Which is the correct answer? I already have something but not sure if correct

Answer:

A

Step-by-step explanation:

We are given a right triangle with a base of x feet and a height of h feet, where x is constant and h changes with respect to time t.

The angle in radians is defined by:

[tex]\displaystyle \tan(\theta)=\frac{h}{x}[/tex]

And we want to find the relationship that describes dθ/dt and dh/dt.

So, we will differentiate both sides with respect to t where x is a constant:

[tex]\displaystyle \frac{d}{dt}[\tan(\theta)]=\frac{d}{dt}\Big[\frac{h}{x}\Big][/tex]

Differentiate. Apply the chain rule on the left. Again, remember that x is just a constant, so we can move it outside the derivative operator. Therefore:

[tex]\displaystyle \sec^2(\theta)\frac{d\theta}{dt}=\frac{1}{x}\frac{dh}{dt}[/tex]

Since we know that tan(θ)=h/x, h is the opposite side of our triangle and x is the adjacent. Therefore, by the Pythagorean Theorem, our hypotenuse will be:

[tex]\text{Hypotenuse}=\sqrt{h^2+x^2}[/tex]

Since secant is the ratio of the hypotenuse to adjacent:

[tex]\displaystyle \sec(\theta)=\frac{\sqrt{h^2+x^2}}{x}[/tex]

So:

[tex]\displaystyle \sec^2(\theta)=\frac{x^2+h^2}{x^2}[/tex]

By substitution, we have:

[tex]\displaystyle \Big(\frac{x^2+h^2}{x^2}\Big)\frac{d\theta}{dt}=\frac{1}{x}\frac{dh}{dt}[/tex]

By multiplying both sides by the reciprocal of the term on the left:

[tex]\displaystyle \frac{d\theta}{dt}=\frac{1}{x}\Big(\frac{x^2}{x^2+h^2}\Big)\frac{dh}{dt}[/tex]

Therefore:

[tex]\displaystyle \frac{d\theta}{dt}=\frac{x}{x^2+h^2}\frac{dh}{dt}[/tex]

Our answer is A.

Answer:

x = 200 students

y = 300 non-students

hope that helps

Answer:

[tex]2(4 + 7) = 22[/tex]

[tex]3(\frac{1}{3} - p) = 1 - 3 p[/tex]

Step-by-step explanation:

Given

1 & 2

Required

Rewrite and simplify

[tex]1.\ 2(4 + 7)[/tex]

Apply distributive property

[tex]2(4 + 7) = 2 * 4 + 2 * 7[/tex]

[tex]2(4 + 7) = 8 + 14[/tex]

[tex]2(4 + 7) = 22[/tex]

[tex]2.\ 3(\frac{1}{3} - p)[/tex]

Apply distributive property

[tex]3(\frac{1}{3} - p) = 3*\frac{1}{3} - 3 * p[/tex]

[tex]3(\frac{1}{3} - p) = \frac{3}{3} - 3 * p[/tex]

[tex]3(\frac{1}{3} - p) = 1 - 3 * p[/tex]

[tex]3(\frac{1}{3} - p) = 1 - 3 p[/tex]

Answer:

c=64.2

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

-8ab = ?

Plug in the values for a and b.

-8(1/4)(6)

Multiply.

-2(6)

= -12

Answer:

x = 15 cm

Step-by-step explanation:

Triangle area:

[tex] area = \frac{(20)(15)}{2} = \frac{300}{2} = 150 \: cm[/tex]

Then rectangle area:

[tex]area = (10)(x) \\ 150 = 10x \\ x = \frac{150}{10} \\ x = 15 \: cm[/tex]

Answer:

[tex] |x - 12| + 6 = 56 \\ x - 12 + 6 = 56 \\ x - 6 = 56 \\ \boxed{x = 62} \\ |x - 12| + 6 = 56 \\ - (x - 12) + 6 = 56 \\ 12 - x + 6 = 56 \\ - x + 18 = 56 \\ - x = 38 \\ \boxed{x = - 38} \\ \boxed{A. \: x = 62 \: or \: x = - 38}[/tex]

Answer:

sdfshefvhwedsbdhcfbHISE

Step-by-step explanation:

FSDSd

Answer:

49097

Step-by-step explanation:

Well the answer was in delta math what can I say

Answer:

$49677.4

Step-by-step explanation:

