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3 years ago

The average number of students per class at a middle school

Mathematics

1 answer:

Tasya [4]3 years ago

8 0

Answer:

s = 22t or $\frac{t}{s} = \frac{1}{22}$ , when s is students and t is teachers.

Step-by-step explanation:

I. Given t = teacher, s = student

When 1 teacher per 22 students so...

s = 22t

If there're 10 teachers

s = 22(10)

= 220 or $\frac{t}{s} = \frac{1}{22}$

Hope that help :)

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Integration of sin^2 2x cos^3 2x dx

lilavasa [31]

$\int\left[\sin^2(2x)\cos^3(2x)\right]dx=\int\left[\sin^2(2x)\cos^2(2x)\cos(2x)\right]dx\\\\\text{Use the trigonometric identity}\sin^2(x)+\cos^2(x)=1\to\cos^2(x)=1-\sin^2(x)\\\\=\int\left\{\sin^2(2x)[1-\sin^2(2x)]\cos(2x)\right\}dx\\\\\text{substitute}\ \sin2x=t\ \to\ 2\cos2x\ dx=dt\ \to\ \cos2x\ dx=\dfrac{1}{2}\ dt\\\\=\dfrac{1}{2}\int\left[t^2(1-t^2)\right]dt=\dfrac{1}{2}\int(t^2-t^4)dt=\dfrac{1}{2}\left(\dfrac{1}{3}t^3-\dfrac{1}{5}t^5\right)+C$

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4 0

3 years ago

Question 4 Given: f(x) = -3x – 3 and g(x) = x2 + 5 Find (f - g) ().

Aleonysh [2.5K]

Answer:

We get $\mathbf{(f-g)(x)= -x^2-3x-8}$

Step-by-step explanation:

We are given:

$f(x) = -3x - 3\\ g(x) = x^2 + 5$

We need to find (f-g)(x) (assuming there is x in the bracket, i.e. (f - g) () should be (f-g)(x))

We would simply subtract f(x) and g(x)

$(f-g)(x)\\= -3x-3-(x^2+5)\\Multiply\:minus\:sign\:with\:terms\:inside\:the\:bracket\\=-3x-3-x^2-5\\Combining\:like\:terms:\\=-x^2-3x-3-5\\=-x^2-3x-8$

So, We get $\mathbf{(f-g)(x)= -x^2-3x-8}$

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3 years ago

Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

nydimaria [60]

Answer: For 10 sessions, the cost of the two plans the same.

Step-by-step explanation:

Let x= Number of sessions.

Given: Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

Total charge for x sessions = 50+30x

Nicole's fitness center charges a yearly fee of $250 plus $10 for each session with a trainer.

Total charge for x sessions = 250+10x

When both plan charges the same, then

$50+30x=250+10x\\\\\Rightarrow\ 30x-10x=250-50\\\\\Rightarrow\ 20x=200\\\\\Rightarrow\ x=10$

i.e. For 10 sessions, the cost of the two plans the same.

3 0

3 years ago

Write the following equation in standard form: y + 4 = -3(x + 2)

Irina18 [472]

Answer:

-3x-y=10

Step-by-step explanation:

y+4=-3(x+2)

y+4=-3x-6

y=-3x-6-4

y=-3x-10

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5 0

3 years ago

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jeka57 [31]

The last side would be 10

8 0

3 years ago