Help plz 20 points question is in the pic

Answer:

[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex] at [tex]x=12[/tex]

Step-by-step explanation:

[tex]\frac{dx}{dt}=2[/tex]

[tex]\frac{d\theta}{dt}=?[/tex]

[tex]x=12[/tex]

[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]

[tex]cos(\theta)=\frac{x}{13}[/tex]

[tex]\frac{d}{dt}cos(\theta)=\frac{d}{dt}\frac{x}{13}[/tex]

[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}\frac{dx}{dt}[/tex]

[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}(2)[/tex]

[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{2}{13}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]

[tex]cos(\theta)=\frac{x}{13}[/tex]

[tex]cos(\theta)=\frac{12}{13}[/tex]

[tex]\theta=cos^{-1}(\frac{12}{13})[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(cos^{-1}(\frac{12}{13}))}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-13(\frac{5}{13})}[/tex]

[tex]\frac{d\theta}{dt}=\frac{2}{-5}[/tex]

[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex]

The value of θ is given by the inverse sine function, from which the rate of

change of θ with respect to x can be derived.

Reasons:

[tex]\displaystyle \frac{dx}{dt} = \mathbf{2 \ units \ per \ second}[/tex]

[tex]\displaystyle cos(\theta) = \frac{x}{13}[/tex]

[tex]\displaystyle \theta = arccos \left(\frac{x}{13}\right)[/tex]

[tex]\displaystyle \frac{d}{dx} \theta = \frac{d\left(arccos \left(\frac{x}{13}\right)\right)}{dx} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}}[/tex]

Using chain rule of differentiation, we have;

[tex]\displaystyle \frac{d\theta}{dt} = \mathbf{ \frac{d\theta}{dx} \times \frac{dx}{dt}}[/tex]

Therefore;

[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-x^2} }{x^2-169}\times \frac{dx}{dt} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}\times 2}[/tex]

When x = 12, we get;

[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-12^2} }{12^2-169}\times 2 = -\frac{2}{5} = -0.4[/tex]

The rate of change of the angle, θ, with time at the instant when x = 12 is -0.4 rad/s

Learn more about rate of change here:

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Answer:

C

Step-by-step explanation:

i need a points point muna

Answer:

burrito

Step-by-step explanation:

burrito

Answer:

16

Step-by-step explanation:

[tex]2 \times (4 + (12 + 16) \div 7 \\ (12 + 16) = 28 \div 7 = 4 + 4 = 8 \\ 2 \times 8 = 16[/tex]

Answer:

$o.44

Step-by-step explanation:

20/100×0.55 =0.11

0.55-0.11 = 0.44

Answer:

3

Step-by-step explanation:

The two numbers are 3 and 7, and 3 is the smaller one

Step-by-step explanation:

x, y are the 2 numbers.

x + y = 10

y - x = 4

that gives us

y = x + 4

and we use that in the first equation :

x + x + 4 = 10

2x = 6

x = 3

y = x + 4 = 3 + 4 = 7

so, yes, the smaller number is 3.

1. Assuming OP || NM, considering the triangle proportionality theorem possible measurements for the segments are: ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units

2. The possible values are decided by assuming  [tex]\frac{ON}{LO} = \frac{PM}{LP} = 3[/tex] using the triangle proportionality theorem.

3. Another method is applying the AA Similarity Theorem to compare corresponding side lengths of the triangles that are proportional to each other.

Triangle proportionality theorem states that if a line is parallel to one of the sides of a triangle intersects two of the other two sides, it divides the two sides into proportional corresponding segments.

1. Assuming that OP || NM, we would apply the triangle proportionality theorem to have the following ratio:

[tex]\frac{ON}{LO} = \frac{PM}{LP}[/tex]

Using the above ratio, we can choose the following possible lengths for the segments:

ON = 3 units

LO = 1 unit

PM = 6 units

LP = 2 units

2. The values are decided assuming that the ratio, [tex]\frac{ON}{LO} = \frac{PM}{LP} = 3[/tex]

This means that the ratio of the proportional segments, irrespective of the their measurement should give you an assumed equal ratio of 3:1.

Therefore, since:

[tex]\frac{3}{1} = 3\\\\\frac{6}{2} = 3[/tex]

The measurements, ON = 3 units, LO = 1 unit, PM = 6 units, LP = 2 units are therefore possible measurements.

