement is:

Both f(x) and g(x) increase on the interval of (–4 , ∞).

Where f(x) is actually increasing on all it's domain which is  (-∞, ∞), so the statement is true.

If you want to learn more about increasing functions:

https://brainly.com/question/4025726

#SPJ1

Answer:

Both f(x) and g(x) have a common domain on the interval (0, ∞).

Step-by-step explanation:

The person explained it perfectly in this link shown below

https://brainly.com/question/28219401?referrer=searchResults

pls give me brainist for finding the answer

Also, the answer to the question

"What type of function is f(x) = 2x^3 – 4x^2 + 5?"

A) Exponential

B) Logarithmic

C) Polynomial

D) Radical

The answer is C) Polynomial

Explanation:

The exponential equation would look like this: f(x) = 2^x

with x for the exponent

The logarithmic equation would look like this: f(x) = log2 + 4

with log in the equation

The radical equation would look like this: f(x) = x^2 + 4x -1

                                                                              3x^2 -9x +2

With divide by something

Answer:

x = 60

Step-by-step explanation:

Let x = ?

120 + 95 +85 +x =360

x +300 =360

x = 360-300

x = 60

Answer:

The answer is 240 degrees

Step-by-step explanation:

A full circle is 360 degrees.

We know one angle is 120 degrees.

360-120=240 degrees

Answer:

answer down below

Step-by-step explanation:

Answer:

[tex]C=20degrees[/tex]

Step-by-step explanation:

[tex]75 -55=20[/tex]

or [tex]20+55=75[/tex]

So the degrees of Angle C is [tex]20[/tex]

[tex]cos^{-1}[cos(\omega)]\implies \omega \\\\[-0.35em] ~\dotfill\\\\ cos\left( -\frac{\pi }{6} \right)\implies \stackrel{symmetry~identity}{cos\left( \frac{\pi }{6} \right)} \\\\\\ cos^{-1}\left[ cos\left( -\frac{\pi }{6} \right) \right]\implies cos^{-1}\left[ cos\left( \frac{\pi }{6} \right) \right]\implies \cfrac{\pi }{6}[/tex]

why did we use the positive version of π/6?

well, the inverse cosine function has a range of [0 , π], and -π/6 is on the IV Quadrant, out of the range for it, however it has a twin due to symmetry on the I Quadrant, that is π/6, thus the reason.

The angle in the interval (0, pi) whose cosine value is √3 / 2 is π/6 radians.

Cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse of a right angled triangle.

We have to find the angle in the interval (0, π) such that the cosine of the angle is √3 / 2.

We know that, ratio of sides of 30-60-90 triangle is 1 : √3 : 2.

Hypotenuse = 2x

Adjacent side to 30° = √3 x

Cos (30°) = Adjacent side / Hypotenuse

               = √3 x / 2x

               = √3 / 2

30 degrees is equivalent to 30 × (π/180) = π/6 in radians

Hence π/6 is the angle in the interval (0, π) whose cosine value is √3 / 2.

Learn more about Cosine Functions here :

https://brainly.com/question/17954123

#SPJ2

Answer:

36

Step-by-step explanation:

[tex] \frac{40}{32} = \frac{45}{?} \\ \frac{32 \times 45}{40 } = 36[/tex]

If quadrilateral H is a scaled copy of quadrilateral G then the value of i is 36.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.

Given that Quadrilateral H is a scaled copy of quadrilateral G.

Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.

The sides are proportional.

40/32 = 45/i

We have to find the value of i

Apply cross multiplication

40i=45(32)

40i = 1440

Divide both sides by 40

i = 1440/40

i = 36

Hence, if quadrilateral H is a scaled copy of quadrilateral G then the value of i is 36.

To learn more on Quadrilateral click:

https://brainly.com/question/29934440

#SPJ2

Answer:

So the answer is (15.8)