I have tried multiple times but still could not get the correct answer or at least accurate answers

a) The rate of change of the volume of the box is 8m³/s.

b) The rate of change of the surface area of the box is -19m²/s.

c) The rate of change of the diagonal of the box is 1m/s.

Let the rate of change of  the edge length x, y, and z of a closed rectangular box are:

dx/dt= 1m/s

dy/dt= -2 m/s

dz/dt= 0.5 m/s

a) The volume of the box

From the formula of the volume,

V=xyz

Then,

differentiate w.r.t t

[tex]\frac{dV}{dt} = xy\frac{dz}{dt} + yz\frac{dx}{dt} +xz\frac{dy}{dt}[/tex]

[tex]\frac{dV}{dt} = xy(0.5)+ yz(1)+xz(-2)[/tex]

put the value of x, y, z , then we get

[tex]\frac{dV}{dt} = 2.3.(0.5)+ 3.5.(1)+2.5.(-2)[/tex]

[tex]\frac{dV}{dt} = 3+ 15 - 10[/tex]

[tex]\frac{dV}{dt} = 8m^3/s[/tex]

The rate of change of the volume of the box is 8m³/s.

b) surface area of the box

surface area of the rectangular box is

s = 2xy + 2yz + 2zx

differentiate w.r.t t

[tex]\frac{ds}{dt} = 2(y + z)\frac{dx}{dt} + 2(z + x)\frac{dy}{dt} +2(x + y)\frac{dz}{dt}[/tex]

[tex]\frac{ds}{dt} = 2(y + z)(1) + 2(z + x)(-2)+2(x + y)(0.5)[/tex]

[tex]\frac{ds}{dt} = 2(3 + 5)(1) + 2(5 + 2)(-2)+2(2 + 3)(0.5)[/tex]

[tex]\frac{ds}{dt} = 16 -40 + 5[/tex]

[tex]\frac{ds}{dt} = -19m^2/s[/tex]

The rate of change of the surface area of the box is -19m²/s.

c) diagonal of the box

lengths of  the boxes for the diagonal is

s = 2x² + y² + z²

differentiate equation w.r.t t

[tex]\frac{ds}{dt} = 4x\frac{dx}{dt} + 2y\frac{dy}{dt} +2z\frac{dz}{dt}[/tex]

[tex]\frac{ds}{dt} = 4.2.1+ 2.3.(-2) +2.5.(0.5)[/tex]

[tex]\frac{ds}{dt} = 8 -12 + 5[/tex]

[tex]\frac{ds}{dt} =1m/s[/tex]

The rate of change of the diagonal of the box is 1m/s.

a) The rate of change of the volume of the box is 8m³/s.

b) The rate of change of the surface area of the box is -19m²/s.

c) The rate of change of the diagonal of the box is 1m/s.

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First, let's distribute the exponent -3 for 2 and ten, like this:

Now, we can apply the next property when we have a number raised to a negative power:

Then:

And when we have a division of the same number raised to different powers we can apply:

then:

Now, as we know, having 10 raised to 6 means that we are multiplying ten by ten 6 times, when we do this we get:

And with 2 raised to three we get:

Then we have:

Let us find the angles of the parallelogram below

Theorem+: opposite angles of a parallelogram are the same

Hence the angles of the parallelogram are 110, 70, 110, and 70

As all the options are the same equation

so, we need to know the type of the sign of the inequality

As shown in the graph

The line is shaded so, the sign is < or >

The shaded area which is the solution of the inequaity is below the line

So, the sign is <

So, the answer is option B) 14x + 7y < 21

1. Quadratic curve

2. Odd degree function

3. TWO REAL ZEROS

Answer:

2x+19

Step-by-step explanation:

Let x be the number

2x+19

We need to solve the next expressions:

17. 19yd. 28in.- 16yd. 31in

We need to solve subtract each expression.

Then:

19yd. 28in.- 16yd. 31in =

19yd - 16yd and 28in-31in

3yd -3in

Then, we have the next equivalent.

1 yard = 36 in

So:

36 in - 3 in = 33 in

Therefore

19yd. 28in.- 16yd. 31in = 2 yard 33

18 61wk. 4da.- 18wk. 6da.

