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miss Akunina [59]
3 years ago
15

Can someone check these questions?

Mathematics
1 answer:
bulgar [2K]3 years ago
3 0
4
4 is correct

5
The second one is also correct.
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Find an asymptote of this conic section. 9x^2-36x-4y^2+24y-36=0
ki77a [65]
We will begin by grouping the x terms together and the y terms together so we can complete the square and see what we're looking at. (9x^2-36x)-(4y^2+24y)-36=0.  Now we need to move that 36 over by adding to isolate the x and y terms.  (9x^2-36x)-(4y^2+24y)=36.  Now we need to complete the square on the x terms and the y terms.  Can't do that, though, til the leading coefficients on the squared terms are 1's.  Right now they are 9 and 4.  Factor them out: 9(x^2-4x)-4(y^2-6y)=36.  Now let's complete the square on the x's. Our linear term is 4.  Half of 4 is 2, and 2 squared is 4, so add it into the parenthesis.  BUT don't forget about the 9 hanging around out front there that refuses to be forgotten.  It is a multiplier.  So we are really adding in is 9*4 which is 36.  Half the linear term on the y's is 3.  3 squared is 9, but again, what we are really adding in is -4*9 which is -36.  Putting that altogether looks like this thus far: 9(x^2-4x+4)-4(y^2-6y+9)=36+36-36.  The right side simplifies of course to just 36.  Since we have a minus sign between those x and y terms, this is a hyperbola.  The hyperbola has to be set to equal 1.  So we divide by 36.  At the same time we will form the perfect square binomials we created for this very purpose on the left: \frac{(x-2)^2}{4}- \frac{(y-3)^2}{9}=1.  Since the 9 is the bigger of the 2 values there, and it is under the y terms, our hyperbola has a horizontal transverse axis.  a^2=4 so a=2; b^2=9 so b=3.  Our asymptotes have the formula for the slope of m=+/- \frac{b}{a} which for us is a slope of negative and positive 3/2.  Using the slope and the fact that we now know the center of the hyperbola to be (2, 3), we can solve for b and rewrite the equations of the asymptotes.  3= \frac{3}{2}(2)+b give us a b of 0 so that equation is y = 3/2x.  For the negative slope, we have 3=- \frac{3}{2}(2)+b which gives us a b value of 6.  That equation then is y = -3/2x + 6.  And there you go!
8 0
3 years ago
In the inequality, 3x&gt;9, can x=3?<br> Yes or no
seraphim [82]

Step-by-step explanation:

no

because it will become

3(3)>9

9>9

it must be more than 9 unless the symbol is

\geqslant

4 0
2 years ago
Is 1/4 greater or is 5/4 grater
Bumek [7]

Answer: 5/4

Step-by-step explanation:

if two number have the same denominator, then the number with the greatest numerator is the greatest.

Basically if the bottom number of two fractions are the same, the bigger top number is the bigger number.

8 0
3 years ago
Read 2 more answers
A cylindrical tank has a height of 10 feet and a radius of 4 feet. Jane fills the tank with water at a rate of 8 cubic feet per
ki77a [65]

<u>Given</u>:

A cylindrical tank has a height of 10 feet.

The radius of the cylindrical tank is 4 feet.

Jane fills the tank with water at a rate of 8 cubic feet per minute.

We need to determine the time it will take for Jane to completely fill the tank without overflowing it.

<u>Volume of the cylinder:</u>

The volume of the cylinder can be determined using the formula,

V=\pi r^2 h

Substituting the values, we have;

V=(3.14)(4)^2(10)

V=(3.14)(16)(10)

V=502.4

Thus, the volume of the cylinder is 502.4 cubic feet.

<u>Time taken:</u>

The time taken can be determined using the formula,

Time = \frac{Volume}{Rate \ of\  filling}

Substituting the values, we have;

Time = \frac{502.4}{8}

Time = 62.8

Thus, Jane takes 62.8 minutes to completely fill the tank without overflowing it.

3 0
3 years ago
Can someone please help me with this question?
neonofarm [45]

Answer:

hectors toy

Step-by-step explanation:

0.7 is equal to 0.70 and 0.72 > 0.70

5 0
3 years ago
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