3. Using the AA Similarity Theorem to prove that ΔLPO ≅ ΔLMN, the corresponding sides of both triangles will be proportional.

LP/LM = LO/LN = PO/MN

We can use this to choose possible measurements while assuming a ratio between the proportional sides of both triangles.

Let's assume that: LP/LM = LO/LN = PO/MN = 1/4

Let,

LO = 1 unit

LN = 4 units

Therefore, ON = LN - LO = 4 - 1 = 3 units.

Same way the other possible measures can be gotten provided a ratio is assumed.

Learn more about triangle proportionality theorem on:

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Answer:

24

Step-by-step explanation:

a - and a - make a +

so -3 x -8 becomes positive

so 3 x 8 = 24

Answer:

Step-by-step explanation:

Given system of linear equations:

Add up the equations to eliminate y:

Find y:

Answer:

6

Step-by-step explanation:

im not sure but I think 6 is the answer

we have:   4x - t = a ⇒ 4x = a + t ⇒ x = [tex]\frac{a+t}{4}[/tex]

ANSWER: x = [tex]\frac{a+t}{4}[/tex]

ok done. Thank to me :>

Answer:

0.274714403

Step by step explanation:

Step-by-step explanation:

the answer should be 1004

Answer:

your welcome... hope this helps

Step-by-step explanation:

Answer:

2x - 3y = 19

Step-by-step explanation:

y=(-5--1)/(2-8)*(x -8)+-1

y=-4/-6(x-8)-1

3y=2x-16-3

3y=2x-19

2x-3y=19

Tan(48.9) = x/138

X = 138 x tan(48.9)

X = 158.2

Step-by-step explanation:

Male ratio: 204:306 = 2:3 (66%)

Female ratio: 180:420 = 3:7 (42%)

Hope that helps

Answer:

both are non smokers is 0.48.

Answer: B. (-3, 0)

Step-by-step explanation:

y = -3x - 9...(1)

y = 3x + 9...(2)

Substitute (1) into (2)

3x+9=-3x-9

6x=-18

x=-3

Substitute y=0 into (1)

y=3(-3)+9

y=0

Therefore, the solution to the system is the ordered pair (-3, 0)

Answer:

9/25

Step-by-step explanation:

find a number that both the top and bottom are divisible by,

23 is the greatest common division we can make such that the top and bottom remain whole numbers

so,

[tex]\frac{207 }{575}[/tex] ÷23

=(207/23)÷(575/23)

=[tex]\frac{9}{25}[/tex]

Answer:

the first number is 75 and the second number is 100

Answer:

options a is answer

Step-by-step explanation:

options a is answer

Answer: 64€

Step-by-step explanation:

89 - 25 = 64

Can i have brainliest

Answer:

64 cents

Step-by-step explanation:

Assuming the 'c' symbol represents an American currency symbol

Answer:

Shop Y

Step-by-step explanation:

In order to compare, we need to make both the same units first. Since they give us the conversion factor 1 CAD=0.75 GBP, we can plug this in to the shoes from shop X. We get 35.90*0.75=26.93 GBP.

Now we can compare. Since 21 GBP < 26.93 GBP, we can see that shop Y's shoes are cheaper, and therefore the better deal.

[tex] {5}^{2} + {x}^{2} = {8}^{2} [/tex]

[tex]25 + {x}^{2} = 64[/tex]

Subtract both sides 25

[tex]25 - 25 + {x}^{2} = 64 - 25[/tex]

[tex] {x}^{2} = 39[/tex]

Thus :

[tex]x = \sqrt{39} [/tex]

[tex]x = 6.245[/tex]

Answer:

1280

Step-by-step explanation:

divide 1400 by 210

then multiply by 18

subtract that answer (120) from 1400,

and you get 1280

Answer:

  a) best form: (b)  f(x)= 1/2(x -3) (x -7)

  b) zeros: x=3, x=7

Step-by-step explanation:

The factored form most quickly tells you the zeros of the function. The zeros are the values of x that make the factors zero: the opposite of the binomial's constant.

  f(x)= 1/2(x -3)(x -7) reveals the zeros to be x=3 and x=7

Answer:

khan

Step-by-step explanation:

Answer:

B) Yes, they are both right angles.

Step-by-step explanation: