Question 6 of 10
sin(7pie/6)=

Complete question

A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.

What is the rate of change of the distance between the bottom of the ladder and the wall at that instant(in meters per minute)

Answer:

[tex]\frac{dx}{dt}=11.94m/min[/tex]

Step-by-step explanation:

From the question we are told that

Slant height [tex]z=29m[/tex]

Change in Vertical height  [tex]\triangle y=7m/s[/tex]

Horizontal length [tex]x=21[/tex]

Generally in finding the distance form the  top to the bottom of the wall it is mathematically given by

 [tex]x^2+y^2=z^2[/tex]

 [tex]21^2+y^2=29^2[/tex]

 [tex]y^2=29^2+21^2[/tex]

 [tex]y=35.81[/tex]

Generally solving for the differential equation is mathematically represented as

 [tex]x^2+y^2=29^2[/tex]

 [tex]2x*\frac{dx}{dt} +2y*\frac{dy}{dt} =0[/tex]

 [tex]x*\frac{dx}{dt} +y*\frac{dy}{dt} =0[/tex]

 [tex](21)*\frac{dx}{dt} +(35.81)*(-7) =0[/tex]

 [tex](21)*\frac{dx}{dt} -250.64 =0[/tex]

 [tex]\frac{dx}{dt}=\frac{250.64}{21}[/tex]

 [tex]\frac{dx}{dt}=11.94m/min[/tex]

The rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.

Let us consider that distance between the top of the ladder and the ground is x meter and distance between the bottom of the ladder and the wall is y meter.

So, A right angle triangle is formed.

Since, the bottom of the ladder is 21 meters from the wall.

So,    [tex]y=21[/tex]

Applying Pythagoras theorem,

                         [tex]x^{2} +y^{2}=(29)^{2} \\\\x^{2} +(21)^{2}=(29)^{2} \\\\\\x^{2} =841-441=400\\\\x=\sqrt{400} =20[/tex]

Given that,   the distance between the top of the ladder and the ground is decreasing at 7 meters per minute.

                           [tex]\frac{dx}{dt}=-7meter/min[/tex]

Differentiate below equation with respect to time.

                     [tex]x^{2} +y^{2}=(29)^{2} \\\\2x\frac{dx}{dt}+2y\frac{dy}{dt}=0 \\\\2(20)(-7)+2(21)\frac{dy}{dt}=0\\\\\frac{dy}{dt}=\frac{280}{42}=6.67meter/min.[/tex]

Thus, the rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.

Learn more about Differentiation here:

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Answer:

5x + 15

Step-by-step explanation:

3(2x + 5)-x

6x + 15 - x

5x + 15

Hope this Helps!!!

Answer:

1x²+5 x 6x

Step-by-step explanation:

Answer:

I'm sorry but I have no clue. Actually I think it's C.

Step-by-step explanation:

Answer:

median: 44

first quartile: 25

third quartile: 61.5

interquartile range: 36.5

Step-by-step explanation:

For the given data set median is 44, first quartile is 25, third quartile is 61.5 and interquartile range is 36.5.

The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.

Formula to find the interquartile range is Interquartile range = Upper Quartile - Lower Quartile =Q2=Q3-Q1

The given date set is 28,46,25,76,18,25,47,83,44.

The data in order 18,25,25,28,44,46,47,76,83.

Here,

Median =44

First quartile=Q₁=25

Third quartile=Q₃= (47+76)/2

= 61.5

Now, interquartile range (IQR)

= Q₃-Q₁

= 61.5-25

= 36.5

Therefore, for the given data set median is 44, first quartile is 25, third quartile is 61.5 and interquartile range is 36.5.

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Answer:

a(7) = 21

Step-by-step explanation:

Using the recursive formula and a(1) = 0, a(2) = 1 , then

a(3) = a(2) + 2a(1) = 1 + 2(0) = 1 + 0 = 1

a(4) = a(3) + 2a(2) = 1 + 2(1) = 1 + 2 = 3

a(5) = a(4) + 2a(3) = 3 + 2(1) = 3 + 2 = 5

a(6) = a(5) + 2a(4) = 5 + 2(3) = 5 + 6 = 11

a(7) = a(6) + 2a(5) = 11 + 2(5) = 11 + 10 = 21

For this problem, we're finding the percent of 300. To do that we:

1. Multiply 300 by 15.

300 x 15 = 4500

2. Divide 4500 by 100. (% = 100)

4500 / 100 = 45

Therefore, the unit price is 45. But we're not done. We need to subtract 45 by 300.

