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Ede4ka [16]
2 years ago
5

Y

Mathematics
1 answer:
inn [45]2 years ago
3 0

The rotation of the triangle ABC 360 degrees about the y-axis forms a cone

<h3>How to determine the shape after rotation?</h3>

From the question, we understand that the triangle ABC is a right triangle

The vertical cross-section of a cone is a right triangle.

This means that a right triangle can be rotated 360 degrees on one of its legs (opposite or adjacent) to form a cone

Hence, the rotation of the triangle ABC forms a cone

Read more about rotation at:

brainly.com/question/13147596

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Find the inverse of each given functions.<br> f(x) = 4x − 12
Paha777 [63]

Answer:

y=1/4x+3

Step-by-step explanation:

To find the inverse, switch x and y or f(x)

f(x)=4x-12

y=4x-12

x=4y-12

Add 12 to both sides

x+12=4y-12+12

x+12=4y

Divide both sides by 4

x+12/4=y

1/4x+12/4=y

1/4x+3=y

y=1/4x+3

7 0
3 years ago
Read 2 more answers
Your brother works for a company that cleans and paints the outside of houses at a rate of $35 per hour. The company charges a f
Reptile [31]

Answer:

<h2>The x represents the hours my bro will work for in that company </h2>

8 0
3 years ago
Read 2 more answers
There are 4 people at a party. Consider the random variable X=’number of people having the same birthday ’ (match only month, N=
yulyashka [42]

Answer:

S = {0,2,3,4}

P(X=0) = 0.573 , P(X=2) = 0.401 , P(x=3) = 0.025, P(X=4) = 0.001

Mean = 0.879

Standard Deviation = 1.033

Step-by-step explanation:

Let the number of people having same birth month be = x

The number of ways of distributing the birthdays of the 4 men = (12*12*12*12)

The number of ways of distributing their birthdays = 12⁴

The sample space, S = { 0,2,3,4} (since 1 person cannot share birthday with himself)

P(X = 0) = \frac{12P4}{12^{4} }

P(X=0) = 0.573

P(X=2) = P(2 months are common) P(1 month is common, 1 month is not common)

P(X=2) = \frac{3C2 * 12P2}{12^{4} } + \frac{4C2 * 12P3}{12^{4} }

P(X=2) = 0.401

P(X=3) = \frac{4C3 * 12P2}{12^{4} }

P(x=3) = 0.025

P(X=4) = \frac{12}{12^{4} }

P(X=4) = 0.001

Mean, \mu = \sum xP(x)

\mu = (0*0.573) + (2*0.401) + (3*0.025) + (4*0.001)\\\mu = 0.879

Standard deviation, SD = \sqrt{\sum x^{2} P(x) - \mu^{2}}  \\SD =\sqrt{ [ (0^{2} * 0.573) + (2^{2}  * 0.401) + (3^{2} * 0.025) + (4^{2} * 0.001)] - 0.879^{2}}

SD = 1.033

4 0
3 years ago
Stefan spent half of his weekly allowance on clothes. To earn more money his parents let him wash the car for $5
Alenkasestr [34]
8-5=3 is the remaining half
weekly allowance=2(1÷2) where (1÷2) is 3
2×3=6

The weekly allowance should be 6.
7 0
2 years ago
1.) What are the zeros of the polynomial? f(x)=x^4-x^3-16x^2+4x+48.
Lerok [7]

Answer:

3.) \displaystyle [x - 2][x^2 + 2][x + 4]

2.) \displaystyle 2\:complex\:solutions → x^2 + 3x + 6 >> -\frac{3 - i\sqrt{15}}{2}, -\frac{3 + i\sqrt{15}}{2}

1.) \displaystyle 4, -3, 2, and\:-2

Step-by-step explanation:

3.) By the Rational Root Theorem, we would take the Least Common Divisor [LCD] between the leading coefficient of 1, and the initial value of −16, which is 1, but we will take 2 since it is the <em>fourth root</em> of 16; so this automatically makes our first factor of \displaystyle x - 2.Next, since the factor\divisor is in the form of \displaystyle x - c, use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

2| 1 2 −6 4 −16

↓ 2 8 4 16

__________________

1 4 2 8 0 → \displaystyle x^3 + 4x^2 + 2x + 8

You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [x⁴ + 2x³ - 6x² + 4x - 16]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x³, the 4x² follows right behind it, bringing 2x right up against it, and bringing up the rear, 8, giving you the quotient of \displaystyle x^3 + 4x^2 + 2x + 8.

However, we are not finished yet. This is our first quotient. The next step, while still using the Rational Root Theorem with our first quotient, is to take the Least Common Divisor [LCD] of the leading coefficient of 1, and the initial value of 8, which is −4, so this makes our next factor of \displaystyle x + 4.Then again, we use Synthetic Division because \displaystyle x + 4is in the form of \displaystyle x - c:

−4| 1 4 2 8

↓ −4 0 −8

_____________

1 0 2 0 → \displaystyle x^2 + 2

So altogether, we have our four factors of \displaystyle [x^2 + 2][x + 4][x - 2].

__________________________________________________________

2.) By the Rational Root Theorem again, this time, we will take −1, since the leading coefficient & variable\degree and the initial value do not share any common divisors other than the <em>special</em><em> </em><em>number</em> of 1, and it does not matter which integer of 1 you take first. This gives a factor of \displaystyle x + 1.Then start up Synthetic Division again:

−1| 1 3 5 −3 −6

↓ −1 −2 −3 6

__________________

1 2 3 −6 0 → \displaystyle x^3 + 2x^2 + 3x - 6

Now we take the other integer of 1 to get the other factor of \displaystyle x - 1,then repeat the process of Synthetic Division:

1| 1 2 3 −6

↓ 1 3 6

_____________

1 3 6 0 → \displaystyle x^2 + 3x + 6

So altogether, we have our three factors of \displaystyle [x - 1][x^2 + 3x + 6][x + 1].

Hold it now! Notice that \displaystyle x^2 + 3x + 6is unfactorable. Therefore, we have to apply the Quadratic Formula to get our two complex solutions, \displaystyle a + bi[or zeros in this matter]:

\displaystyle -b ± \frac{\sqrt{b^2 - 4ac}}{2a} = x \\ \\ -3 ± \frac{\sqrt{3^2 - 4[1][6]}}{2[1]} = x \\ \\ -3 ± \frac{\sqrt{9 - 24}}{2} = x \\ \\ -3 ± \frac{\sqrt{-15}}{2} = x \\ \\ -3 ± i\frac{\sqrt{15}}{2} = x \\ \\ -\frac{3 - i\sqrt{15}}{2}, -\frac{3 + i\sqrt{15}}{2} = x

__________________________________________________________

1.) By the Rational Root Theorem one more time, this time, we will take 4 since the initial value is 48 and that 4 is the root of the polynomial. This gives our automatic factor of \displaystyle x - 4.Then start up Synthetic Division again:

4| 1 −1 −16 4 48

↓ 4 12 −16 −48

___________________

1 3 −4 −12 0 → \displaystyle x^3 + 3x^2 - 4x - 12

We can then take −3 since it is a root of this polynomial, giving us the factor of \displaystyle x + 3:

−3| 1 3 −4 −12

↓ −3 0 12

_______________

1 0 −4 0 → \displaystyle x^2 - 4 >> [x - 2][x + 2]

So altogether, we have our four factors of \displaystyle [x - 2][x + 3][x + 2][x - 4],and when set to equal zero, you will get \displaystyle 4, -3, 2, and\:-2.

I am delighted to assist you anytime.

3 0
3 years ago
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