The product of -8 and -4 is -32.


True False

Answer:

18

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) a^3-64b^3

=(a)^3-(4b)^3

=(a-4b)(a^2+4ab+16b^2)

b) 3x^3-81y^3z^6

=3(x^3-27y^3z^6)

=3{(x)^3-(3yz^2)^3}

=3(x-3yz^2)(x^2+3xyz^2+9y^2z^4)

c)16a^3b^3-54c^3d^3

=2(8a^3b^3-27c^3d^3)

=2{(2ab)^3-(3cd)^3

=2(2ab-3cd)(4a^2b^2+6abcd+9c^2d^2)

hope u got!!

The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

Learn more about derivative

brainly.com/question/29144258

#SPJ11

Answer:

The answer is 4u-14.

Have a great rest of your day!

Answer:

4(u-2) - 6

separate bracket

4u-8-6

4u-14

The dP/dt of the adiabatic expansion is -42/11 kPa/min

An adiabatic process is a process in which there is no exchange of heat from the system to its surrounding neither during expansion nor during compression

Given b=1.5, P=7 kPa, V=110 cm³, and dV/dt=40 cm³/min

PVᵇ = C

Taking logs of both sides gives:

ln P + b ln V = ln C

Taking partial derivatives gives:

\(\frac{1}{P}\frac{∂P}{∂t} + \frac{b}{V}\frac{∂V}{∂t} = 0\)

Substitutituting the values b, P, V and dV/dt into the derivative above:

1/7 x dP/dt +  1.5/110 x 40 = 0

1/7 x dP/dt +  6/11 = 0

1/7 x dP/dt = - 6/11

dP/dt = - 6/11 x 7

dP/dt = -42/11 kPa/min

Therefore, the value of  dP/dt is -42/11 kPa/min

Learn more about adiabatic expansion on:

https://brainly.com/question/6966596

#SPJ1

The kinetic energy of the roller coaster at the bottom of the hill is approximately 594,576 J.

The potential energy of the roller coaster at the top of the hill can be calculated as:

PE = mgh

where m is the mass of the car and its passengers, g is the acceleration due to gravity \((9.8 m/s^2\)), and h is the height of the hill (62 m). Thus, we have:

PE =\((1088 kg)(9.8 m/s^2)(62 m) = 670,720 J\)

At the bottom of the hill, all of the potential energy has been converted to kinetic energy. The kinetic energy of the roller coaster can be calculated as:

\(KE = (1/2)mv^2\)

where v is the speed of the roller coaster at the bottom of the hill. Thus, we have:

\(KE = (1/2)(1088 kg)(33 m/s)^2 = 594,576 J\)

Therefore, the kinetic energy of the roller coaster at the bottom of the hill is approximately 594,576 J.

for such more question on kinetic energy

https://brainly.com/question/28109294

#SPJ4

Answer:

P,M,R

Step-by-step explanation:

collinear points are two or more points that form a straight line

Option - B is the correct answer.

We have the following figure given in the question.

We have to determine which three points are collinear.

Three or more points are said to be collinear if they lie on a single straight line.

According to question, we have to check which three points lie on a straight line.

It can be seen that two set of points - (P, M, R) and (N, M, O) lie on the same straight line. Of the options mentioned one is - (P, M, R).

Hence, the correct option is Option - B.

To solve more questions on Collinear points, visit the link below -

https://brainly.com/question/13069924

#SPJ6

Because of gravity, the item accelerates continuously. The ball took 2 seconds to reach the ground, hence option (d) is accurate.

The metric system and the International Systems in Units both use the metre (m), also spelt as meter, as the basic unit of length (SI). Inside the British Imperial & American Customary systems, it is equivalent to around 39.37 inches.

Metric is the preferred word outside of North America for the measuring unit that is equivalent to about 1.094 yards, with American spelling being meter. Metric in American English and Metric everywhere else are terminology used in music and poetry respectively.

To know more about Meter visit:

https://brainly.com/question/29438351

#SPJ1

Answer:

8km/h

Step-by-step explanation:

24/3

8

Hope it helps!

Answer:

To convert 24 km/s to km/h use direct conversion formula below.

24 km/s = 86393.088552916 km/h.

You also can convert 24 Kilometers/Second to other Speed (popular) units.

Step-by-step explanation:

goo gle

Answer:

x=+17

Step-by-step explanation:

6x+7=8x-27

We move all terms to the left:

6x+7-(8x-27)=0

We get rid of parentheses

6x-8x+27+7=0

We add all the numbers together, and all the variables

-2x+34=0

We move all terms containing x to the left, all other terms to the right

-2x=-34

x=-34/-2

x=+17

Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest then the initial deposit was $4700

Use the simple interest formula

I = P r t

where I = simple interest

P = principal

r= rate of interest

t= number of years

5922=Px6.3%x20

5922=Px1.26

P=5922/1.26

P=4700

learn more about of amount here

https://brainly.com/question/27054498

#SPJ4

The equation states that the gradient of the natural logarithm of the density of component A, denoted as (∇ ln(ρA)), is equal to the negative divergence of the velocity vector (∇ · V).

