If f(x) = x³ - 2, find f(3).

Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

Volume of Cone = [tex]\pi r^{2} \frac{h}{3}[/tex]

a) Given Diameter , d = 15.5cm and Length , h = 350cm,

we first find the radius.

[tex]r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm[/tex]

We will now find the volume of the cone.

Volume of cone  [tex]\pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}[/tex]

We know the density of ice is 0.93 grams per [tex]1cm^{3}[/tex]

[tex]1cm^{3} =0.93g\\\frac{168175\pi }{24} cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g[/tex](Nearest Gram)

b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

and the new length, h = 350cm - 15cm = 335cm

Now we will find the volume of this newly-shaped cone.

Volume of cone = [tex]\pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}[/tex]

Volume of cone being melted = New Volume - Original volume

= [tex]\frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}[/tex]

c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = [tex]\pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}[/tex]

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = [tex]5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}[/tex]

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= [tex]\frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}[/tex]

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

The algebraic expression for the given word problem is 12/y + 7

From the question, we are to write the algebraic expression for the given word problem

The given word problem is

"the quotient of 12 and a number y increased by 7"

First,

"the quotient of 12 and a number y" can be expressed as

12/y

Then,

"the quotient of 12 and a number y increased by 7" becomes

12/y + 7

Hence, the algebraic expression for the given word problem is 12/y + 7

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Answer:

Step-by-step explanation:

The time required to clean 200 square feet will be 80 minutes. Option B is correct.

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

Let x be the cleaning time for the 200 square feet area;

From the table, it is observed that for a 1 sq. foot area the time needed to clean will be 0.4 minutes.

1 square feet = 0.4 minute

200 square feet = 200 × 0.4

200 square feet  = 80 minute

The time required to clean 200 square feet will be 80 minutes.

Hence, option B is correct.

The table is attached in the attachment.

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Step-by-step explanation:

Q9

a) :

First, find the common difference for the sequence. add the first term to the second term

3+3= 6

add second term to the third term

3+6=9

add third term to the fourth term

6+9=15

b) 15 +24= 39

24+39=63

39+63= 102

Q10

a) 2 , 10 , 8

b) find the common difference for the sequence. Subtract the first term from the second term.

10-2= 8

Subtract the second term from the third term

8-10= -2

c) 10

Answer:

There is no definitive answer to this question since different wigs are made with different kinds of synthetic fibers. Some synthetic fibers are more resistant to heat than others, so it really depends on the specific wig. In general, however, it is generally not recommended to use heat on synthetic wigs, as it can damage the fibers.

Answer:

263 8/9 millilitres

Step-by-step explanation:

9.5 litres = 9500 millilitres

9500/36 = 263 8/9

Answer:

I don't know how to answer this, sorry!

Step-by-step explanation:

.

Using linear function concepts, we have that from the information given:

A linear function is modeled by:

y = mx + b

In which:

From the information given, the y-intercept is of 25 and the slope is of $2.50, hence the value after t months is given by:

V(t) = 25 - 2.5t.

Thus:

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Answer:

7720 mm²

Step-by-step explanation:

area = 2 × 80 mm × 40 mm + 2 × 80 mm × 5.5 mm + 2 × 40 mm × 5.5 mm

area = 7720 mm²

The integer that represents the horizontal translation of f(x) to g(x) is 4

The attached graph represents the missing piece in the question

From the graph, we can see that:

The function g(x) is 4 units to the left of the function f(x)

This means that:

g(x) = f(x + 4)

Hence, the integer that represents the horizontal translation of f(x) to g(x) is 4

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The errors Emma made are

From the question, we are to determine the errors that Emma made

The given statement is

"The quotient of six and a number, x, is the same as negative two times the difference of x and 4.5"

"The quotient of six and a number, x", can be expressed as

6/x

"Two times the difference of x and 4.5", can be expressed as

2(x - 4.5)

Hence, the errors Emma made are

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Answer:

First we have to find the value of x;

then we have to find the value of y;

Step-by-step explanation:

here,

2x= 12

x = 12\2

x = 6

now,

4y = 12

y = 12\4

y = 3

° the value of x is 6

° ° the value of y is 3

Then the most profitable investment is the first machine (third option) because for each dollar, it produces 2 pounds of candy.

The first option is a worker that costs $10 per hour and produces 8lb, then this worker gives:

8lb/$10= 0.8 pounds per dollar.

The second worker costs $12 per hour, and produces 16lb per hour, so this worker gives:

16lb/$12 = 1.33 pounds per dollar.

The third option is a machine that cost $5 per hour and produces 10lb per hour, then:

10lb/$5 = 2 pound per dollar.

The last option costs $8 per hour, and produces 14 pounds per hour, then:

14lb/$8 = 1.75 pounds per dollar.

Then the most profitable investment is the first machine (third option) because for each dollar, it produces 2 pounds of candy.

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Answer:

let x be thomas age

3x for huilans age since huilans age is 3 time thomas age

both of their ages add to 76

ie. x + 3x =76

solve for x

4x = 76

x = 76 ÷ 4

x = 19. thomas age

to get huilans age : take 19 × 3 = 57

Answer:

If this is the question about sample space, a possible answer is 24 and 64 ways in sample space.

