Let θ (in radians) be an acute angle in a right triangle, and let x and y, respectively, be the lengths of the sides adjacent and opposite θ. Suppose also that x and y vary with time.

a. How are dθ/dt, dx/dt and dy/dt related?

Please give steps and explain!

Answer: 8 L of 100% pure acid and 64 L of 10% acid must be combined

Step-by-step explanation:

According to the dilution law,

[tex]C_1V_1+C_2V_2=C_3V_3[/tex]

where,

[tex]C_1[/tex] = concentration of pure acid solution = 100 %

[tex]V_1[/tex] = volume of pure acid solution = x L

[tex]C_2[/tex] = concentration of another acid solution= 10%

[tex]V_2[/tex] = volume of another acid solution= (72-x) L

[tex]C_3[/tex] = concentration of resulting acid solution = 20 %

[tex]V_1[/tex] = volume of resulting acid solution = 72 L

Putting the values in the equation:

[tex]100\times x+10\times (72-x)=20\times 72[/tex]

[tex]x=8L[/tex]

Therefore, the laboratory technician must take 8 L of 100% pure acid and (72-8) = 64 L of 10% acid to get 72​-liter batch of a 20​% acid solution.

Answer:

both alicia and jamal

Step-by-step explanation:

From the given steps we can see that both Alicia and Jamal completed the proof correctly.

Option C

Given :

3x+7=x-5

prove: x=-6

Alicia's workout

3x+7=x-5 : given

2x+7=-5: subtraction property of equality

2x=-12: subtraction property of quality

x=-6: division property of equality

Alicia's steps are correct. She proved x=-6

jamal's work

3x+7=x-5 : given

7=-2x-5 : subtraction property of equality

12=-2x: addition property of equality

-6=x proved

Jamal's steps are also correct. Jamal started by subtracting 3x from both sides. That approach is also correct. He proved x=-6

so, both Alicia and Jamal are correct

Learn more :  brainly.com/question/20473805

the answer would be p-28=c

Mark Me Brainliest !

Answer:

P - 28 = C

Step-by-step explanation:

P (Regular Price  )

C ( Cost Savings )

You Noticed These Jeans You Liked.

You Couldn't Afford Them So You Waited Til The Price Dropped.

When Prices Drop Its Either 1 of 2 Reasons

Holiday Seasons Or Price Elasticity

So These Jeans Become $28 On The Market.

Simply You Figure Out How Much You'll Save By Comparing The Original Price To The Discounted Price.

There For Your Answer Will Be The Following :

Regular Price - Discounted Price = Cost Savings

To solve for R in the equation [tex]C=2\pi R[/tex] divide both sides by 2π to get [tex]R = C / (2\pi )[/tex].

To solve the equation [tex]C=2\pi R[/tex] for R, we need to isolate R on one side of the equation. Here are the steps to do this:

Start with the original equation: [tex]C=2\pi R[/tex]

Divide both sides of the equation by 2π to isolate [tex]R: R = C / (2\pi ).[/tex]

Given variation, this is also equivalent to [tex]r=1/2\pi C[/tex].

Now, R is the subject of the equation, and you can use this formula to find the radius (R) if you know the circumference (C) of a circle.

the probability of a loss is 0.6.

To find the probability of a loss, we first need to understand that in this context, the sum of all possible outcomes (win, draw, and loss) must equal 1.

Given:

- Probability of a win = 0.24

- Probability of a draw = 0.16

Let's denote the probability of a loss as [tex]\( P(\text{loss}) \).[/tex]

We know that:

[tex]\[ P(\text{win}) + P(\text{draw}) + P(\text{loss}) = 1 \][/tex]

So, to find [tex]\( P(\text{loss}) \),[/tex] we rearrange the equation:

[tex]\[ P(\text{loss}) = 1 - (P(\text{win}) + P(\text{draw})) \][/tex]

[tex]\[ P(\text{loss}) = 1 - (0.24 + 0.16) \][/tex]

[tex]\[ P(\text{loss}) = 1 - 0.4 \][/tex]

[tex]\[ P(\text{loss}) = 0.6 \][/tex]

Therefore, the probability of a loss is 0.6.

Answer:

The value for x will be 5.

Step-by-step explanation:

As the segment AB and BC are tangent to the circle D, it will have the same long. Due to segment longitude is written as function of the variable x, it requires  to solve the following equation:

[tex]long(AB)= 3x+2= long(BC)= x+12[/tex]  

[tex]3x+2=x+12[/tex]  

[tex]3x-x= 12-2[/tex]  

[tex]2x= 10[/tex]  

[tex]x= 5[/tex]

we have

[tex]f(x)=4x+8[/tex]

Step 1

Let

[tex]y=f(x)[/tex]

[tex]y=4x+8[/tex]

Step 2

exchanges the variable x for y and the variable y for x

[tex]x=4y+8[/tex]

Step 3

Isolate the variable y

[tex]4y=x-8[/tex]

[tex]y=\frac{1}{4}x-2[/tex]

Step 4

Let

[tex]h^{-1}(x)=y[/tex]

[tex]h^{-1}(x)=\frac{1}{4}x-2[/tex] ------> the inverse function

therefore

the answer is

[tex]h^{-1}(x)=\frac{1}{4}x-2[/tex]

The inverse of the function f(x) = 4x + 8 is h(x) = (x - 8) / 4.

