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Kryger [21]
3 years ago
12

Choose the correct graph to fit the inequality x^2 - y^2 < 9

Mathematics
1 answer:
Makovka662 [10]3 years ago
5 0
There is no pictures to choose the right one among tem.

However the equation could be rewritten as follows:

y=√(x²-9)

It is a HORIZONTAL parabola with the following constraint: 3=<x=<-3
You might be interested in
Nathaniel builds birds and birdhouses using Lego blocks. Let B represent the number of birds and H represent the number of birdh
N76 [4]

Answer:

At-most 3 birdhouses.

Step-by-step explanation:

Let B represent the number of birds and H represent the number of birdhouses that Nathaniel can build with his Lego blocks.

We have been given that Nathaniel builds birds and birdhouses using Lego blocks. The inequality 43B+215H\leq3000 represents the number of birds and birdhouses Nathaniel could build.

To find the number of birdhouses that Nathaniel can build after making 50 birds, we will substitute B=50 in our given inequality and then solve for H.

43*50+215H\leq3000

2150+215H\leq3000

Let us subtract 2150 from both sides of our inequality.

2150-2150+215H\leq3000-2150

215H\leq850

Let us divide both both sides of our inequality by 215.

\frac{215H}{215}\leq\frac{850}{215}

H\leq3.953488

As Nathaniel can make build less than or equal to 3.953488 and the biggest integer less than or equal to 3.953 is 3, therefore, Nathaniel can build at-most 3 birdhouses with remaining Lego blocks.

3 0
2 years ago
Read 2 more answers
Need help ASAP! due soon!!!
-BARSIC- [3]

Answer:

Option B

Step-by-step explanation:

First make x = 4 and y = 3 in the equation y = -1/2x + 5

it should look like 3 = -1/2(4) + 5 now we can solve

   -1/2 * 4 = -2         →      3 = -2 +5

       -2 + 5 = 3         →          3 = 3

5 0
2 years ago
Find the Volume: 3.2 cm<br> 7 cm<br> 4.8 cm
REY [17]
V = 0.5*b*h*l
v = 0.5*4.8*3.2*7
v = 0.5*107.52
v = 53.76cm3
7 0
2 years ago
Find the unit tangent vector T and the principal unit normal vector N for the following parameterized curve.
const2013 [10]

Answer:

a.

T(t) = ( -sin(t^2), cos(t^2) )\\\\N(t) = T'(t) / |T'(t) |  =   (-cos(t^2) , -sin(t^2))

b.

T(t) =r'(t)/|r'(t)| =  (2t/ \sqrt{4t^2   + 36} , -6/\sqrt{4t^2   + 36},0)

N(t) =T(t)/|T'(t)| =  (3/(9 + t^2)^{1/2} , t/(9 + t^2)^{1/2},0)

Step-by-step explanation:

Remember that for any curve      r(t)  

The tangent vector is given by

T(t) = \frac{r'(t) }{| r'(t)| }

And the normal vector is given by

N(t) = \frac{T'(t)}{|T'(t)|}

a.

For this case, using the chain rule

r'(t) = (  -10*2tsin(t^2) ,   102t cos(t^2)   )\\

And also remember that

|r'(t)| = \sqrt{(-10*2tsin(t^2))^2  +  ( 10*2t cos(t^2) )^2} \\\\       = \sqrt{400 t^2*(  sin(t^2)^2  +  cos(t^2) ^2 })\\=\sqrt{400t^2} = 20t

Therefore

T(t) = r'(t) / |r'(t) | =  (  -10*2tsin(t^2) ,   10*2t cos(t^2)   )/ 20t\\\\ = (  -10*2tsin(t^2)/ 20t ,   10*2t cos(t^2) / 20t  )\\= ( -sin(t^2), cos(t^2) )

Similarly, using the quotient rule and the chain rule

T'(t) = ( -2t cos(t^2) , -2t sin(t^2))

And also

|T'(t)| = \sqrt{  ( -2t cos(t^2))^2 + (-2t sin(t^2))^2} = \sqrt{ 4t^2 ( ( cos(t^2))^2 + ( sin(t^2))^2)} = \sqrt{4t^2} \\ = 2t

Therefore

N(t) = T'(t) / |T'(t) |  =   (-cos(t^2) , -sin(t^2))

Notice that

1.   |N(t)| = |T(t) | = \sqrt{ cos(t^2)^2  + sin(t^2)^2 } = \sqrt{1} =  1

2.   N(t)*T(T) = cos(t^2) sin(t^2 ) - cos(t^2) sin(t^2 ) = 0

b.

Simlarly

r'(t) = (2t,-6,0) \\

and

|r'(t)| = \sqrt{(2t)^2   + 6^2} = \sqrt{4t^2   + 36}

Therefore

T(t) =r'(t)/|r'(t)| =  (2t/ \sqrt{4t^2   + 36} , -6/\sqrt{4t^2   + 36},0)

Then

T'(t) = (9/(9 + t^2)^{3/2} , (3 t)/(9 + t^2)^{3/2},0)

and also

|T'(t)| = \sqrt{ ( (9/(9 + t^2)^{3/2} )^2 +   ( (3 t)/(9 + t^2)^{3/2})^2  +  0^2 }\\= 3/(t^2 + 9 )

And since

N(t) =T(t)/|T'(t)| =  (3/(9 + t^2)^{1/2} , t/(9 + t^2)^{1/2},0)

6 0
3 years ago
Please help me. This is due today
sattari [20]

Answer:

it answer is 3 because it is trigonometry

3 0
2 years ago
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