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3 years ago

Given f(x) = 9x - 5 and g(x) = x², choose the expression for (fºg)(x).

Mathematics

1 answer:

svetlana [45]3 years ago

5 0

Answer:

9x² -5

Step-by-step explanation:

(f○g)(x) means f(g(x))

Put the definition of g(x) in place of x in the definition of f(x):

f(g(x)) = f(x²) = 9(x²) - 5

(f○g)(x) = 9x² - 5

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The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

3 years ago

X = 8 – 2y x + 3y = 12 What value of x satisfies the system of equations?

lora16 [44]

Answer: its 0 of 4 you can pick but i think its 4

Step-by-step explanion: i am not good at explaning this math but i know the answer

8 0

2 years ago

Consider f and c below. f(x, y, z) = (y2z + 2xz2)i + 2xyzj + (xy2 + 2x2z)k,

qaws [65]

$\dfrac{\partial f}{\partial x}=y^2z+2xz^2$
$f(x,y,z)=xy^2z+x^2z^2+g(y,z)$

$\dfrac{\partial f}{\partial y}=2xyz+\dfrac{\partial g}{\partial y}=2xyz$
$\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

$\dfrac{\partial f}{\partial z}=xy^2+2x^2z+\dfrac{\mathrm dh}{\mathrm dz}=xy^2+2x^2z$
$\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=0$

$\implies f(x,y,z)=xy^2z+x^2z^2+C$

8 0

3 years ago

Please help guys I need it

Inessa05 [86]

Answer:

a= 20

b= 169.7

c= 29.71

Step-by-step explanation:

The formula of a triangle is (h*b)/2

a= (5*8)/2

b= to find the height, you can use the pythagorean theorem 18^2 - 6^2 = square root of 288. Which is 12root 2 or 16.97. (16.97*20)/2

c= using the pythagorean theorem- 11^2 = 7^2 - c^2 = square root 73, or 6root 2, or 8.49. (8.49* 7)/2

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2 years ago

An electronics manufacturer produces 196 refrigerators in a day. According to the manufacturer’s records, three of the refrigera

muminat

If there are 196 refrigerators produced daily, that means that 8 are produced in an hour. subtract 8 and 3 and you get 5 refrigerators that are not defects. now multiply 5 by 24, about 120 refrigerators out of the 196 are not defects.

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2 years ago

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