I need this ASAP!
Solve:

Answer:

Workdone = 4900joules

Step-by-step explanation:

Work-done = force x distance

Force = mass x acceleration

If we suppose that the aquarium is at height 0 at the top and height 1 at the bottom (since it's 1m deep), then we need to lift the slide at height x by x metres.

Mass = Density x Volume, therefore force needed to lift the slice is given is

F = density*volume*∆x*acceleration

Since we the mass changes as we take out water then there will be a change in height, for this reason we have ∆x.

Acceleration is due to gravity, therefore g=9.8m/s²

Density = 1000kg/m³

Volume = 4*1*1 = 4m³

F = 1000*4*∆x*9.8 = 39200∆x

Since our distance from the top of the aquarium to the bottom is x metres, then

Work-done = 39200x∆x

To find the total workdone, we find the integral of 39200xdx and the limit will be from 0 to 0.5 since we are to pump halfway of the aquarium. Integrating that we have

19600*x² limit from 0 to 0.5

19600(0.5² – 0²) = 19600(0.25 – 0) = 19600(0.25) = 4900joules

Answer:

3825

Step-by-step explanation:

Answer:

7t/5^3 + 5t^2 + 4t^3

Step-by-step explanation:

The area of the region is equal to the area under the curve y = cos(x) over the interval 0 ≤ x ≤ π/6, given by the integral

[tex]\displaystyle\int_0^{\frac\pi6}\cos(x)\,\mathrm dx = \sin(x)\bigg|_0^{\frac\pi6}=\sin\left(\frac\pi6\right)-\sin(0)=\boxed{\frac12}[/tex]

which follows from

• the fact that d/dx [sin(x)] = cos(x)

• the fundamental theorem of calculus

Answer:1.40

2.20

3.100

4.39

5.7

7

Step-by-step explanation:

Answer:

117

Step-by-step explanation:

angle 2 = 117 so angle 1 has to =63 because they have to equal 180 (supplementary angles)

angle 1 =63 .  angle 3 =117

angle 7 is the same measurement of angle 3

hope this makes sense

Answer:

117 degrees

Step-by-step explanation:

angle 1 and 2 are supplementary angles which are angles whose measurements add up to 180 degrees

this means angle 1 = 63 degrees

63 + 117 = 180

angle 1 and 3 are linear pair angles which means they also equal 180 degrees

angle 3 = 117 degrees

angle 3 and angle 7 are corresponding angles which means their degrees are equal to each other

angle 7 = 117 degrees

The relationship between angle 2 and 7 would be alternate exterior angles

Answer:

D

Step-by-step explanation:

it is a quadratic trinomial

Answer:

38 plus 52 is in fact 90, but Sin and Cos will be different.

Step-by-step explanation:

Honestly I haven't learned Sin or Cos

Answer:

Step-by-step explanation:

it's not possible

I think -7 is the right answer but it's not possible actually

Answer:

c. -7

Step-by-step explanation:

(x+57) + (63+67) = 180

(x+57) + 130 = 180

x + 187 = 180

x = 180-187

x = -7

why did I make it equal to 180?

all the angles in a triangle always equal 180 :)

Answer:

16

Step-by-step explanation:

Equation : 6x+2=5x+18

Like Terms : x + 2 = 18

Like Terms Again : x = 16

Answer:

6x+2=5x+18

6x-5x=18-2

X=16

Step-by-step explanation:

First you need to group numbers of like terms in one side. Then when you take the other number to the other side of equal sign changes it's form eg +6 change to - 6

Answer:

24 in long by 12 in wide.

Step-by-step explanation:

l=2w

288=(2w)×w

288=2w^2

144=w^2

12=w

width is 12 inches. Plug that in to find length...

l=2×12

l=24

Answer:

First: 6 Second: 8 Third:16

Step-by-step explanation:

First number:x

Second number: 1.5x-1

Third number: 3x-2

x+1.5x-1+3x-2=30

5.5x-3=30

5.5x=33

x=33/5.5=6

So First =6

Second= 1.5(6)-1=8

Third " 3(6)-2=16

Answer:

C) 16 points

Step-by-step explanation:

Answer:

Answer and steps in picture.

Answer:

115

Step-by-step explanation:

1, 7, 13, 19, 25...

1, 1+6, 1+6+6, 1+6+6+6, 1+6+6+6+6...

