PLEASE HELP!! 40 POINTS!!

Cone details:

Sphere details:

================

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

Using Pythagoras Theorem

(a)

TO² + TU² = OU²

(h-10)² + r² = 10²                                   [insert values]

r² = 10² - (h-10)²                                     [change sides]

r² = 100 - (h² -20h + 100)                       [expand]

r² = 100 - h² + 20h -100                        [simplify]

r² = 20h - h²                                          [shown]

r = √20h - h²                                       ["r" in terms of "h"]

(b)

volume of cone = 1/3 * π * r² * h

===========================

[tex]\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)[/tex]

[tex]\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)[/tex]

[tex]\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)[/tex]

[tex]\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)[/tex]

To find maximum/minimum, we have to find first derivative.

(c)

First derivative

[tex]\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )[/tex]

apply chain rule

[tex]\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}[/tex]

Equate the first derivative to zero, that is V'(x) = 0

[tex]\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0[/tex]

[tex]\Longrightarrow \sf 40h-3h^2=0[/tex]

[tex]\Longrightarrow \sf h(40-3h)=0[/tex]

[tex]\Longrightarrow \sf h=0, \ 40-3h=0[/tex]

[tex]\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}[/tex]

maximum volume:                when h = 40/3

[tex]\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )[/tex]

[tex]\sf \Longrightarrow maximum= 1241.123 \ cm^3[/tex]

minimum volume:                 when h = 0

[tex]\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)[/tex]

[tex]\sf \Longrightarrow minimum=0 \ cm^3[/tex]

Answer:

(a)  see step-by-step

[tex]\textsf{(b)}\quad V=\dfrac{20}{3} \pi h^2-\dfrac13 \pi h^3[/tex]

[tex]\textsf{(c)}\quad h=\dfrac{40}{3}[/tex]

Step-by-step explanation:

A right triangle can be drawn with vertices at the center O, the base angle of the cone and the center of the base of the cone (see annotated image).

Side lengths of the formed right triangle:

Using Pythagoras' Theorem [tex]a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)

[tex]\implies r^2+(h-10)^2=10^2[/tex]

[tex]\implies r^2+h^2-20h+100=100[/tex]

[tex]\implies r^2+h^2-20h=0[/tex]

[tex]\implies r^2=20h-h^2[/tex]

[tex]\textsf{Volume of a cone}=\dfrac13 \pi r^2h[/tex]
(where r is the radius and h is the height)

Substitute the expression for [tex]r^2[/tex] found in part (a) into the equation so that volume (V) is expressed in terms of h:

[tex]\begin{aligned}V & =\dfrac13 \pi r^2h\\\\ \implies V & =\dfrac13 \pi (20h-h^2)h\\\\ & = \dfrac13 \pi (20h^2-h^3)\\\\ & = \dfrac{20}{3} \pi h^2-\dfrac13 \pi h^3 \end{aligned}[/tex]

To find the value of h such that the volume of the cone is a maximum, differentiate V with respect to h:

[tex]\begin{aligned}V & =\dfrac{20}{3} \pi h^2-\dfrac13 \pi h^3\\\\ \implies \dfrac{dV}{dh} & =2 \cdot \dfrac{20}{3} \pi h-3 \cdot \dfrac13 \pi h^2\\\\ & = \dfrac{40}{3} \pi h- \pi h^2\\\\ & = \pi h\left(\dfrac{40}{3}-h\right)\end{aligned}[/tex]

Set it to zero:

[tex]\begin{aligned}\dfrac{dV}{dh} & =0\\\\ \implies \pi h\left(\dfrac{40}{3}-h\right) & = 0\end{aligned}[/tex]

Solve for h:

[tex]\begin{aligned} \pi h & = 0 \implies h=0\\ \dfrac{40}{3}-h & =0\implies h=\dfrac{40}{3}\end{aligned}[/tex]

Substitute the found values of h into the equation for Volume:

[tex]\begin{aligned}\textsf{when}\:h=0:V &=\dfrac{20}{3} \pi (0)^2-\dfrac13 \pi (0)^3\\\\ \implies V & =0\sf \:cm^3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{when}\:h=\dfrac{40}{3}:V &=\dfrac{20}{3} \pi \left(\dfrac{40}{3}\right)^2-\dfrac13 \pi \left(\dfrac{40}{3}\right)^3\\\\ \implies V & =\dfrac{32000}{27} \pi -\dfrac{64000}{81} \pi\\\\ & = \dfrac{32000}{81} \pi \\\\ & = 1241.123024..\sf \:cm^3\end{aligned}[/tex]

Therefore, the value of h such that the volume of the cone is a maximum is:

[tex]h=\dfrac{40}{3}[/tex]

Answer:

197.92 in³

Step-by-step explanation:

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substituting the given values into the formula:

[tex]\begin{aligned} \implies \textsf{Volume of a cylinder} & =\sf \pi (3)^2(7)\\ & = \sf 63 \pi\\ & = \sf 197.92\:in^3\:(nearest\:hundredth)\end{aligned}[/tex]

Answer:

denominator

Step-by-step explanation:

the upper part is numerator

so the lower is denominator

Answer:

one part of a whole

Step-by-step explanation:

A unit fraction shows one part of a whole number

(*) Sorry for my late answer but I hope this helps others that are looking for this.

