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Rama09 [41]
1 year ago
13

Solve the inequality 2x>30+5/4x

Mathematics
1 answer:
insens350 [35]1 year ago
8 0

Answer:

Step-by-step explanation:

2x > 30+\frac{5}{4x} \\2x-\frac{5}{4x} > 30\\\frac{8x^2-5}{4x} > 30\\case~1\\if~x > 0\\8x^2-5 > 120x\\8x^2-120x > 5\\x^2-15x > \frac{5}{8} \\adding~(-\frac{15}{2} )^2~to~both~sides\\(x-\frac{15}{2} )^2 > \frac{5}{8}+\frac{225}{4} \\(x-\frac{15}{2} )^2 > \frac{455}{8} \\x-\frac{15}{2} < -\sqrt{\frac{455}{8} }  \\x < \frac{15}{2}-\sqrt{\frac{455}{8} } \\or~x < 0\\rejected~as~x > 0

x-\frac{15}{2} > \sqrt{\frac{455}{8} } \\x > \frac{15}{2} +\sqrt{\frac{455}{8} }

case~2

if~x < 0\\8x^2-5 < 120x\\8x^2-120x < 5\\x^2-15x < \frac{5}{8} \\adding~(-\frac{15}{2} )^2\\(x-\frac{15}{2} )^2 < \frac{5}{8} +(-\frac{15}{2} )^2\\|x-\frac{15}{2} | < \frac{5+450}{8} \\-\sqrt{\frac{455}{8} } < x-\frac{15}{2} < \sqrt{\frac{455}{8} } \\\frac{15}{2} -\sqrt{\frac{455}{8} } < x < \frac{15}{2} +\sqrt{\frac{455}{8} } \\but~x < 0\\7.5-\sqrt{\frac{455}{8} } < x < 0

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For f(x) = √x-3 find f(f^-1(4))
vlada-n [284]

Answer:

4

Step-by-step explanation:

f⁻¹(x) = x²+3, but none of that matters, since f(f⁻¹(x)) = x

3 0
3 years ago
Determine all real values of p such that the set of all linear combination of u = (3, p) and v = (1, 2) is all of R2. Justify yo
Rama09 [41]

Answer:

p ∈ IR - {6}

Step-by-step explanation:

The set of all linear combination of two vectors ''u'' and ''v'' that belong to R2

is all R2 ⇔

u\neq 0_{R2}      

v\neq 0_{R2}

And also u and v must be linearly independent.

In order to achieve the final condition, we can make a matrix that belongs to R^{2x2} using the vectors ''u'' and ''v'' to form its columns, and next calculate the determinant. Finally, we will need that this determinant must be different to zero.

Let's make the matrix :

A=\left[\begin{array}{cc}3&1&p&2\end{array}\right]

We used the first vector ''u'' as the first column of the matrix A

We used the  second vector ''v'' as the second column of the matrix A

The determinant of the matrix ''A'' is

Det(A)=6-p

We need this determinant to be different to zero

6-p\neq 0

p\neq 6

The only restriction in order to the set of all linear combination of ''u'' and ''v'' to be R2 is that p\neq 6

We can write : p ∈ IR - {6}

Notice that is p=6 ⇒

u=(3,6)

v=(1,2)

If we write 3v=3(1,2)=(3,6)=u , the vectors ''u'' and ''v'' wouldn't be linearly independent and therefore the set of all linear combination of ''u'' and ''b'' wouldn't be R2.

7 0
3 years ago
Can someone please teach me how to to this<br> Item: $30 Discount: 15%
seraphim [82]

Answer:

$25.5

Step-by-step explanation:

Sure, so the total of the

Item:

30 Dollars ($)

and the discount price is

15 percent (%)

So 30 times 0.15 because 30 is the price in total and 0.15 is the percentage but in a decimal form.

30 times 0.15 equals 4.5

4.5 is the amount that 15 % equals.

30 minus (-) 4.5 because once again the total is 30 and since we have a discount price then we minus (-) the discount price by the total and you get

A total with the discount price as 25.5 Dollars or $25.5

Hope this helps ;)

5 0
3 years ago
Greg bought a new car for £18000.
Whitepunk [10]

Answer:

£9318.96

Step-by-step explanation:

18000×0.7×0.86^(2)=£9318.96

3 0
3 years ago
An airplane took 5 hours to travel 3,420 kilometers.how many kilometers did the plane travel in one hour
tino4ka555 [31]

Answer:

684 Hours.

Step-by-step explanation:

If the plane travelled that distance in 5 hours, then all you need to do is divide the distance by 5 to get the distance travelled in one hour. This is obviously presuming that the speed travelled was constant or that this is an average figure.

3420/5 = 684.

8 0
3 years ago
Read 2 more answers
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