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2 years ago

Use Descartes’s rule of signs to determine the possible number of positive and negative real zeros of f(x)=8x^4-6x^3-4x^2-7x+3

1 answer:

5 0

let's recall Descartes rule of signs, to get the Real Positive ones we start by checking the sign changes for f(x), and to get the Real Negative ones we check the sign changes for f( -x ).

Check the picture below.

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A pump fills a pool at the rate of 20 cubic meters in an hour. If each cubic meter of water costs $10, how many minutes will the

fomenos

The first thing any good mathematician does is convert the measurements to the same unit as what the question is asking. In this problem, it states that the pool fills at a rate of 20 cubic meters per hour. Just keep in mind that an hour is 60 minutes.

The next step is to see how many cubic meters will cost $300. This can be done by dividing 300 by 10. This gets you 30 cubic meters of water.

You already know that 60 minutes is 20 cubic meters of water. That leaves the remaining 10 cubic meters of water. By dividing the rate given, you get that 30 minutes is 10 cubic meters of water. Add the 60 and 30 together to get 90 minutes.

It will take 90 minutes for the pump to use $300.

7 0

3 years ago

Please answer question three and four if you can :)<br> Show full working out ty;)

nikklg [1K]

Step-by-step explanation:

Let D be the mid point of side BC, [B(2, - 1), C(5, 2)].

Therefore, by mid-point formula:

$D = ( \frac{2 + 5}{2}, \: \: \frac{ - 1 + 2}{2} ) = ( \frac{7}{2}, \: \: \frac{ 1}{2} ) \\ \therefore D= (3.5, \: \: 0.5) \\ \& \: A=(-1,\:\:4)...(given) \\\\ now \: by \: distance \: formula \\ \\ Length \: of \: segment \: AD \\ = \sqrt{( - 1 - 3.5)^{2} + {(4 - 0.5)}^{2} } \\ = \sqrt{(4.5)^{2} + {(3.5)}^{2} } \\ = \sqrt{20.25 + 12.25 } \\ = \sqrt{32.5} \\ \red{ \boxed{\therefore Length \: of \: segment \: AD = 5.7 \: units}}$

4 (a)

Equation of line AB[A(2, 1), B(-2, - 11)] in two point form is given as:

$\frac{y-y_1}{y_1-y_2} =\frac{x-x_1}{x_1 - x_2} \\\\\therefore \frac{y-1}{1-(-11)} =\frac{x-2}{2 - (-2) } \\\\\therefore \frac{y-1}{1+11} =\frac{x-2}{2 +2} \\\\\therefore \frac{y-1}{12} =\frac{x-2}{4} \\\\\therefore \frac{y-1}{3} =\frac{x-2}{1} \\\\\therefore y-1= 3(x - 2)\\\\\therefore y= 3x - 6+1\\\\\therefore y= 3x - 5\\\\ \huge \purple {\boxed {\therefore 3x - y-5=0}} \\$

is the equation of line AB.

Now we have to check whether C(4, 7) lie on line AB or not.

Let us substitute x = 4 & y = 7 on the Left hand side of equation of line AB and if it gives us 0, then C lies on the line.

$LHS = 3x - y-5\\=3\times 4-7-5\\= 12-12\\=0\\= RHS$

Hence, point C (4, 7) lie on the straight line AB.

4(b)

Like we did in 4(a), first find the equation of line AB and then substitute the coordinates of point C in equation and if they satisfy the equation, then all the three points lie on the straight line.

4 0

3 years ago

It costs $2.50 to rent a pair of bowling shoes and $1.75 for each game bowled.

garri49 [273]

I think it would be $77.00

3 0

3 years ago

Find the quotient and express it in the simplest form

pychu [463]

2i(4+5i)(4-5i) =82i
4+i nothing more can be done it is at simplest form

so $\frac{82i}{4+i}$ = $\frac{82}{17} + \frac{328}{17} i$

so your answer is $\frac{82}{17} + \frac{328}{17} i$

5 0

3 years ago

Help me pleaseee asap !!!

frosja888 [35]

Step-by-step explanation:

5x+3x-14=180

8x-14=180

8x=180+14

8x=174

x=174/8

x= 21.75°

if x is 21.75°, then 5x is 108.75°

which means 3x-14 is 51.25°

therefore, f +108.75+51.25=180

f = 180-160

f=20°

4 0

2 years ago