All categories

1 year ago

Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q5

Mathematics

1 answer:

snow_tiger [21]1 year ago

4 0

Answer:

$T\text{he domain of H\lparen x\rparen is }\lbrace x\lvert x-3,1\rbrace$

Step-by-step explanation:

The domain of a function is all the set of possible x-values that the function can take. Then, for the given function:

$H\left(x\right)=\frac{-7x^2}{\left(x-1\right)\left(x+3\right)}$

The function is undefined when the denominator is equal to 0, then equalize each factor of the denominator to 0:

$\begin{gathered} x-1=0 \\ x=1 \\ \\ x+3=0 \\ x=-3 \\ \\ \text{ Then, the domain of H\lparen x\rparen is }\lbrace x\lvert x\ne-3,1\rbrace \end{gathered}$

You might be interested in

Find the total surface area of this cylinder . Give your answer to 1 decimal place 7cm 15 cm

Leto [7]

Answer:

Step-by-step explanation:

r = 7 cm

h = 15cm

pi = 3.14

Top and bottom (These questions drive you crazy when you don't know if there is both a top and bottom).

Area = 2* pi *r^2 = 2 * 3.14 * 7^2

Area = 2 * 3.14 * 49

Area = 307.72 Don't round this.

Cylinder body

Cylinder body = Circumference * h = 2*pi * r * h

Cylinder body = 2* 3.14 * 7 * 15

Cylinder body = <u> 659.4</u>

<u />

Total = 967.12

Rounded 967.1 Answer

3 0

3 years ago

Can you help me get this answer

scoundrel [369]

Answer:

y = f(x-1) - 3

is the correct function

3 0

2 years ago

Which expression is equivalent to<br> 1/3/?

Rzqust [24]

Answer:

2\5,3\7,4\9,5\11

Thats the answer

3 0

3 years ago

The sum of twice a number and 8 is 44. what's the number? show your work.

mezya [45]

Answer:

Step-by-step explanation:

We can work backwards with this and take 44-8=36

Then we divide it by two and thats 18

3 0

2 years ago

1. if csc β = 7/3 and cot β = - 2√10 / 3, Find sec β

slava [35]

Step-by-step explanation:

$\tan \beta = \frac{1}{ \cot \beta } = - \frac{3}{2 \sqrt{10} } = - \frac{3 \sqrt{10} }{20}$

$\csc \beta \tan \beta = \frac{1}{ \cos \beta } = \sec \beta$

Therefore,

$\sec \beta = ( \frac{7}{3} )( - \frac{3 \sqrt{10} }{20} ) = - \frac{7 \sqrt{10} }{20}$

$\csc y = \frac{1}{ \sin y} = - \frac{ \sqrt{6} }{2}$

$= > \sin y = - \frac{ \sqrt{6} }{3}$

Use the identity

$\cos y = \sqrt{1 - \sin ^{2} y} \: \: \: \: \: \: \: \: \: \: \: \\ = \sqrt{1 - {( - \frac{ \sqrt{6} }{3}) }^{2} } = - \frac{ \sqrt{3} }{3}$

We chose the negative value of the cosine because of the condition where cot y > 0. Otherwise, choosing the positive root will yield a negative cotangent value. Now that we know the sine and cosine of y, we can now solve for the tangent:

$\tan \beta = \frac{ \sin y}{ \cos y} =( - \frac{ \sqrt{6} }{3} )( - \frac{3}{ \sqrt{3} } ) = \sqrt{2}$

3. Recall that sec x = 1/cos x, therefore cos x = 5/6. Solving for sin x,

$\sin x = \sqrt{1 - \cos ^{2} x} = \sqrt{ \frac{11}{6} }$

Solving for tan x:

$\tan x = \frac{ \sin x}{ \cos x} = (\frac{ \sqrt{11} }{ \sqrt{6} } )( \frac{6}{5} ) = \frac{ \sqrt{66} }{5}$

5 0

3 years ago