MATHEMATICS HIGH SCHOOL

What is the degree of each monomial?

7m6n5

Answers

Answer 1
Answer: The answer would be 11, in this case.

The exponent of m is 6, and the exponent of n is 5.
 
To find the degree add 6 + 5.

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A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r?

Answers

Given:
radius of the cone = half the radius of the cylinder
height of the cone = radius of the cylinder

Volume of the cone = π r² h/3

let x be the radius of the cylinder

V = 3.14 * (x/2)² * x/3
V = 3.14 * (x/2 * x/2) * x/3
V = 3.14 * x²/4 * x/3
V = 3.14x³ / 12
The answer is π r³/12.

The radius of the cylinder is r.
The radius of the cone is half of the radius of the cylinder: r/2.
The height of the cone is equal to the radius of the cylinder: r.

If the volume of the cone is π r²h/3, and the radius of the cone is r/2, and the height of the cone is r, then:
V = π × r² × h / 3
V = π × (r/2)² × r / 3
V = π × r²/4 × r / 3
V = π r³/12

Does x-4=5 has one solution

Answers

Yes, if you do it correctly by following the Algebraic way you would get:

x-4=5 
you need to find x.
you can do this by subtracting 4 from the x side and adding it to 5.
so it would be x= 5+4
then you jsut add 5 and 4 and you get x.
so x = 9.
Hi there! If you add 4 to both sides, x-4+4=5+4 which gets us 9. Therefore, x-4=5 does have a solution. The solution is 9.

What is the answer for number 1

Answers

r = -2 :) hope this helps

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Step-by-step explanation:

What is the value of the expression when a = 3 and b = 2?3a^3 + 2b^3
--
A. 78
B. 97
C. 135
D. 745

Please don't respond with the answer alone, I'd like to know how to work through it. :)

Answers

3a³ + 2b³ = ?

Substitute for values:

3a³ + 2b³
a = 3
3 × 3³ + 2b³

b = 2
3a³ + 2 × 2³

Full question:

3 × 3³ + 2 × 2³

3 × 3³ + 2 × 2³
3 × 27 + 2 × 2³
3 × 27 + 2 × 8
81 + 16
97

The value of the expression 3a³ + 2b³ when a = 3 and b = 2 is 97.

3 × 3³ + 2 × 2³ = 97

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)

The sum of two numbers is 17 and their different is 5. Find two answers

Answers

x+ y = 17\n x=y-5 \n \ny-5+y=17\nx=y-5\n\n2y=17+5\nx=y-5\n\n2y=22\ \ /:2 \nx=y-5\n\ny=11 \nx=11-5\n \ny=11 \nx=6 \n\nAnswer : \ are \ the \ two \ numbers \ 11 \ and \ 6
x + y = 17 \n x = y - 5 \n \n y - 5 + y = 17 \n 2y = 17 + 5 \n 2y = 22 \n y = 22/2 \n y = 11 \n \n x = y - 5 \n x = 11 - 5 \n x = 6 \n \n \left \{ {{y=11} \atop {x=6}} \right.
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