300 - 45 = 255

Now, our answer is 255 and the unit price is 45.

Let me know of any questions!

Answer:

[tex]F = 1.8C +32[/tex]

[tex]F = 86^{\circ}F[/tex]

Step-by-step explanation:

Represent Celsius with C and Fahrenheit with F.

So, we have:

[tex](C_1,F_1) = (100,212)[/tex]

[tex](C_2,F_2) = (0,32)[/tex]

Solving (a): Represent as a linear equation

First, we calculate the slope:

[tex]m = \frac{F_2 - F_1}{C_2 - C_1}[/tex]

This gives:

[tex]m = \frac{32 - 212}{0 - 100}[/tex]

[tex]m = \frac{-180}{- 100}[/tex]

[tex]m = 1.8[/tex]

The linear equation is then calculated using:

[tex]F - F_1 = m(C -C_1)[/tex]

Where

[tex](C_1,F_1) = (100,212)[/tex]

[tex]m = 1.8[/tex]

[tex]F - 212 = 1.8(C -100)[/tex]

[tex]F - 212 = 1.8C -180[/tex]

Make F the subject

[tex]F = 1.8C -180+212[/tex]

[tex]F = 1.8C +32[/tex]

Solving (b): The value of F when C = 30

Substitute 30 for C in [tex]F = 1.8C +32[/tex]

[tex]F = 1.8 * 30 + 32[/tex]

[tex]F = 54 + 32[/tex]

[tex]F = 86[/tex]

Answer:

person above me is wrong

Answer:

118

Step-by-step explanation:

15(8)-2

120-2

118

Brainly plss?

Answer:

118

Step-by-step explanation:

you do 15 x 8 then subtract 2 from the product

Step-by-step explanation:

1st point=(-2,2)x1=-2,y1=2

2nd point=(3,-2)x2=3,y2=-2

slope=y2-y1/x2-x1

According to the question,

slope=-2-2/3-(-2)=-4/5

Answer:

C spinner with 7 equal sides

Step-by-step explanation:

Answer: Yes. They'll both make 4 apple pies.

Step-by-step explanation:

Jennifer makes 13 apple pies using 338 apples. The fraction of apple pies made based on the number of apples will be:

= 13 / 338

= 0.03485

Mateo used 9 apple pies using 216 apples. The fraction of apple pies made based on the number of apples will be:

= 9 / 216

= 0.0417

When they each have 105 apples, the number of apple pies that Mateo will make will be:

= 0.03485 × 105

= 3.65925

= 4 apple pie approximately

Jennifer will make:

= 0.0417 × 105

= 4.3785

= 4 apple pie approximately

Answer:

6

Step-by-step explanation:

3x+11 = 29

3x =  29 - 11 = 18

x = 18/3 = 6

Answer:

Step-by-step explanation:

The two triangles are congruent. The diagonal is equal to itself in both triangles.

Triangle XYW = Triangle XYZ  by SSS

Answer:

[tex]\frac{9}{10}[/tex] ÷ [tex]\frac{3}{5}[/tex]

=3/5

=1.5

Step-by-step explanation:

4(2x-1)+3(2x+5)

8x-4+6x+15

8x+6x-4+15

14x+11

Answer:

14x +11

Step-by-step explanation:

4(2x-1)+3(2x+5)=8x-4+6x+15

=14x+11

Answer:

15.51

Step-by-step explanation:

Answer:

15.51

Step-by-step explanation:

The calculator is $49.50.

The radio is $114.99.

First, we add them together.

49.50+114.99 = 164.49

that is the total cost of both the radio and calculator.

Next, we subrtact  180.00-164.49= 15.51.

Answer:

Yes (2,7) Is A solution of the system

Step-by-step explanation:

Answer:

7241.25 mm squared

Step-by-step explanation:

The surface area of a cylinder is denoted by: , where r is the radius and h is the height.

Here, we know that the diameter is 39.2 mm, and since diameter is twice the radius, then r = d/2 = 39.2/2 = 19.6 mm. We also know that the height is 39.2 mm

using this formula for surface area of cyclinder: 2πrh+2π

diameter = 2r --> 39.2 = 2r

so r= 19.6

The answer is 7241.25 mm squared.