We need to subtract both expression:

Then

61wk - 18wk = 43kw

4da-6da = -2da

Where 1 week = 7 days

Then

7 da - 2da = 5 da

Hence, 43kw -1 wk = 42 wk.

The result is:

42 wk 5 da

21. 8tbsp. 2tsp. * 15

We need to convert 2ts into tbsp and then multiply the result by 15.

If

1 tsp ------- 0.333tbsp

Then

2tp ------ 2(0.333tbsp)= 0.66666 tbsp

Now

(8tbsp + 0.6666 ) * 15 = 130 tbsp

In order to determine which is the equivalent equation, simplify the given expression:

-2x + 5 - 3x = 5x + 25 simplify like terms left side

-2x - 3x + 5 = 5x + 25

-5x + 5 = 5x + 25 subtract 5x both sides and subtract 5 both sides

-5x - 5x = 25 - 5 simplify both sides

-10x = 20

Hence,the equivalent expression is -10x = 20

The most appropriate choice for geometric series will be given by

The equation is [tex]y = 80 (1.2)^x[/tex] and it is a geometric function.

What is geometric series ?

The series in which the ratio between consecutive terms of the series are same is called geometric series

For example, 2, 4, 8, 16, ... is a geometric series in which ratio between two consecutive terms is 2.

Number of pieces of art in 2004 = 80

Number of pieces of art  in 2005 = [tex]80 \times 1.2[/tex]

Number of pieces of art in 2006 =  [tex]80\times (1.2)^2[/tex]

Number of pieces of art after x years from 2004 = [tex]80 \times (1.2)^x[/tex]

The equation is [tex]y = 80 (1.2)^x[/tex]

This is a geometric function

The graph has been attached here.

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∵ m< OZQ = m[tex]\because m\angle OZP=62[/tex]Substitute the measures of the given angles in the equation above

Subtract 62 from both sides

The measure of angle PZQ is 63 degrees

The distance between the parallel lines is [tex]\frac{3}{5}}[/tex].

The given parallel lines are

[tex]y= $-$3x+4\\y= $-$3x+1[/tex]

We have to find the distance between the given parallel lines.

The formula is used to solve the distance between two parallel lines [tex]ax+by+c_{1}=0[/tex] and [tex]ax+by+c_{2}=0[/tex] is

[tex]d=|c_{2} $-$c_{1}|\frac{1}{\sqrt{a^{2}+b^{2}}}[/tex]

The first given line is [tex]y= $-$3x+4[/tex]

We can write that line as [tex]3x$-$y $-$4=0[/tex]

The second given line is [tex]y= $-$3x+1[/tex]

We can write that line as [tex]3x$-$y $-$1=0[/tex]

Comparing the both given parallel lines with the standard equation of line.

After comparing we get

[tex]a=3, b= $-$1, c_{1}= $-$4, c_{2}= $-$1[/tex]

Putting the value in the formula

[tex]d=|(-1) -(-4)|\frac{1}{\sqrt{(3)^{2}+(-4)^{2}}}\\d=|-1+4|\frac{1}{\sqrt{9+16}}\\d=|3|\frac{1}{\sqrt{25}}\\d=\frac{3}{5}}[/tex]

Hence, the distance between the parallel lines is [tex]\frac{3}{5}}[/tex].

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1 pizza contain 8 slices, so we can state a rule of three as:

then, x is given by

which gives

that is, 3/4 of pizza is equivalent to 6 slices. So, there are 8 - 6 = 2 slices left of one pizza.

However, they bought 3 large pizzas and ate almost one of them. So, there are 2x8 = 16slices plus 2 slices, that is, 18 slices are left.

Paul is the oldest and Fred is the youngest of the three.

Younger is a comparative adjective that generally indicates more youthful.

Similar to old, elder simply indicates older in age. It is a comparative version of old.

Given that x is a natural number, let Bill's age equal x years.

Paul's age is thus calculated as (x + a) Years, where an is any positive integer.

Fred is also younger than Bill.

So, Fred's age is equal to x - k, where k is any positive integer.

As a result, if we arranged Fred, Bill, and Paul's ages, they would be

Bill, Fred, and Paul

x-k < x < x+a

As a result, we can conclude that Paul is the oldest and Fred is the youngest of the three.

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Given:

Required:

To find the correct one.