To derive equation (25-11), we start with the general form of the conservation of mass equation:

∂(ρA) / ∂t + ∇ · (ρA V) = ṁA_gen Where:

ρA is the density of component A,

t is time,

V is the velocity vector,

∇ is the gradient operator,

ṁA_gen is the net rate of generation of component A within the control volume.

Assuming steady-state conditions (no change with time) and neglecting any mass generation or consumption, we can simplify the equation to:

∇ · (ρA V) = 0

This equation states that the divergence of the mass flux of component A is zero, indicating a steady-state condition.

By applying the divergence theorem, we can rewrite the equation as:

∫(∇ · (ρA V)) dV = 0

Using the product rule of divergence, we have:

∫(∇ρA · V + ρA ∇ · V) dV = 0

Since the control volume is arbitrary, the integral can be simplified to:

∇ρA · V + ρA ∇ · V = 0

Rearranging the equation, we obtain:

∇ρA · V = -ρA ∇ · V

Dividing both sides by ρA, we get:

V · (∇ρA / ρA) = -∇ · V

Finally, recognizing that the left side of the equation is the gradient of the natural logarithm of ρA (i.e., (∇ ln(ρA))), we have:

(∇ ln(ρA)) · V = -∇ · V

Learn more about divergence theorem here:

https://brainly.com/question/10773892

#SPJ11

Translation, rotation, and reflection are three of the fundamental transformations.

To learn more about transformation refer to:

https://brainly.com/question/4289712

#SPJ1

Answer:

=

64 / 7x -2

Step-by-step explanation:

You multiply 16 and 4/7 than you take away 2 I think im bad at this-

Answer:

Step-by-step :

a) To find the constant proportionality, we can use the formula:

Number of applications = k * (number of workers) * (number of hours)

where k is the constant proportionality we want to find. We can plug in the values given in the problem:

466 = k * 8 * 12

Solving for k:

k = 466 / (8 * 12) = 4.875

So the formula is:

Number of applications = 4.875 * (number of workers) * (number of hours)

b) If 3 workers are sick, then 8 - 3 = 5 workers are left. To find how long they will have to work to assemble 466 applications, we can again use the formula:

466 = 4.875 * 5 * (number of hours)

Solving for the number of hours:

number of hours = 466 / (4.875 * 5) = 19.07 hours (rounded to two decimal places)

So the remaining workers will have to work for approximately 19.07 hours to assemble 466 applications.

c) If the task has to be accomplished in 4 hours, we can again use the formula with the new values:

466 = 4.875 * (number of workers) * 4

Solving for the number of workers:

number of workers = 466 / (4.875 * 4) = 23.97

Since we cannot have a fraction of a worker, we need to round up to the nearest whole number of workers.
Therefore, we would need to hire 24 temporary workers to accomplish the task in 4 hours.

Answer:

B

Step-by-step explanation:

Let’s first look at the y-intercept. Since the equation is in y = mx + b form, we know that m is the slope and b is the y-intercept, so the slope is 1/2 and the y-intercept is 2, or (0,2). We can narrow down our search by noticing that C and D don’t intersect (0,2). That leaves A and B.

The slope is calculated by (y_1 - y_2)/(x_1 - x_2) given points (x_1, y_1) and (x_2, y_2). The slope for A is (4-0)/(2-(-2)) = 4/4 = 1 and the slope for B is (2-0)/(0-(-4)) = 2/4 = 1/2. The slope of B matches the slope that we are looking for. So, the answer is B.

The time taken to hit the ground is 13 seconds.

It should be noted that the function that was given based on the information is:

h(t) = 16t²

where h = height

t = time

Therefore, when the height is 2704ft, the time will be:

h(t) = 16t²

2704 = 16t²

t² = (2704 / 16)

t² = 169

t = ✓169

t = 13

The time taken is 13 seconds.

Learn more about functions on:

brainly.com/question/25638609

#SPJ1

Answer:

umm well i honestly forgot!

Step-by-step explanation:

but here is a fun fact During your lifetime, you will produce enough saliva

Answer:

I think the answer is 78.

Answer:

Answer is 2

Step-by-step explanation:

Because The other answers dont punctuation and answer 2 explains as the president

Answer:

six plastic bricks and four wooden blocks

Step-by-step explanation:

plastic bricks=10

wooden blocks:5

lets make plastic x and wooden y

if we made an eight pound mixture of only plastic bricks, that would get us to 80, but would not be enough weight. if we substitute one x pound for two y, we would have 9 pounds and $80. if we substitute this again, we have ten pounds and $80. we added four wooden blocks, and we took two away from the 8 plastic we had, so that is 6 plastic. so we have 6x and 4y, using the variables I assigned for the blocks above.