I got 100% (edge)  ;)

take for granted 1. Consider as true or real, anticipate correctly, as in I took it for granted that they'd offer to pay for their share but I was wrong. [c. 1600] 2. Underestimate the value of, become used to, as in The editors felt that the publisher was taking them for granted.

Answer:

24

Step-by-step explanation:

[tex]\sf Given\:fraction:\dfrac{48}{72}[/tex]

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 72:  1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

So the greatest common factor (GCF) of 48 and 72 is 24.

Therefore, to simplify the fraction, divide the numerator and denominator by 24:

[tex]\sf \implies \dfrac{48}{72}=\dfrac{48 \div 24}{72 \div 24}=\dfrac{2}{3}[/tex]

Answer:

24

Step-by-step explanation:

Factors of 48 and 72

Solving

Answer:

its the same thing as 3 x3 or 3+3 it always come´s back as 9 or 6 Becasue of its rotation

Step-by-step explanation:

Option D is correct. The number of team members who prefer tacos is the same as the combined number of team members who prefer hamburgers or pizza.

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

Coach Rodriguez is planning an end-of-season celebration for the swim team.

To decide what food to serve, she surveys a random sample of students on the team Food for End-of-Season Celebration.

We can see that,

The number of team members who prefer tacos = 12

The combined a number of team members who prefer hamburgers or pizza = 7 + 5

         = 12.

So, The number of team members who prefer tacos is the same as the combined number of team members who prefer hamburgers or pizza.

The inference supported by the data collected in the survey would be option D.

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Answer:

The number of team members who prefer hamburgers is the same as the combined number of team members who prefer pizza or chicken fingers.

Step-by-step explanation:

Test approved

Answer:

1/6

Step-by-step explanation:

First one red  4 out of 9  =  4/9

now there are 8 marbles left and 3 are red

prob of red is now   3 out of 8 = 3/8

4/9 * 3/8 =   12/72 = 1/6

Using exponential function concepts, it is found that the range of f(x) is given by:

{y | y > –4}

An exponential function is defined by:

[tex]y = ab^x + k[/tex]

The value of k is the asymptote of the function, hence the range is {y|y>k}.

In this problem, the function is given by:

[tex]f(x) = \left(\frac{3}{4}\right)^x - 4[/tex]

Hence k = -4 and the range is {y | y > –4}.

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Answer:

the answer is A

Step-by-step explanation:

i got it right on edge 2022

Answer:

100

Step-by-step explanation:

10x10=100

Answer:

10.50 Miles per hour

Step-by-step explanation:

42/4 = 10.50 easy

Answer:

D. (7, 0)

Step-by-step explanation:

The rule for a reflection over the y-axis is (x, y) → (x, -y)

This means that the x-values stay the same while the y-values change.

Q(x, y) → (x, -y)

Q(3, 0) → (3, 0)

Q'(3, 0)

P(x, y) → (x, -y)

P(5, 6) → (5, -6)

P'(5, -6)

R(x, y) → (x, -y)

R(7, 0) → (7, 0)

R'(7, 0)

Therefore, the correct answer is D.

Hope this helps!

Answer:

1571 + 64x < 2187

Step-by-step explanation:

Answer:

The expression represent the total amount of price money is 3x-150.

The expressions let X be the amount of money for first place. This means X-50 would be the amount of second place because each subsequent place after 1st wins $50 less than the previous place. Thirds, would be X-50-50 or X-100.

That is X = first place and each place after that is 50 less so 2nd place would be  x - 50 and third place would be x - 100.

Thus the total amount of money would be all of the values combined which is

x + (x - 50) + (x - 100)

Combinimg the like terms

What is the combinimg the like terms?

To combine like terms, we have to add the coefficients and keep the variables the same. We add like terms to make one term.

x+x-50+x-100

3x-150

3x - 150

Therefore the option b is correct.

So the expression represent the total amount of price money is 3x-150.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the slope formula.

[tex]\underline{\text{SLOPE:}}[/tex]

[tex]\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{Rise}{Run} }[/tex]

[tex]\sf{y_2=9}\\\\\\\sf{y_1=5}\\\\\\\sf{x_2=3}\\\\\\\sf{x_1=1}[/tex]

[tex]\sf{\dfrac{9-5}{3-1} }[/tex]

Solve.

[tex]\sf{\dfrac{9-5}{3-1}=\dfrac{4}{2}=\boxed{\sf{2}}[/tex]

I hope this helps. Let me know if you have any questions.

Answer:

Step-by-step explanation:

.8 millimeters :1 meters

Answer: 5 METERS ACCORDING TO IXL

Step-by-step explanation:

Answer:

-3, -12

Step-by-step explanation:

Only the y coordinate should change. A translation of -6 units would be -12 meaning it is (-3, -12)

Answer:

52.25 MPH

Step-by-step explanation:

Using the formula given D=RT we simply plug in values,

313.5=6R

313.5/6=R

52.25=R

Considering the hypotheses tested, it is found that the p-value for Nicolas's test is of 0.101.