Explanation:

The given quation is:

4 + x +8 =24

Subtract 8 on both sides

4 + x +8 - 8 = 24 -8

4 + x = 16

Final Answer:

Thus the first option is the correct answer.

The time needed to travel a certain distance varies inversely with the rate of speed, so:

8hours----------------------------->36mi/h

xhours----------------------------->60mi/h

4.8 hours or 4 hours and 48 minutes

Solution

Given that

Half life is 1690 years.

Let A(t) = amount remaining in t years

SInce A(1690) = (1/2)A0 and A0 = 70

So,

Therefore, the answer is 55.407 g

Given the picture, we have:

Enclosed area: A = x*y

Fence Length: F= 2x+y

Okay, here we have this:

Considering the provided graph, we are going to find the measure of the angle "3", so we obtain the following:

Since angle 3 and 4 form a straight angle, that is to say that these two angles are supplementary, then we have:

Finally we obtain that the correct answer is the option C.

The domain of the function √(100x²) will be (-∞,∞) as the definition of domain states that the set of inputs that a function will accept is known as the domain of the function in mathematics. 

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input.

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Here,

The function is √(100x²).

The domain would be (-∞,∞).

The set of inputs that a function will accept is known as the domain of the function in mathematics, and the domain of the function √(100x²) will be (-∞,∞), according to the definition of domain.

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Answer:

y= 4x +1

Step-by-step explanation:

The equation of a line, in slope-intercept form, is given by y= mx +c, where m is the slope and c is the y-intercept.

Given that the slope is 4, m= 4.

Substitute m= 4 into y= mx +c:

y= 4x +c

To find the value of c, substitute a pair of coordinates the line passes through.

When x= -2, y= -7,

-7= 4(-2) +c

-7= -8 +c

c= -7 +8

c= 1

Substitute the value of c into the equation:

Thus, the equation of the line is y= 4x +1.

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Answer:

Explanation:

Given the equation:

On observation, the equation cannot be factorized, so we make use of the quadratic formula.

Comparing with the form ax²+bx+c=0: a=1, b=3, c=-7

Substitute these values into the formula.

We then simplify and solve for x.

The Pythagorean theorem states:

where a and b are the legs and c is the hypotenuse of a right triangle.

Substituting with c = 9 and a = 5, we get:

Given:

The original selling price of 1 swimsuit = $44.95

The selling price of 1 marked down swimsuit = $16.90

Using the provided formula:

Where,

M is the markdown

S is the original selling price

N is the reduced price

Substituting we have:

Solving for N:

Hence, the reduced price is $28.05

Answer:

$28.05

Answer:

12.1 units

Step-by-step explanation:

The map of Roaring River shows1 inch to be an equivalent of 25 miles. If therefore, the river is shown as 5.5 inches long on the map;

The river is "actually" 137.5 miles long

The most appropriate choice for profit will be given by-

Profit percent after selling a bag of garri is 25%

What is profit?

If the selling price of an article is more than the cost price of the article, then the difference between selling price and the cost price of the article gives the profit

Profit = SP - CP

Here,

Cost price of a bag of Garri = N320

Selling price of a bag of Garri = N400

Profit = N(400 - 320)

         = N80

Profit Percent = [tex]\frac{80}{320} \times 100[/tex]

                       = 25%

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We have to graph the function F(x) defined as:

We can graph it as:

To see the complete graph we have to show the horizontal axis from x = -30 to x = 30 and the vertical axis from y = -80 to y = 80.

Answer: Option B

To find the step where the error was made, we are going to correctly solve the equation:

We need to solve for x, first we subtract 3 from each side:

We divide by 2 each side:

The first step that shows an error in the solution of the equation is the Step 2, because when we have two negative numbers, we add them, we do not subtract them.

Answer: B. Step 2

we have

-6, 1, 8, 15, ...

so

a1=-6

a2=1

a3=8

a4=15

a2-a1=1-(-6)=7

a3-a2=8-1=7

a4-a3=15-8=7

so

the common difference is

d=7

Part 2

write an equation

we have that

The equation of a general aritmetic sequence is equal to

an=a1+(n-1)d

we have

d=7

a1=-6

substitute

an=-6+(n-1)7

an=-6+7n-7

an=7n-13

Part 3

Find 12th term

we have

n=12

a12=-7(12)-13

a12=71