In 2nd number, 1 plus one 6

In 3rd number, 1 plus two 6s

:

In 20th, 1 plus nineteen 6s

1 + 6 × 19 = 115

Answer:

The cone volume that has a diameter of 20cm and a height of 12cm is 5,026.548246 cm^3 or 5,027 cm^3

Make sure to round your answer to the nearest significant figure that you're asked.

Step-by-step explanation:

The formula for the volume of a cone is (height x π x (diameter / 2)^2)/3, where (diameter / 2) is the radius of the base (d - 2 x r), so another way to write it is (height x π x radius^2) / 3

Answer:

2/10 + 30/100 = 50/100

Step-by-step explanation:

First, you want to multiply 2/10 by 10, to get the same common denominator in both numbers, you would get 20/100. Then, its pretty simple from there, you just add the number that gets you to 50, which is 30, 20 + 30 =50. I Hope This Helps :)

The required missing number is 30. So, the correct answer is (a) 30.

Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. It involves the basic operations of addition, subtraction, multiplication, and division.

Here,
To find the missing number, we can use the fact that 50/100 is equivalent to 1/2.

So, we need to find a number that, when added to 2/10, gives 1/2 as the sum.

We can write this as an equation:

2/10 + x/100 = 1/2

Multiplying both sides by 100 to eliminate the denominator, we get:

20 + x = 50

Subtracting 20 from both sides, we get:

x = 30

Therefore, the missing number is 30. So, the correct answer is (a) 30.

Learn more about arithmetic here:

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Answer:

I don’t think it’s a right triangle

Step-by-step explanation:

5^2 + 8^2 should equal 12^2 for it to be a right triangle.

Proportionately, the number of times that Hannah will have to tie the blanket is 48 times.

Proportion is the relationship between two numerical values or variables.  It shows the share or portion of a variable to the whole number.

Proportions are expressed as ratios, usually using fractions, decimals, or percentages.

The length of the fleece tie blanket = 36 inches

The width of each tie = 3/4 inches

The proportion of 3/4 inches to an inch = 0.75 (3/4)

The number of times to tie the blanket = 48 times (36/0.75)

Thus, the number of times that Hannah will tie the blanket is 48 times.

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480 because 6,720 divided by 14 is 480

The probability that exactly 3 of the 4 employees selected will have children is given by binomial distribution formula  ⁴C₃(0.60)³(0.40)

What is a Binomial Distribution?

The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.

The formula for Binomial Distribution is given by

P ( x ) = ⁿCₓ pˣq⁽¹⁻ˣ⁾

where

n = number of trials

x = number of successes

p = probability of getting a success in one trial

q = probability of getting a failure in one trial

q = 1 - p

Given data ,

Let the total number of employees be = 500

Now , the probability of success of selecting employees having children is given by p = 0.60

So , the value of q = 1 - p

q = 1 - 0.60

q = 0.40

So , The probability that exactly 3 of the 4 employees selected will have children is given by binomial distribution formula

where,

P ( x ) = ⁿCₓ pˣq⁽¹⁻ˣ⁾

where

n = number of trials

x = number of successes

p = probability of getting a success in one trial

q = probability of getting a failure in one trial

q = 1 - p

Substituting the values in the equation , we get

P ( x ) = ⁴C₃(0.60)³(0.40)

On simplifying the equation , we get

P ( x ) = 4 x 0.246 x 0.4

P ( x ) = 0.3456

Therefore , the value of P ( x ) is 0.3456

Hence , The probability that exactly 3 of the 4 employees selected will have children is given by binomial distribution formula ⁴C₃(0.60)³(0.40)

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Answer:

Step-by-step explanation:

A = L x W

so you know that the length is 3m longer than the width, so you could use a formula to represent that

w = L + 3

you then substitute the second equation into the first to solve for L

70 = L x (l +3)

70 = L^2 + 3l

you could then rearrange the formula and solve for l using the quadratic formula  

0 = L^2 + 3l - 70

l = -3 +- (square root (3)^2 - 4(1)(70)) / 2(1)

l = -3 +- (square root 9 + 280) / 2

l = -3 +- (square root 289) / 2

l = -3 +- 17 / 2

then you solve for the two separate roots

l = -3 + 17 /2

l = 14 / 2

l = 7

or  

l = -3 - 17 / 2

l = -20 / 2

l = -10

since a length cannot be negative, this root is not viable. therefore l = 7

to solve for w you would use

w = l + 3

w = 7 + 3

w = 10  

hope this helps. :)))