↓Practice Provided Below ↓

Answer:

*8

Step-by-step explanation:

6.75*8=54

Answer:

8

Step-by-step explanation:

..…..............…...

Answer:

$2650

Step-by-step explanation:

= 2000 × 0.0325 × 10 = 650

= $ 650.00

Answer:

56.55m³

Step-by-step explanation:

use a calculator, not brainly

Answer:

78.75 ?

Step-by-step explanation:

calculator..

The volume of water remain in the tank after 30 seconds is 78.75 liters.

The given parameters;

The amount of water drained after 30 seconds is calculated as follows;

[tex]V_1 =2.5 \ \frac{liters}{\min} \times \frac{1 \min}{60 \ s} \times 30 \ s\\\\V_1 = 1.25 \ liters[/tex]

The volume of water remain in the tank after 30 seconds is calculated as follows;

V₂ = V₀ - V₁

V₂ = 80 liters - 1.25 liters

V₂ = 78.75 liters

Thus, the volume of water remain in the tank after 30 seconds is 78.75 liters.

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[tex]\tt{PQ=TS }[/tex]

[tex]\tt{ PW=TW }[/tex]

[tex]\tt{ QW=SW }[/tex]

SO,

it is S-S-S

side-side-side

Answer:

graph the point (0, -5) and from that point go up 1 unit and to the right 5 units (5, -4) and plot that point; connect the two points

Step-by-step explanation:

Here it's given that ∆ABC is a isosceles triangle. We know that in a isosceles triangle opposite angles are equal. And the angles opposite to equal sides are also equal.

Hence here ,

Figure :-

[tex] \setlength{\unitlength}{1 cm}\begin{picture}(12,12)\put(0,0){\line(1,0){4}}\put(4,0){\line(-1,2){2}}\put(0,0.001){\line(1,2){2}}\put(0,0.01){\line(1,1){2}}\put(3.99,0){\line(-1,1){2}}\put(0,-0.3){$\bf B $}\put(4,-0.3){$\bf C$}\put(2,4.2){$\bf A$}

\put(1.8,2.2){$\bf o$}\end{picture}[/tex]

If LaTeX doesn't work on app kindly see the attachment .

Here we will use a theorem which is ,

[tex]\large\underline{\underline{\textsf{\textbf{\red{\blue{$\leadsto$} Theorem :- }}}}}[/tex]

Hence here,

[tex]\tt:\implies \angle ABC =\angle ACB \\\\\tt:\implies \dfrac{1}{2}\times \angle ABC = \dfrac{1}{2}\times \angle ACB \\\\\tt:\implies \boxed{\bf \blue{\angle OBC = \angle OCB} }[/tex]

Now in ∆OBC , we can see that ∠OBC = ∠OCB. (just proved ) . Hence we can say that sides OB and OC are equal. Since the sides opposite to equal angles are equal. Therefore in ∆OBC , two sides are equal.

Therefore ∆ OBC is an isosceles triangle.

Answer:

See Below.

Step-by-step explanation:

We are given the isosceles triangle ΔABC. By the definition of isosceles triangles, this means that ∠ABC = ∠ACB.

Segments BO and CO bisects ∠ABC and ∠ACB.

And we want to prove that ΔBOC is an isosceles triangle.

Since BO and CO are the angle bisectors of ∠ABC and ∠ACB, respectively, it means that ∠ABO = ∠CBO and ∠ACO = ∠BCO.

And since ∠ABC = ∠ACB, this implies that:

∠ABO = ∠CBO =∠ACO = ∠BCO.

This is shown in the figure as each angle having only one tick mark, meaning that they are congruent.

So, we know that:

[tex]\angle ABC=\angle ACB[/tex]

∠ABC is the sum of the angles ∠ABO and ∠CBO. Likewise, ∠ACB is the sum of the angles ∠ACO and ∠BCO. Hence:

[tex]\angle ABO+\angle CBO =\angle ACO+\angle BCO[/tex]

Since ∠ABO =∠ACO, by substitution:

[tex]\angle ABO+\angle CBO =\angle ABO+\angle BCO[/tex]

Subtracting ∠ABO from both sides produces:

[tex]\angle CBO=\angle BCO[/tex]

So, we've proven that the two angles are congruent, thereby proving that ΔBOC is indeed an isosceles triangle.