The rate at which the gas powered pump deliver water is 160.9 litres per seconds

The gas powered water pump delivers 42.50 gallons of water per minute.

Therefore,

1 gallon = 3.78541 litres

42.50 gallons = ?

cross multiply

volume = 42.50 × 3.78541 = 160.879925 litres

Hence,

60 seconds = 1 minutes

1 second = ?

time = 1 / 60 = 0.01666666666 seconds

Hence,

rate = 160.9 litres per second

learn more on rate here: https://brainly.com/question/20561529

#SPJ1

Answer:

x + $0.15

Explanation:

If you see well $0.15 + $0.50 = $0.65

and then $0.65 + $0.15 = $0.80

Answer:

f(n) = 0.15n + 0.35

Step-by-step explanation:

Answer:

Find the volume of this prism.

Answer:

24% or d

Step-by-step explanation:

The total quantity produced when p = 5 is 26 in the long run.

In the short run, each firm will produce where its marginal cost equals the market price, which we'll denote as p.

So, for Type A firms, the short-run supply curve is:

q4(p) = (p-2)/2

And for Type B firms, the short-run supply curve is:

qB(p) = (p-2)/6

The short-run market supply is simply the sum of the quantities supplied by each type of firm at a given price level. So, if there are 10 Type A firms and 6 Type B firms, the short-run market supply at a price level of p is:

Qs(p) = 10q4(p) + 6qB(p)

= 10(p-2)/2 + 6(p-2)/6

= 8p - 20

The total quantity produced when p=5, we can substitute p=5 into the market supply equation we just derived:

Qs(5) = 8(5) - 20

= 20

So, the total quantity produced when p=5 is 20.

The long run, firms can enter or exit the market, and as a result, the number of firms in each market may change.

In this case, we'll assume that the number of Type A and Type B firms can adjust freely in the long run, and that each firm earns zero economic profit in the long run.

If there are zero economic profits, each firm's total revenue (TR) must equal its total cost (TC), which means that price must equal average total cost (ATC).

For Type A firms, ATC4(q) = TC4(q)/q = 1/q + 2 + q, so:

5 = 1/q + 2 + q

Rearranging and solving for q, we get:

q4 = 2

So each Type A firm will produce 2 units of output in the long run.

For Type B firms, ATCB(q) = TCB(q)/q = 6/q + 2 + 3q, so:

5 = 6/q + 2 + 3q

Rearranging and solving for q, we get:

qB = 1

So each Type B firm will produce 1 unit of output in the long run.

If there are 10 Type A firms and 6 Type B firms, the total quantity produced in the long run when p=5 is:

Qlr = 10q4 + 6qB

= 10(2) + 6(1)

= 26

So, the total quantity produced when p = 5 is 26 in the long run.

For similar question on quantity produced:

https://brainly.com/question/14039381

#SPJ11

Answer: a= x^2 + 4x

Step-by-step explanation:

length= x

width= x+4

area= length x width

area = x(x+4)

area= x^2 + 4x

hope this helps :)

The probability of randomly choosing atleast one defective item would be 0.33657

Given the Parameters :

Defect rate = P(defect) = 0.05

Probability = required outcome / Total possible outcomes

P(atleast 1 is defective) = 1 - P(none is defective)

P(not defective) = 1 - P(defective) = 1 - 0.05 = 0.95

P(none is defective) = P(non defective)^5

P(none defective) = 0.95 × 0.95 × 0.95 × 0.95 × 0.95 × 0.95 × 0.95 × 0.95= 0.6634

P(atleast one is defective) = 1 - 0.6634 = 0.33657

Therefore, probability of atleast one defective item is 0.33657

learn more about of probability here

https://brainly.com/question/11443428

#SPJ4

Answer:

We know that a(1)=1

a(1)=3*1(1-1)=3*1*0=3*0=0 (any no.multiplied by 0 is equal to 0)

a(2)=3*2(2-1)=3*2*1=6*1=6

Similarly,

a(3)=18

a(4)=36

a(5)=60

Hence, the first five terms of sequence a(n)=3*a(n-1), where a(1)=1 are 0,6,18,36,60.

Thanks for reading.

Answer:

a, 6

Step-by-step explanation:

7x + 2y = 48

7x + 2(3) = 48

7x + 6 = 48

7x = 48 - 6

7x = 42

x = 42 / 7

x = 6

Answer:

1.50

Step-by-step explanation:

7.5 is 1.5 x 5 so, 1 x 1.5 = 1.5

If you need to paint your house, you estimate how much paint you will need. Like 4 gallons or whatever.