Step-by-step explanation:

Hopefully, this is helpful :)

Answer:

a gas can hold 7×10=70 litters of gas

Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, we have that:

Hence the number of ways by which they can go on stage is:

N = 2 x 3! = 12.

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Answer:

Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.

What is the arrangements formula?

The number of possible arrangements of n elements is given by the factorial of n, that is:

A_n = n!A

n

=n!

In this problem, we have that:

For the first dragon, either the green or the blue dragon, hence two outcomes.

For the remaining dragons, there are 3! possible ways.

Hence the number of ways by which they can go on stage is:

N = 2 x 3! = 12.

Answer:

See below

Step-by-step explanation:

Isosceles because two sides are same length

                 and

Obtuse because there is an interior angle greater than 90 °

Step-by-step explanation:

Answer:

The answer would be A. 3/4

Step-by-step explanation:

To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

The algebraic expression that represents the reduced price is p - 125

The reduction is given as:

Reduction = $125

The original price is given as:

Original = P

The reduced price is calculated as:

Reduced price = original - reduction

This gives

Reduced price = p - 125

Hence, the algebraic expression that represents the reduced price is p - 125

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Answer:

75

Step-by-step explanation:

Since they sold 75% of the raffle tickets and the total is 100 raffle tickets, you simply need to find 75% of 100. To find x% of a, you simply convert x% to a decimal by dividing by 100 and then multiplying it by a. So the general formula to find x% of a would be: [tex]a*\frac{x}{100}[/tex]. In this case a=100, and x=75. So you have the equation: [tex]100*\frac{75}{100} = \frac{100 * 75}{100}=\frac{75}{1} = 75[/tex]

Answer: 75 tickets

Step-by-step explanation:

- percentages are out of 100, they are a rate, number, or amount in each hundred

- for example, (10/100) x 100 (because it’s out of 100) = 10%
- or it could be (6/40) x 100 (because it’s out of 100) = 15%

- so because they started with 100 tickets, it’s just (75/100) x 100 =75

hope this helps :)

The required x = $2,831.49. Option B) is correct.

7-year loan of $20,000 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7.

When some apply there money on something so that he can get higher value in returns of his money.

for the final 4 years

20000=2500/1.08+5000/(1.08^2)+7500/(1.08^3)+x/(1.08^4)+x/(1.08^5)+x/(1.08^6)+x/(1.08^7)

x = $2,831.49

Thus the required value of x = $2,831.49.

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Answer:

no

Step-by-step explanation:

Answer:

b = 5.3

A = 48.6

B = 41.4

Step-by-step explanation:

Attached is the Pics contain the Pythagoras Theorem and Trigonometric Identities.

So for our Right-Angled Triangle we have from Pythagoras Identity that

[tex]a^{2} +b^{2} =c^{2}[/tex]  ,, Then [tex]b^{2} =c^{2} -a^{2}[/tex]  where a=6 , c=8

by substituting,

[tex]b^2=8^2-6^2=28\\ b=\sqrt{28} =2\sqrt{7}=5.3[/tex]

Now to find A , we will use the Trigonometric Identities

Since    [tex]sin(A)=\frac{Opposite}{Hypotenuse}=\frac{a}{c} =\frac{6}{8}=\frac{3}{4} \\[/tex]

[tex]A=sin^{-1} (\frac{3}{4} )=48.6\\[/tex]

Since in any Triangle A+B+C=180

Then B=180-A-C=180-48.6-90=41.4

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The correct option is B.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

[tex]c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}[/tex]

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

The length of the sidelink b using the cosine rule can be written as,

[tex]b = \sqrt{a^2+c^2-2ac\cos(\angle B)}\\\\b = \sqrt{4^2+5^2 - 2(4)(5)(\cos 60^o)}\\\\b = \sqrt{16+25-20}[/tex]

Hence, the correct option is B.

The complete question is:

Consider ABC with the measure of angle B equal to 60 degrees, and side lengths a=4 and c=5. Which option lists an expression that is equivalent to the length of side b?

Options are given in the image below.

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The velocity equation is:

[tex]v(x) = 108 - 24x[/tex]

Such that:

[tex]v(0) = 108 ft/s\\v(2) = 60ft/s\\[/tex]

And the velocity is zero for x = 4.5

We know that the position equation is:

[tex]f(x) = 108*x - 12*x^2[/tex]

To get the velocity, we need to differentiate with respect to x, so we get:

[tex]v(x) = \frac{df(x)}{dx} = 108 - 2*12*x = 108 - 24*x[/tex]

Now we want to get the velocity for x = 0 and x = 2, we will get:

[tex]v(0) = 108 - 24*0 = 108\\\\v(2) = 108 - 24*2 = 60[/tex]

Then, when x = 0, the velocity is 108 ft/s, when x = 2 the velocity is 60 ft/2.

Finally, we need to solve:

[tex]v(x) = 108 - 24*x = 0\\\\x = 108/24 = 4.5[/tex]

The velocity is zero when x = 4.5

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Using Pythagoras theorem,  we know that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

Therefore,

c²= a²+ b²

where

Therefore,

3² + 4² = 5²

Hence,

Knowing that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle

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