Given data

Interest rate r= 5%

Final amount A = $77,000

time t= 9 years

let us apply the compound interest formula

[tex]A=P(1+r)^t[/tex]

Substitute

[tex]77000=P(1+0.05)^9\\\\77000=P(1.05)^9\\\\77000=P*1.55[/tex]

Divide both sides by 1.55

P=77000/1.55

P=$49677.4

Hence the principal amount should be $49677.4

Answer:

if you mean the power of these letters then the answer is

x^2,y^2 and z

as they are common in both lists

Answer:

790 m^2

Step-by-step explanation:

well in the figure we have to areas

the rectangle of the side

well the area of the rectangle is base times height

we have a base of 11 and a height of 17

[tex]A_{rs}=11*17\\\\A_{rs}=187[/tex]

the triangle

well the area of a triangle is base times height over 2

we have a base of 16 and a height of 15

[tex]A_t = \frac{16\cdot 15}{2}\\\\A_t= 8\cdot15\\\\A_t=120[/tex]

the rectangle of the base

we have a base of 16 and a height of 11

so

[tex]A_{rb} = 16\cdot 11\\\\A_{rb} = 176[/tex]

so the total area is

[tex]A_T = 2(A_{rs})+2(A_{t})+1(A_{rb})\\\\A_T= 2(187)+2(120)+1(176)\\\\A_T=374+240+176\\\\A_T = 790[/tex]

so that's our answer the surface area is 790 m^2

Answer:

2

Step-by-step explanation:

Answer:

you just changfe it as u switch it

Step-by-step explanation:

======================================================

Explanation:

There are 8+11 = 19 movies that are either horror or mystery.

This is out of 9+12+8+11+4 = 44 movies total.

Divide the two sums to get 19/44 = 0.43181818181818 approximately.

This rounds to 0.432

There's roughly a 43.2% chance of picking a horror or mystery movie.

This is not the correct answer.

1. 2.30 is not even close to the point given in the number line.

2. My guess for the correct answer would be 0.23 because in between 0.2 and 0.3 is 0.25, so the best answer would be 0.23.

Answer:

80 gallons and a leaking problem.

Step-by-step explanation:

please mark brainliest, give a thanks, and rate a five stars if this helped! feel free to ask anymore questions if you need any more help! thanks!

(lol optional): add my sc: tealyn337

Answer:

A

Step-by-step explanation:

It is letter A I got 100!

Answer:

A

Step-by-step explanation:

EDGE 2021

Answer: 8x^2 - 10x - 3

Step-by-step explanation:

first, we multiply the parentheses.

2x x 4x + 2x - 3 x 4x - 3

then, we calculate all of that junk.

8x^2 + 2x - 12x - 3

finally, we collect the like terms.

8x^2 - 10x - 3

Answer:

8x^2-10x3

Step-by-step explanation:

8x^(add the 2 upbove the x)-10x-3

Answer:

Each large box weighs 15.25 kg, and each small box weighs 6.25kg

Step-by-step explanation:

Let's define the variables:

A = weight of a large box.

B = weight of a small box.

We know that:

"A delivery of 5 large boxes and 3 small boxes has a total weight of 95 kilograms."

We can write this as:

5*A + 3*B = 95 kg

We also know that:

"A delivery of 2 large boxes and 6 small boxes has a total weight of 68 kilograms."

2*A + 6*B = 68kg

Then we have the system of equations:

5*A + 3*B = 95 kg

2*A + 6*B = 68kg

To solve this, the first step is to isolate one of the variables in one of the equations.

I will isolate the variable A in the second equation:

A = 68kg/2 - 6*B/2 = 34kg - 3*B

A = 34kg - 3*B

Now we can replace this in the first equation:

5*( 34kg - 3*B) + 3*B = 95 kg

170kg - 15*B + 3*B = 95 kg

170kg - 12*B = 95 kg

170kg - 95kg = 12*B

75kg = 12*B

75kg/12 = B = 6.25kg.

Now we can replace this on the equation A = 34kg - 3*B to find the value of A.

A = 34kg -3*6.25kg = 15.25kg

Answer:

Using the point (-2,-4) it would be:

y + 4 = 1/3(x + 2)

Using the point (4,-2) it would be:

y + 2 = 1/2 (x - 4)

Step-by-step explanation:

hope this helps :)