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2 years ago

Someone please help quick if possible

Mathematics

1 answer:

gladu [14]2 years ago

7 0

Answer:

Answer is in attachment.

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Find the equation of all tangent lines having slope of -1 that are tangent to the curve y=(9)/(x+1)

fredd [130]

Answer:

$f(x)=\frac9{x+1}\\ f'(x)=-\frac9{(x+1)^2}\\ f'(x)=-1\ \iff\ -\frac9{(x+1)^2}=-1\ \to \ \frac9{(x+1)^2}=1\ \to \ (x+1)^2=9\\ |x+1|=3\ \to \ x+1=3\ \vee\ x+1=-3\\ x_1=2\ \vee\ x_2=-4\\ f(x_1)=f(2)=\frac9{2+1}=3\\ f(x_2)=f(-4)=\frac9{-4+1}=-3$

First tangent line:

$y=f'(x_1)\cdot (x-x_1)+f(x_1)\ \to \ y=-1(x-2)+3\ \to \ y=-x+5$

Second tangent line:

$y=f'(x_2)\cdot (x-x_2)+f(x_2)\ \to \ y=-1(x+4)-3\ \to \ y=-x-7$

Notice: slope of -1 means that both $f'(x_1), \ f'(x_2)$ are equal to -1, so $f'(x_1)=-1 \ and \ f'(x_2)=-1$

6 0

2 years ago

Read 2 more answers

Please help as soon as possible

MAVERICK [17]

Answer: Your Answer is: -8/17

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2 years ago

Whay will most likely happen to students test scores if the number of hours they use social media increases? A test score will i

Len [333]

C as when they put more hours into the social media they will study less and less which leads to less test scores

4 0

2 years ago

two buildings stand 90 ft apart at their closest points, the angle of depression from the top of the taller building to the top

noname [10]

<span>A new kind of temporary pavilion support for a square roof uses just two poles set at the diagonal corners of a square. The allowable distance between the poles is 18 feet. Find the area of the roof. The sides will have lengths of 18/sqrt(2). Since they are perpendicular, the area of the square will be (18^2)/2 = 81*4/2 = 162 square feet.

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8 0

2 years ago

___ tens 15 ones=4 tens 5 ones

saw5 [17]

Answer:

3 tens

Step-by-step explanation:

4 tens and 5 ones is 45

so 45 minus 15 is 30

so 3 tens

3 0

2 years ago