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Eduardwww [97]
3 years ago
7

Write an inequality that represents the graph below:

Mathematics
1 answer:
Ray Of Light [21]3 years ago
5 0

Answer:

X is greater than 3

X > 3

Step-by-step explanation:

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Please help me with this!<br> I will give you a thanks!
Grace [21]
-2 + 6
.................
4 0
3 years ago
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Please solve this simultaneous equation, i'm not that good at it.<br><br> 2r-s=10<br> rs-s^2=12
o-na [289]

Answer:

s = 6, r = 8 or s = 4, r = 7

Step-by-step explanation:

2r - s = 10

2r = 10 + s

r = 5 + s/2 --(1)

rs - s^2 = 12 --(2)

sub (1) into (2):

(5 + s/2)s - s^2 = 12

5s + 0.5s^2 - s^2 = 12

-0.5s^2 + 5s - 12 = 0

s^2 - 10s + 24 = 0

(s - 6)(s - 4) = 0

therefore s = 6 or s = 4

when s = 6, r = 8 and when s = 4, r = 7

if you would like to discover more about simultaneous equations, you can have a look at my Instagram page (learntionary). I'll be posting mathematics related stuff there and some of my notes (simultaneous enq notes are already posted!)

7 0
2 years ago
I need your Help, please!<br> THX:)
USPshnik [31]
450 miles
1 in. Per 60 miles
460/60 = 7.5 inches
7 0
2 years ago
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Can anyone help me integrate :
worty [1.4K]
Rewrite the second factor in the numerator as

2x^2+6x+1=2(x+2)^2-2(x+2)-3

Then in the entire integrand, set x+2=\sqrt3\sec t, so that \mathrm dx=\sqrt3\sec t\tan t\,\mathrm dt. The integral is then equivalent to

\displaystyle\int\frac{(\sqrt3\sec t-2)(6\sec^2t-2\sqrt3\sec t-3)}{\sqrt{(\sqrt3\sec t)^2-3}}(\sqrt3\sec t)\,\mathrm dt
=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\sqrt{\sec^2t-1}}\,\mathrm dt
=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\sqrt{\tan^2t}}\,\mathrm dt
=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{|\tan t|}\,\mathrm dt

Note that by letting x+2=\sqrt3\sec t, we are enforcing an invertible substitution which would make it so that t=\mathrm{arcsec}\dfrac{x+2}{\sqrt3} requires 0\le t or \dfrac\pi2. However, \tan t is positive over this first interval and negative over the second, so we can't ignore the absolute value.

So let's just assume the integral is being taken over a domain on which \tan t>0 so that |\tan t|=\tan t. This allows us to write

=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\tan t}\,\mathrm dt
=\displaystyle\int(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\csc t\,\mathrm dt

We can show pretty easily that

\displaystyle\int\csc t\,\mathrm dt=-\ln|\csc t+\cot t|+C
\displaystyle\int\sec t\csc t\,\mathrm dt=-\ln|\csc2t+\cot2t|+C
\displaystyle\int\sec^2t\csc t\,\mathrm dt=\sec t-\ln|\csc t+\cot t|+C
\displaystyle\int\sec^3t\csc t\,\mathrm dt=\frac12\sec^2t+\ln|\tan t|+C

which means the integral above becomes

=3\sqrt3\sec^2t+6\sqrt3\ln|\tan t|-18\sec t+18\ln|\csc t+\cot t|-\sqrt3\ln|\csc2t+\cot2t|-6\ln|\csc t+\cot t|+C
=3\sqrt3\sec^2t-18\sec t+6\sqrt3\ln|\tan t|+12\ln|\csc t+\cot t|-\sqrt3\ln|\csc2t+\cot2t|+C

Back-substituting to get this in terms of x is a bit of a nightmare, but you'll find that, since t=\mathrm{arcsec}\dfrac{x+2}{\sqrt3}, we get

\sec t=\dfrac{x+2}{\sqrt3}
\sec^2t=\dfrac{(x+2)^2}3
\tan t=\sqrt{\dfrac{x^2+4x+1}3}
\cot t=\sqrt{\dfrac3{x^2+4x+1}}
\csc t=\dfrac{x+2}{\sqrt{x^2+4x+1}}
\csc2t=\dfrac{(x+2)^2}{2\sqrt3\sqrt{x^2+4x+1}}

etc.
3 0
3 years ago
Matthew purchased a desk that was on sale for 45% off the orginal price of $480.If the sales tax was 8% (of the sale price), how
Yanka [14]

Answer:

285.12

Step-by-step explanation:

discount amount = 45/100 x 480= 45x48/10

=216.0

price after discount= 480-216=264

sales tax= 8/100 x 264=21.12

total money spent = 264+21.12=285.12

3 0
2 years ago
Read 2 more answers
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