At the null hypotheses, it is tested if the mean is of 24, that is:

[tex]H_0: \mu = 24[/tex]

At the alternative hypotheses, it is tested if it is different, hence:

[tex]H_1: \mu \neq 24[/tex]

As we are testing if the mean is different of a value, we have a two-tailed test, with t = -1.79 and 12 - 1 = 11 df. Hence, using a t-distribution calculator, the p-value is of 0.101.

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Answer:

C

Step-by-step explanation:

H(4) simply means that where there is X, it must be substituted by the value 4

So lets see step by step:

A. h(4)=2 (incorrect)(there is no X to substitute on the right side and it is stated that H is non linear. This 2 would mean that H is a straight line)

B. (4)^3 -4= 60 (incorrect as answer needs to be 2)

C. 2^4 - 14=2 (correct, as answer is 2 and equation is non linear)

D. 1/2 (4) +3 = 5 (incorrect)

Hence your answer is C

Answer:

Margo makes 2/3 shots and making 4 shots and missing 2 shots equals 6 so 4/6 reduces to 2/3.

Step-by-step explanation:

4/6 = 2/3

From the graph and orientation of the parametric equations: A. the graph is a circle with a radius of 4. The orientation is counterclockwise as t increases.

In geometry, the relationship between the rectangular coordinates (x, y) and polar coordinates (r, t) is given by these polar functions:

x = rcost and y = rsint.

Where:

Mathematically, the standard form of the polar equation of a circle is given by;

x² + y² = r²

Given the following data;

x = 16cost  ⇒ x² = 16cos²t

y = 16sint   ⇒ y² = 16sin²t

Evaluating, we have:

x² + y² = 16

r² = 16

r = √16

Radius, r = 4.

Also, the orientation is counterclockwise as t increases because the angle gets bigger (increases).

x = 3t    .....equation 1.

y = t²     .....equation 2.

Making t the subject of formula in eqn. 1, we have:

t = x/3    .....equation 3.

Substituting eqn. 3 into eqn. 2, we have:

y = (x/3)²

rsinθ = (rcosθ/3)²

rsinθ = r²cos²θ/9

9rsinθ = r²cos²θ

9sinθ = rcos²θ

r = 9sinθ/cos²θ

r = 9 × (sinθ/cosθ) × 1/cosθ

r = 9tanθsecθ.

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Answer:

I think it's easiest to count the ways that they can consecutively sit together and subtract this from the total number of seating arrangements.

There are 6 groups of 3 consecutive seats.  Within each group there are 3!=6 ways the three people can be arranged

Then the remaining 5 people can be arranged 5!=120 ways in the remaining seats.

So there are 6*6*120 = 4320 arrangements where they DO sit consecutively

There are 8! = 40320 total arrangements.

So there are 40320 - 4320 = 36000 arrangements where the 3 do not sit consecutively.

Step-by-step explanation:

Answer:

28c-12 and  it would be 4(7e-3 and i did not copy from googe i did this on my own

Step-by-step explanation:

Answer:

[tex] \: [/tex]

Step-by-step explanation:

So, here we are to factor the polynomial :

[tex] \\ \longrightarrow \sf \qquad28c - 12\\ \\[/tex]

[tex]\longrightarrow \sf \qquad4(7c - 3)\\ \\[/tex]

Some points to know :

Answer:

see explanation

Step-by-step explanation:

the tan , sin , cos ratios are used to find sides and angles in a right triangle.

There is no indication on the diagram that the triangle is right.

then the use of the tan ratio is an error if the triangle is not right.

Answer:

The answer is -19

Step-by-step explanation:

Given information -19y^2 , y=-1

-19 * y^2

-19 * (-1)^2

-19 * 1 = -19

Answer:

B) 24

Step-by-step explanation:

distance = 6 km

we want the speed in km/h, so let's turn everything into either km or h if possible

time = 7:45 am - 7: 30 am = 15 minutes

60 minutes = 1 hour

1 hour / 60 minutes = 1

15 minutes * 1 = 15 minutes * 1 hour/60 minutes = 15 / 60 hours = 1/4 hours = 0.25 hours

note that we multiply by 1 hour / 60 minutes, not 60 minutes/ 1 hour. this is because we want the minutes to cross out -- because the original is given in minutes ( 15 minutes = 15 minutes/1) and is in the numerator, we need minutes in the denominator of 1 hour/60 minutes to cross it out

km = 6

h = 0.25

km/h = 6/0.25 = 24

Answer:

Below in bold.

Step-by-step explanation:

Nth term an = a1 + d(n - 1)   where a1 = term 1 and d = common difference.

Here a1 = 5 and d = 8-5 = 3.

So an = 5 + 3(n - 1)

15th term a15

=  5 + 3(15 - 1)

= 5 + 42

= 47.

Answer: 120 And 300

Step-by-step explanation: Ratio 2:5 = 7

1/7 of 420 = 60

Ratio 1 = 60

Ratio 2 = 60 ×2

Ratio 5= 60 ×5