The inverse of the function f(x) = 4x + 8 can be found by switching the x and y variables and solving for y. So, we have:

x = 4y + 8

Now, we rearrange the equation to isolate y:

x - 8 = 4y

y = (x - 8) / 4

Therefore, the inverse function is h(x) = (x - 8) / 4.

Answer:

Step-by-step explanation:

P(t)=130t -0.4t^4 +1200

The population will be max when first differential of p(t) =0

So p'(t) =130-1.6t^3=0

1.6t^3=130

t^3 =130/1.6

t^3 =81.25

t = cube root of 81.25

t =4.3 months

P(max) =130(4.3) -0.4(4.3)^4 +1200

= 559-136.75+1200

=1622

Population will disappear when p(t) =0

The probability that the number on the tile is a multiple of 7 or a multiple of 8 is 0.24 or 24%.

To find the probability that a tile picked at random has a number that is a multiple of 7 or a multiple of 8, we need to count the number of tiles that satisfy this condition and divide it by the total number of tiles.

First, let's find how many numbers from 1 to 50 are multiples of 7 and multiples of 8 separately.

Multiples of 7:

7, 14, 21, 28, 35, 42, 49

There are 7 multiples of 7 between 1 and 50.

Multiples of 8:

8, 16, 24, 32, 40, 48

There are 6 multiples of 8 between 1 and 50.

However, we need to be careful not to count the numbers that are multiples of both 7 and 8 (multiples of 56). There's only one such number in the range (56).

So, the total number of tiles with numbers that are multiples of 7 or multiples of 8 is 7 + 6 - 1 = 12.

The total number of tiles from 1 to 50 is 50.

Now, we can find the probability:

Probability = [tex]\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}[/tex]

Probability = [tex]\frac{12}{50}[/tex]

Probability = 0.24

So, the probability that the number on the tile is a multiple of 7 or a multiple of 8 is 0.24 or 24%.

The inverse function is [tex]f^{-1}(x) = \frac{x - 3}{2}[/tex].

To find the inverse of the function [tex]f(x) = 2x + 3[/tex], follow these steps:

Replace [tex]f(x)[/tex] with [tex]y[/tex]:
[tex]y = 2x + 3[/tex]

Interchange the variables [tex]x[/tex] and [tex]y[/tex]:
[tex]x = 2y + 3[/tex]

Solve for [tex]y[/tex]:
[tex]x - 3 = 2y[/tex]
[tex]y = \frac{x - 3}{2}[/tex]

Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]:
[tex]f^{-1}(x) = \frac{x - 3}{2}[/tex]

The result of 16 times 9/4 is 36.

The original question appears to be asking how to divide 16 by the fraction 4/9, but it also contains an error in stating the mathematical expression. To divide 16 by 4/9, you need to multiply 16 by the reciprocal of 4/9, which is 9/4. Here's the step-by-step calculation:

Find the reciprocal of 4/9, which is 9/4. Reciprocal means exchanging the numerator and denominator.

Multiply 16 by the reciprocal (16 * 9/4).

Come up with the solution: (16 * 9) / 4 = 144 / 4 = 36.

Therefore, 16 divided by 4/9 equals 36.

Let the depth of the river = d

So in order to find the product, you simply multiply

so the product of 86 and the depth of the river would be 86 * d

or 86d.

Hope this answers your question. Have a great day!

The height of the building is approximately 78.4 meters.

To find the height of the building, we can use the formula d = v0t + 1/2gt2, where d is the height, v0 is the initial horizontal speed, t is the time, and g is the acceleration due to gravity. In this case, since the ball is thrown horizontally, the initial vertical speed is 0 and there is no initial vertical acceleration. So, d = 0(4.0) + 1/2(9.8)(4.0)2. Solving this equation gives us a height of approximately 78.4 meters.

Answer:

45 or more

Step-by-step explanation:

If x is the amount of pastries they sell, we need to multiply it by $3.00 to know how much they raise. Total earnings: $3.00x

They need to raise at least $135, that is $135 or more.

So, $3.00x has to be greater than $135 or equal.

Written as an inequality is:

$3.00x [tex]\geq[/tex] $135

We divide both sides by $3.00 and we have:

x [tex]\geq[/tex] $135/$3.00 = 45

Therefore, they need to sell 45 or more pastries to meet the goal.

Answer:

b

Step-by-step explanation: