3. The upward velocity of the water in a particular fountain is given in feet per second by
v = -32t + 44, where t is the number of seconds after the water leaves the fountain. While
going upward the water slows down until, at the top, the water has a velocity of zero. How long
does it take each water particle to reach its maximum height?

Answer:

[tex]\frac{400}{3} \pi[/tex]

Step-by-step explanation:

Formula for Cone: π[tex]r^{2}\frac{h}{3}[/tex]

Since we have all the components, we can find the volume of the cone.

R = 10

H = 4

π[tex]10^{2}\frac{4}{3}[/tex]

10×10 = 100

100π[tex]}\frac{4}{3}[/tex]

[tex]}\frac{4}{3}[/tex]×100

4       100          400

---  ×   -----    =    ------

3          1              3

Answer: [tex]\frac{400}{3} \pi[/tex]

Hope this helped.

Find the volume of a cone with radius 10 feet and height of 4 feet.

Given Data :

Radius = 10 feet

Height = 4 feet

Formulae :

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \blue{ \underline{ \overline{ \green{ \boxed{ \frak{{ \sf V}olume_{(Cone)} = \pi {r}^{2} \frac{h}{3}}}}}}}[/tex]

Putting the values we get

[tex] \frak{ Volume_{(Cone)} = 3.14 × (10)² × \frac{4}{3} }[/tex]

[tex] \frak{Volume_{(Cone)} = 3.14 × 100 × \frac{4}{3} }[/tex]

[tex] \frak{Volume_{(Cone)} = 314 \times \frac{4}{3} }[/tex]

[tex] \frak{Volume_{(Cone)} = 418.67 \: ft³ }[/tex]

Henceforth, the volume is 418.67 ft³

Answer:

See explanation

Step-by-step explanation:

Given

[tex]\triangle LMN \to \triangle PQR[/tex]

[tex]k = 1.25[/tex]

Required

The length of PQ

[tex]\triangle LMN \to \triangle PQR[/tex] means that the side lengths of LMN are multiplied by 1.25 to get the side lengths of PQR

And it implies that the following sides are corresponding

[tex]LM \to PQ[/tex]

[tex]MN \to QR[/tex]

[tex]LN \to PR[/tex]

So, we have:

[tex]PQ = k * LM[/tex]

[tex]PQ = 1.25* LM[/tex]

The question is incomplete.

Assume LM = 16, then:

[tex]PQ = 1.25* 16[/tex]

[tex]PQ = 20[/tex]

Answer:

Step-by-step explanation:

(4, -6) is in quadrant IV , (quadrant 4)

Answer:

x = 5.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 26 = x /12

12 tan 26 =x

x=5.85279

Rounding to the nearest tenth

x = 5.9

Answer:

SSS Postulate

Step-by-step explanation:

The first says 2 sides are the same

The second says 2 sides are the same

The last says 2 sides are the same

Side side side

SSS Postulate

Answer:

0, 8, 5i, -51

Step-by-step explanation:

Just calculate algebraically. Let me know if you need a more elaborate explanation.

Answer:

The correlation coefficient is approximately -0.9949

Step-by-step explanation:

The given data is presented as follows;

[tex]\begin{array}{lcl}x&&y\\-10&&2\\-8&&-3\\-1&&-15\\-4&&-10\\-6&&-6\\-7&&-5\\-5&&-8\\-3&&-13\\-2&&-14\\-9&&-1\end{array}[/tex]

The correlation coefficient, r is given as follows;

[tex]r = \dfrac{\sum(x_i - \overline x) \cdot (y_i - \overline y)}{\sqrt{\sum (x_i- \overline x)^2\times \sum (y_i- \overline y)^2 } }[/tex]

From MS Excel, we have;

∑([tex]x_i - \overline x[/tex])·([tex]y_i - \overline y[/tex]) = -155.5

∑([tex]x_i - \overline x[/tex])² = 82.5

∑([tex]y_i - \overline y[/tex])² = 296.1

Therefore, r = -155.5/(√(82.5 × 296.1)) ≈ -0.9949

The correlation coefficient, r ≈ -0.9949

2 occurred 3times

[tex]\\ \sf\longmapsto S=6\times 3=18[/tex]

[tex]\\ \sf\longmapsto |S|=18[/tex]

Now

[tex]\\ \sf\longmapsto E=No\:of\:times\: 2\:occured[/tex]

[tex]\\ \sf\longmapsto |E|=3[/tex]

we know

[tex]\boxed{\sf P(E)=\dfrac{|E|}{|S|}}[/tex]

[tex]\\ \sf\longmapsto P(E)=\dfrac{3}{18}[/tex]

[tex]\\ \sf\longmapsto P(E)=\dfrac{1}{6}[/tex]

Answer:

1-[tex]\frac{2 }{\pi }[/tex] = 1- .64 = .36 = 36%

[tex](4\sqrt{2}) ^{2} = 32\\[/tex]

[tex]\pi 4^{2}[/tex]= 16[tex]\pi[/tex]

[tex]\frac{32}{16\pi }[/tex]= [tex]\frac{2 }{\pi }[/tex]

Step-by-step explanation:

Answer:

[tex]344 {cm}^{2} [/tex]

Step-by-step explanation:

[tex]area \: of \: the \: square \\ = 40cm \times 40cm \\ = 1600 {cm}^{3} \\ [/tex]

[tex]area \: of \: the \: circle \\ = \pi {r}^{2} \\ = 3.14 \times {(20)}^{2} \\ = 3.14 \times 400 \\ = 1256 {cm}^{2} \\ [/tex]

[tex]area \: of \: shaded \: region \\ = 1600 {cm}^{2} - 1256 {cm}^{2} \\ = 344 {cm}^{2} \\ [/tex]

Step-by-step explanation:

I can give you a formula SOH-Sinø=Opposite\Hypotenuse

CAH-Cos=Adjacent\Hypotenuse

TOA-Tan=Opposite\Adjacent

Answer:

Step-by-step explanation:

Let the initial number of people on the boat be x:

x - 26 - 22 = 74

x -48 = 74

x = 74 + 48

x = 122

Answered by  G a u t h m a t h

Answer:

Justin did not eat 7/12 of the pizza

Step-by-step explanation:

Marc eats 1/6 × 24 = 4, 24 - 4 = 20 left over

Claudine eats 1/4 × 20= 5, 20 - 5 = 15 left over

Sylvia eats 1/3 × 15 = 5, 15 - 5 = 10 left over

Justin eats 10.

24 - 10 = 14

Justin did not eat 14/24 = 7/12

Answer:

2[tex]\sqrt{10\\}[/tex]

Step-by-step explanation:

Because this is a right triangle, we have:

[tex]x^{2} + 3^{2} = 7^{2} (Pytago)\\x^{2} + 9= 49\\x^{2} =40\\x=\sqrt{40} \\x=2\sqrt{10}[/tex]

Answer:

Step-by-step explanation:

quadratic equation is 4(x+2)(x+5)=0

4(x²+5x+2x+10)=0

4x²+28x+40=0

Answer:

f(x) = 4(x+2)(x+5)

Step-by-step explanation:

The quadratic function is

f(x) = a(x-b1)(x-b2)  where a is a coefficient and b1 and b2 are the zeros

f(x) = a(x --2)(x--5)

f(x) = a(x+2)(x+5)

The leading coefficient is a and we know a =4

f(x) = 4(x+2)(x+5)

Answer:

$5000 per year

Step-by-step explanation:

Given data

initial value of the computer= $30000

Final value = $0

Duration= 6years

Hence the rate of change in the value per year is

=30000/6

=$5000 per year

Answer:

Step-by-step explanation:

-185

Answer: 63.64 cm² (rounded to the hundredth place)

Step-by-step explanation:

Concept:

Here, we need to understand how to find the area of a circle.

The general formula is: A = πr²

π = 3.14 (or any constants that equals to this value)

r = radius = (1/2) diameter

Solve:

π = 22/7

r = d/2 = 9 / 4 = 4.5

A = πr²

A = (22/7) (4.5)²

A = (22/7) (4.5)²

A = 63.64 cm² (rounded to the hundredthe place)

Hope this helps!! :)

Please let me know if you have any question

Answer:

63.64 cm²

Step-by-step explanation:

r = d/2 = 9 / 4 = 4.5

A = πr²

A = (22/7) (4.5)²

A = (22/7) (4.5)²

A = 63.64 cm² (rounded to the hundredth place)

Answer:

C

Step-by-step explanation:

Given 2 secants from an external point to the circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant , that is

ML × KM = MN × MR, substitute values

7 × KM = 6(6 + 8)

7 KM = 6 × 14 = 84 ( divide both sides by 7 )

KM = 12 → C

Answer:

C.) 12

Step-by-step explanation:

I got it correct on founders edtell

Answer: 184.92 lbs

Step-by-step explanation:

If the total amount they made in 2 days was 369.84, the avg per day would just be half of that

369.84/2=184.92 lbs

Answer:

The factory made 184.92 pounds of milk chocolate per day.

Step-by-step explanation:

369.84 ÷ 2 = 184.92

Have a great day :)

Answer:

1050 + (150)times the amount of jobs they do for you during that winter, for A. 0 + (200)times the amount of jokes they do for you during that winter, for B.

Step-by-step explanation:

Boom I would choose B because it would be cheaper, since we do most of the snow removal ourselves.

The 3rd option is correct

Answer:

1/24 (fraction form)

hope this helps

Answer:

So, we need to find irrational numbers between the given pairs.

Remember that the sum between an irrational number and an rational number is irrational.

For example, for the first case, we want a irrational number between:

3.14 and pi:

pi = 3.14159265.... is irrational

pi - 0.0001 = 3.14159265... - 0.0001 = 3.14149265...

So this number:

3.14149265...

is an irrational number larger than 3.14 and smaller than pi.

Second cacse:

3.33 and 1/3

(here the range would be actually:

1/3 = 0.33 and 3.33

So we want an irrational number larger tan 0.33 and smaller than 3.33

here we can just use pi = 3.141592...

third case:

e^2 and √5

Firs let's write these numbers so we can see how they look.

e^2  =7.389...

√5 = 2.236

So we want a number larger than 2.236... and smaller than 7.389...

Again, here we can use pi = 3.141592...

2.236... < 3.141592... < 7.389...

final case:

√(64/2) and √16

we have:

√(64/2) = 5.65

√16 = 4

So we want an irrational number larger than 4 and smaller than 5.65

Again, let's use our beloved number pi.

we have that:

pi + 1  is an irrational number:

pi + 1 = 3.14159265... + 1.0 = 4.14159265....

This number, 4.14159265..., is irrational, is larger than 4 and is smaller than 5.65, so we found the irrational number between the given pair of numbers.

Answer:

3.33 and 1/3

Step-by-step explanation:

Answer:

449 100

Step-by-step explanation:

0.2% × 450000÷ 100=900

450000-900= 449 100

Answer:

Step-by-step explanation:

The answer is 449100 pounds .

Answer:

Step-by-step explanation:

The enlargement of a comic will be very similar to the original. Everything is larger but in the same proportion. The difference is if the original is enlarged so much that the individual pixel in the original comic becomes visible; causing the enlargement to be "pixelated."

If a comic is drawn using a grid, that may reduce pixelation because you can line up things with the grid.

If the comic's size is reduced, then again it will look similar but everything is smaller and in the same proportion. There will not be any pixelation effect.

Answer:

D.

Step-by-step explanation:

The line will be a straight line and will go through AB in the center. Therefore, it will be the perpendicular bisector.