MATHEMATICS HIGH SCHOOL

The volume of a cylinder is 4x3 cubic units and its height is x units.Which expression represents the radius of the cylinder, in units?
2x
4x
2pi x²
4pi x2

Answers

Answer 1

Answer:

Answer:

The answer to your question is r = 2x

Step-by-step explanation:

Volume of a cylinder = V = π r² h

r = radius

h = height = x

Volume = 4x³

Then

r² = $(volume)/(\pi h)$

r² = $(4x^(3) )/(\pi x)$

r² = 4x²

r = 2x

Answer 2

Answer:

Answer:A

Step-by-step explanation:

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Is knowing the coordinates of the vertex of a parabola enough to determine the domain and range?a.No: we would have no information about the domain. b.Yes: if the vertex is at (m,n), then the domain is all reals and the range is y ≤ n. c.No: we would need to know if the vertex is a minimum or a maximum. d.Yes: if the vertex is at (m,n), then the domain is all reals and the range is y ≥ n. Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation. y=2x-x+6 A)( 0.25, 6.125) B)(-0.25, 5.875) C)( 0.25, 5.875) D)( 0.25, 6)
Subtract: 5 – 3 1⁄3
Here's a better picture

Cos3x=4cos^3x-3cosx prove

Answers

$\bf cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)\n\n\n\textit{also recall that }cos(2\theta)=\begin{cases}cos^2(\theta)-sin^2(\theta)\n1-2sin^2(\theta)\n\boxed{2cos^2(\theta)-1}\end{cases}\n\n\nand\qquad sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\n\n-------------------------------$

$\bf cos(3x)=4cos^3(x)-3cos(x)\n\n-------------------------------\n\ncos(3x)\implies cos(2x+x)\implies cos(2x)cos(x)-sin(2x)sin(x)\n\n\n\[2cos^2(x)-1]cos(x)-[2sin(x)cos(x)]sin(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2sin^2(x)cos(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2[1-cos^2(x)]cos(x)\n\n\n2cos^3(x)-cos(x)~~~~-~~~~[2cos(x)-2cos^3(x)]\n\n\n2cos^3(x)-cos(x)~~~~-~~~~2cos(x)+2cos^3(x)\n\n\n4cos^3(x)-3cos(x)$

Solve for x and express your answer as a logarithm.2(10^(3x) ) = 24

Simplify your answer as much as possible.

Use the following notations where necessary:

• For fractions, use the / symbol to separate numerator and denominator, like this: 42/53

• For logs with a base of 10, such as log107, just write the log without the base and place the value in parentheses, like this: log(7)

• For logs with a base other than 10, write the base after an underscore then place the value in parentheses. For example, to write log27, write it like this: log_2(7)

Answers

$2\cdot10^(3x)=24\ \ \ \ |divide\ both\ sides\ by\ 2\n\n10^(3x)=12\iff\log(10^(3x))=\log(12)\n\n3x\log(10)=\log(12)\n\n3x=\log(12)\ \ \ \ |divide\ both\ sides\ by\ 3\n\n\boxed{x=(\log(12))/(3)}\to(\log(12))/(3)=(1)/(3)\log(12)=\log\left(12^(1)/(3)\right)=\boxed{\log\sqrt[3]{12}}$

$Use:\n\log_ab^c=c\log_ab\n\log_aa=1\na^(1)/(n)=\sqrt[n]{a}\n-------------------\n\nAnswer:\boxed{x=(\log(12))/(3)\ other\ form\ x=\log(\sqrt[3]{12})}$

Using the distributive property to find the product (y – 4)(y2 + 4y + 16) results in a polynomial of the form y3 + 4y2 + ay – 4y2 – ay – 64. What is the value of a in the polynomial?

Answers

( y - 4 ) ( y² + 4 y + 16 ) = y³ + 4 y² + 16 y - 4 y² - 16 y - 64
The result is a polynomial of the form:
y³ + 4 y² + a y - 4 y² - a y + 64;
Answer: a = 16

Answer:

The answer is C. 16

Step-by-step explanation:

I got it right on edg. See below.

Entre os alunos que frequentam o Ensino Profissional na escola do Carlos foi recolhida umaamostra de 50 aos quais se colocou a questão:

«Qual das seguintes frases exprime melhor o teu gosto pelo estudo da Matemática?

Gosto muito.
Gosto de certos conteúdos.
Gosto pouco.
Não gosto nada.»
O seguinte gráfico traduz as respostas obtidas à questão anterior.

1.1. Indique a variável em estudo e a sua natureza.

1.2. Calcule a percentagem de alunos que responderam «Gosto muito».

1.3. Observe a seguinte tabela ainda referente à mesma questão.

Rapazes

Raparigas

Gosto muito

12

6

Gosto de certos conteúdos

8

7

Gosto pouco

6

6

Não gosto nada

2

3

Escreva um pequeno texto no qual justifique que, neste estudo, os rapazes mostraram ter um maior gosto pelo estudo da Matemática

Answers

Answer:

taco

Step-by-step explanation:

no hablos espanol

What are the zeros of the polynomial function: f(x) = x3 + x2 – 6x ? ...?

Answers

The solution to the problem is as follows:

　
x³ + x² − 6x = 0
x (x² + x − 6) = 0
x (x − 2) (x + 3) = 0
x = 0, 2, −3

f(x) = 2x³ + 5x² + 6x − 4
f(−x) = −2x³ + 5x² − 6x − 4

Let's look at signs only and how many sign changes there are:
f(x) = + + + −
1 sign change ----> 1 positive root
f(−x) = − + − −
2 sign changes ----> 2 or 0 negative roots

Min. number of real roots = 1 ----> max. number of complex roots = 2
Max. number of real roots = 3 ----> min. number of complex roots = 0

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Select the correct answer.A glass case is in the shape of a rectangular prism. The volume of the case is 4/125 cubic foot. How many cubic blocks with a side length of
*1/5 foot would be required to find the volume of the glass case?
A. 2
B. 3
C. 4
D. 5