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4 years ago

I need help with question a and b

Mathematics

1 answer:

DaniilM [7]4 years ago

5 0

Solving for part A

$f(x) = x^{2} \;\;and\;\; g(x) = \frac{1}{x^{3}} \\\\f(g(x)) = (\frac{1}{x^{3}})^{2} =\frac{1}{x^{6}}$

Domain of composition: x ≠ 0 i.e. Domain is the set of "Real numbers excluding number 0".

Solving for part B

$f(x) = \frac{x}{x-2}\;\;and\;\;g(x) =\frac{3}{x} \\\\f(g(x))=\frac{\frac{3}{x}}{\frac{3}{x}-2}=\frac{\frac{3}{x}}{\frac{3-2x}{x}} =\frac{3}{3-2x}\\\\ Domain:\;3-2x\neq 0 \;\;OR\;\;x\neq \frac{3}{2}$

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The length of minute hand on a wall clock is 14cm. find the areas swept by the minute hand in 30min

ElenaW [278]

In 30 minutes the minute hand makes half a turn around the clock, so it sweeps half a circle.

Given the radius $r$ , the area of a circle is $A = \pi r^2$

In this case, we're interested in half the area of a circle with radius 14cm, so we have

$A^* = \dfrac{\pi \cdot 14^2}{2} = \dfrac{196\pi}{2} = 98\pi$ cm squared.

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3 years ago

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REALLY IMPORTANT

Mashutka [201]

Answer:

we choose (3,4)

Step-by-step explanation:

Given the coordinates:

A (5, 2)
B (5, -2)
C (2,1)
L (-5, 6)
M (-5, -6)

To find a distance between two points or the length of the segment, we use the following formula:

$\sqrt{(x2-x1)^2+(y2-y1)^2}$

Because A and B are located in the same line x =5

=> the lenght of AB = $\sqrt{(-2-2)^{2} } =\sqrt{-4^{2} } =4$

Because A and B are located in the same line x =-5

=> the lenght LM = $\sqrt{(-6-6)^{2} } =\sqrt{-12^{2} } =12$

Because ABC is similar to LMN

=> the ratio of LM : AB = 12:4 = 3:1

<=> the ratio LN : CA = 3:1

We need to find the lenght of CA

= $\sqrt{(2-5)^2+(1-2)^2} = \sqrt{-3^{2} + -1^{2} } = \sqrt{10}$

=> the lenght of LN = 3CA = 3 $\sqrt{10}$

Let (x, y) is the coordinate of N, we have:

The length of LN: $\sqrt{(x+5)^2+(y-6)^2} = 3\sqrt{10}$ = $\sqrt{90}$

Let try all the possible answer;

(3,4) => $\sqrt{(3+5)^2+(4-6)^2} = \sqrt{8^{2} + -2^{2} } = \sqrt{90}$ True

So we choose (3,4)

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3 years ago

What is 5+5 guys i need help

ExtremeBDS [4]

The answer is 10 If you count

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3 years ago

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Q. A______ is a quadrilateral with two sets of parallel sides and 4 right angles

-Dominant- [34]

Answer:

I think it will be rectangle or square

because rectangle and Square have 4 right angles

and each two opposite sides are parallel

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3 years ago

Each of the line segments in the word MATH are numbered in the graph below. Find the slope (as a ratio of rise over run) of each

Leviafan [203]

Answer:

Line 1: $\infty$

Line 2: $-\frac{4}{3}$

Line 3: $\frac{4}{3}$

Line 4: $\infty$

Line 5: $\frac{7}{4}$

Line 6 : $-\frac{7}{3}$

Line 7: 0

Line 8: 0

Line 9: $\infty$

Line 10: $\infty$

Line 11: 0

Line 12: $\infty$

Step-by-step explanation:

Slope of line is given by the formula:

$\text{Slope = }\dfrac{\text{Change in } y\text{ coordinate}}{\text{Change in } x\text{ coordinate}}$

Line 1:

The change in $x$ coordinate is zero.

Therefore slope of line 1 is $\infty$ .

Line 2:

Change in $y$ coordinate = -4

Change in $x$ coordinate = 3

Slope = $-\frac{4}{3}$

Line 3:

Change in $y$ coordinate = 4

Change in $x$ coordinate = 3

Slope = $\frac{4}{3}$

Line 4:

The change in $x$ coordinate is zero.

Therefore slope of line 4 is $\infty$ .

Line 5:

Change in $y$ coordinate = 7

Change in $x$ coordinate = 3

Slope = $\frac{7}{3}$

Line 6:

Change in $y$ coordinate = -7

Change in $x$ coordinate = 3

Slope = $-\frac{7}{3}$

Line 7:

Change in $y$ coordinate = 0

Slope = 0

Line 8:

Change in $y$ coordinate = 0

Slope = 0

Line 9:

The change in $x$ coordinate is zero.

Therefore slope of line 9 is $\infty$ .

Line 10:

The change in $x$ coordinate is zero.

Therefore slope of line 10 is $\infty$ .

Line 11:

The change in $y$ coordinate is zero.

Therefore slope of line 11 is 0.

Line 12:

The change in $x$ coordinate is zero.

Therefore slope of line 12 is $\infty$ .

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