Find the length of the unknown side. Round your answer to the nearest tenth.

Answer:

60°

Step-by-step explanation:

If it a equilateral triangle

Answer:

The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]

Step-by-step explanation:

Given - A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tall man is walking towards the wall at the rate of 30 feet per second.

To find - How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall ?

Proof -

From the given information, the figure becomes

Triangle ABC and Triangle DBE are similar triangle

AC/DE = BC/BE

⇒h/6 = 200/(200-x)

⇒h = 1200/(200 -x)

Now,

Differentiate h with respect to t, we get

[tex]\frac{dh}{dt} = 1200(-\frac{1}{(200-x)^{2} } )(-1)\frac{dx}{dt}[/tex]

⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-x)^{2} } )\frac{dx}{dt}[/tex]

Now,

If the rate of the tip is moving down the wall

At x = 50 feet, dx/dt = 30 feet per second

So,

⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-50)^{2} } )(30)[/tex]

⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)^{2} } (30)[/tex]

⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)(150) } (30)[/tex]

⇒[tex]\frac{dh}{dt} = \frac{24}{15 }[/tex]

So, we get

The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]

Answer:

6

Step-by-step explanation:

(6-3)+3=6

№3

[tex]\sin C = \frac{AB}{AC} = \frac{27}{45} = \frac{3 * 9}{5 * 9} = \frac{3}{5}[/tex]

Answer: D (3/5).

№4

[tex]\cos A = \frac{AB}{AC} = \frac{24}{30} = \frac{3 * 4 * 2}{3 * 5 * 2} = \frac{4}{5}[/tex]

Answer: C (4/5).

№5

[tex]\tan C = \frac{AB}{BC} = \frac{32}{24} = \frac{2 * 2 * 2 * 4}{2 * 2 * 2 * 3} = \frac{4}{3}[/tex]

Answer: D (4/3).

Answer:

3.) Sin C = option D, [tex]\frac{3}{5}[/tex]

4.) Cos A = option C, [tex]\frac{4}{5}[/tex]

5.) Tan C = Option D, [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

3.) Sin C = [tex]\frac{opposite}{hypotenuse} = \frac{27}{45} = \frac{3}{5}[/tex]

4.) Cos A = [tex]\frac{adjacent}{hypotenuse} = \frac{24}{30} = \frac{4}{5}[/tex]

5.) Tan C = [tex]\frac{opposite}{adjacent} = \frac{32}{24} = \frac{4}{3}[/tex]

Hope this helps!

Answer:0.143

Step-by-step explanation:

The slope of the tangent line to y(x) at any given x is equal to the derivative dy/dx at that point. Differentiate to get

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\boxed{4x-3}[/tex]

and evaluate it at x = 3 to get the slope, 4•3 - 3 = 9.

Answer:

need help too

Step-by-step explanation:

Answer:

5.13 feet...take the horizontal component using given data..

Answer:

35A) arc AC = 360-(100+110+80)=

360-290 = 70°

35B) L D = ½× 70 = 35°

35C) L AEC = ½(100+70)=½×170= 85°

35D) L P = ½(100-70) = ½×30 = 15°

Answer:

speed = 54.5 miles/hr

Step-by-step explanation:

speed = distance/time

distaance = 735.75

time = 7 + 6.5 = 13.5

speed = 735.75 / 13.5

speed = 54.5 miles/hr

Answer: 3. 1/3 + 1/4

Step-by-step explanation:

1/3 = 4/12

1/4 = 3/12

4/12 + 3/12 = 7/12

Answer:

71°

Step-by-step explanation:

31-3x+19x-5=90

16x=90-26

16x=64

x=4

m<R=19x-5 = 19(4)-5 = 76-5 = 71

Answer:

x = 4

∠R = 71°

Step-by-step explanation:

COMPLEMENTARY ANGLES: TWO ANGLES WITH A SUM OF 90°.

[tex]31 - 3x + 19x - 5 = 90[/tex]

To make this problem easier to solve, we can combine like terms.

[tex]26 + 16x = 90.[/tex]

Now, we can proceed.

First, subtract 26 from 26 and 90.

[tex]26 - 26 = 0.[/tex] (cancels itself out).

[tex]90 - 26 = 64.\\[/tex]

Now, we are left with 16x = 64.

Lastly, we divide the number in front of the variable by the answer.

[tex]64/16 = 4[/tex]

Therefore, the value of x is 4.

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

Now that we have the value of x, we can use this value to replace the variable (x).

[tex]19x - 5[/tex]

[tex]19 * 4 - 5 = 71.[/tex]

Therefore, the value of ∠R is 71°.

Answer:

Right circular cone

Solve for slant height

l=17cm

r Radius

8

cm

h Height

Answer:

[tex]18.83[/tex]

Step-by-step explanation:

For right triangles only, the tangent of an angle is equal to its opposite side divided by its adjacent side.

Therefore, we have the equation:

[tex]\tan 33^{\circ}=\frac{x}{29},\\x=29\tan 33^{\circ}\approx \boxed{18.83}[/tex]

Answer:

There is none there is no variable.

Step-by-step explanation:

Hope this helps!!

Answer:

there is no co efficient a co efficient is the constant before the variable when its attached.

9514 1404 393

Answer:

  900

Step-by-step explanation:

Let x represent the number. The given relationship is ...

  (3/5)x = 2 +(2/3)x

  -2 = 1/15x . . . . . . . . subtract 2+3/5x from both sides

  -30 = x . . . . . . . . . . multiply by 15

Then the square of the number is ...

  x² = (-30)² = 900

Answer:

[tex]\boxed{\pink{\tt I = \dfrac{1}{3}sin(3x) - 3cos(x) + C}}[/tex]

Step-by-step explanation:

We need to integrate the given expression. Let I be the answer .

[tex]\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]

[tex]\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}[/tex]

Answer:

1/12

Step-by-step explanation:

[tex] \frac{3}{4} - \frac{2}{3} = \frac{9 - 8}{12} = \frac{1}{12} [/tex]

9514 1404 393

Answer:

  (1, 2)

Step-by-step explanation:

PR and QR are vertical and horizontal line segments, respectively. Then ΔQPR is a right triangle, and segment PQ is the hypotenuse. As such, segment PQ is also a diameter of the circumcircle, and its midpoint is the circumcenter.

  Circumcenter = (P+Q)/2 = ((4, 0) +(-2, 4))/2 = (2, 4)/2

  Circumcenter = (1, 2)

Answer:

Graph has the greater unit rate.

Step-by-step explanation:

From the graph attached,

Since, graph shows the proportional relationship,

y ∝ x

y = kx

Here, k = unit rate

If the line given in the graph passes through (0.2, 1.5)

Slope of this line will be,

k = [tex]\frac{1.5}{0.2}[/tex]

k = 7.5

Therefore, unit rate = 7.5

Equation of the line given in the question is,

[tex]y=\frac{11}{2}x+3[/tex]

Comparing this equation with the y-intercept form of the equation,

[tex]y=mx+b[/tex]

Slope of this line 'm' = [tex]\frac{11}{2}[/tex]

                                  = 5.5

Unit rate of the given equation = 5.5

Therefore, graph has the greater unit rate.

If G is the incenter of ∆ABC, then GD = GF = GE.

Given, GD is 3x + 5 and GF is 6x - 4.

According to the above statement,

GD = GF

or, 3x + 5 = 6x - 4

or, 5 + 4 = 6x - 3x

or, 9 = 3x

or, 9/3 = x

or, 3 = x

The value of x is 3.

By putting the value of x in GD or GF, we get

GD = 3(3) + 5 = 9 + 5 = 14

GF = 6(3) - 4 = 18 - 4 = 14

Therefore, GE = 14.

Answer: f (t) = 200 . 0.88t =

Let's solve for f.

ft=(200)(0.88)t

Step 1: Divide both sides by t.

ft

t

=

176t

t

f=176

Answer:

f=176

Step-by-step explanation:

Answer:

D is the correct answer.......

Answer:

Answer C

Step-by-step explanation:

Answer:

answer c

Step-by-step explanation:

trust me

Answer:

The Solar System is the gravitationally bound system of the Sun and the objects that orbit it, either directly or indirectly. Of the objects that orbit the Sun directly, the largest are the eight planets, with the remainder being smaller objects, the dwarf planets and small Solar System bodies.

Step-by-step explanation:

Answer:

its 75

parallel angle degrees always should be 360

Answer:

c = (d/a) - b

Step-by-step explanation:

a(c + b) = d

Divide both sides by a

c + b = d/a

subtract b from both sides

c = (d/a) - b