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skelet666 [1.2K]
3 years ago
13

For y = 3x - 2x^2 +5x^3 show how to find the value for y, when x = 3. Show your work

Mathematics
2 answers:
Mnenie [13.5K]3 years ago
8 0

y \:  =   \: f(x) \:  =  \: 3x \:  -  \: 2 {x}^{2}  \:  +  \: 5 {x}^{3}
Here, y is a cubic function of x.
When x = 3,
y \:  =  \: f(3) \:  =  \: 3(3) \:  -  \: 2 {(3)}^{2}  \:  +  \: 5 {(3)}^{3}
y \:  =  \: 9 \:  -  \: 18 \:  +  \: 135
y \:  =  \: f(3)  \:  =  \: 126
Hence, when x = 3, y = 126.
liq [111]3 years ago
7 0
Y=3(3)-2(3)^2+5(3)^3
y=9-2(3)^2+5(3)^3
y=9-6^2+5(3)^3
y=9-36+5(3)^3
y=9-36+15^3
y=9-36+3,375
y=-27+3,375
y=3,348




Just do the steps as I showed you. Just go little by little for each thing so that you don't mess up our get super confused.
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F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2)<br><br> I need to factor and find the zeros.
Ratling [72]

Answer:

\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)

\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1

Step-by-step explanation:

<u>Given function</u>:

f(x)=3x^3-2x^2-11x+10

If (x + 2) is a factor then:

\implies f(x)=(x+2)(ax^2+bx+c)

Expand:

\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c

\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c

\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c

To find <em>a</em>, compare the coefficients of x³:

\implies a=3

To find <em>b</em>, substitute the found value of <em>a</em> into the coefficient for x² and compare:

\implies 2a+b=-2

\implies 2(3)+b=-2

\implies b=-8

To find <em>c</em>, compare the constants:

\implies 2c=10

\implies c=5

Therefore:

\implies f(x)=(x+2)(3x^2-8x+5)

Now factor (3x²-8x+5):

\implies 3x^2-3x-5x+5

\implies 3x(x-1)-5(x-1)

\implies (3x-5)(x-1)

Therefore the factored function is:

\implies f(x)=(x+2)(3x-5)(x-1)

<u>Zero Product Property</u>

\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}

To find the zeros, set each factor equal to zero and solve for x:

\implies x+2=0 \implies x=-2

\implies 3x-5=0 \implies x=\dfrac{5}{3}

\implies x-1=0 \implies x=1

Therefore, the zeros of the function are:

x=-2, \quad x=\dfrac{5}{3},\quad x=1

3 0
1 year ago
Grace and her father spent 4 1/2 hours over the weekend restoring their fishing boat. This time makes up 6% of the
solong [7]
\frac{9}{2} multiplied by \frac{6}{100}
= 75 hours
4 and a half hour repairs 6% of the entire boat so it is 
4 1/2 multiplied by 6/100's inverse number

6 0
3 years ago
Read 2 more answers
Consider that x=5 and y=7. Is the sum of x + y rational, irrational, or neither irrational nor rational!
nasty-shy [4]
The sum of y+x, or 5+7, is rational.  This is because each integer(non fraction/decimal)is rational, it is also rational.
5 0
3 years ago
Samir is trying to decide between two checking account plans. After researching plans at two banks, he finds that Unity Bank off
GREYUIT [131]

Answer:

The monthly compounded interest rate of 0.14% of Unity Bank is a better plan.

Step-by-step explanation:

<em>Step 1 : Write the formula for calculating a monthly compound interest rate and for calculating an annually compounded interest rate.</em>

Monthly compound interest rate = P(1+r/n)^nxt

<em>n=12 (number of months in a year)</em>

<em>t=1 (number of years)</em>

Annually compound interest rate = P(1+r/n)^nxt

<em>n=1 (because it is for 1 year only)</em>

<em>t=1 (number of years=1)</em>

<em>Step 2 : Lets assume that P is $100 in both banks and time is 1 year.</em>

<em>Step 3 : Lets substitute the values to find out which one is better.</em>

Monthly compound interest rate = P(1+r/n)^nxt

Monthly compound interest rate = 100(1+0.14/12)^12x1

Monthly compound interest rate = 114.93

114.93 - 100 = $14.93 per month

14.93 x 12 = $179.16 for 12 months or 1 year

Annually compound interest rate = P(1+r/n)^nxt

Annually compound interest rate = 100(1+1.6/1)^1x1

Annually compound interest rate = 260

260-100 = $160 for 1 year

Therefore, the monthly compounded interest rate of 0.14% of Unity Bank is a better plan.

!!

8 0
3 years ago
Read 2 more answers
Find the six trig function values of the angle 240*Show all work, do not use calculator
-BARSIC- [3]

Solution:

Given:

240^0

To get sin 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, sin 240 will be negative.

sin240^0=sin(180+60)

Using the trigonometric identity;

sin(x+y)=sinx\text{ }cosy+cosx\text{ }siny

Hence,

\begin{gathered} sin(180+60)=sin180cos60+cos180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ sin180cos60+cos180sin60=0(\frac{1}{2})+(-1)(\frac{\sqrt{3}}{2}) \\ sin180cos60+cos180sin60=0-\frac{\sqrt{3}}{2} \\ sin180cos60+cos180sin60=-\frac{\sqrt{3}}{2} \\  \\ Hence, \\ sin240^0=-\frac{\sqrt{3}}{2} \end{gathered}

To get cos 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, cos 240 will be negative.

cos240^0=cos(180+60)

Using the trigonometric identity;

cos(x+y)=cosx\text{ }cosy-sinx\text{ }siny

Hence,

\begin{gathered} cos(180+60)=cos180cos60-sin180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ cos180cos60-sin180sin60=-1(\frac{1}{2})-0(\frac{\sqrt{3}}{2}) \\ cos180cos60-sin180sin60=-\frac{1}{2}-0 \\ cos180cos60-sin180sin60=-\frac{1}{2} \\  \\ Hence, \\ cos240^0=-\frac{1}{2} \end{gathered}

To get tan 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, tan 240 will be positive.

tan240^0=tan(180+60)

Using the trigonometric identity;

tan(180+x)=tan\text{ }x

Hence,

\begin{gathered} tan(180+60)=tan60 \\ tan60=\sqrt{3} \\  \\ Hence, \\ tan240^0=\sqrt{3} \end{gathered}

To get cosec 240 degrees:

\begin{gathered} cosec\text{ }x=\frac{1}{sinx} \\ csc240=\frac{1}{sin240} \\ sin240=-\frac{\sqrt{3}}{2} \\  \\ Hence, \\ csc240=\frac{1}{\frac{-\sqrt{3}}{2}} \\ csc240=-\frac{2}{\sqrt{3}} \\  \\ Rationalizing\text{ the denominator;} \\ csc240=-\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\  \\ Thus, \\ csc240^0=-\frac{2\sqrt{3}}{3} \end{gathered}

To get sec 240 degrees:

\begin{gathered} sec\text{ }x=\frac{1}{cosx} \\ sec240=\frac{1}{cos240} \\ cos240=-\frac{1}{2} \\  \\ Hence, \\ sec240=\frac{1}{\frac{-1}{2}} \\ sec240=-2 \\  \\ Thus, \\ sec240^0=-2 \end{gathered}

To get cot 240 degrees:

\begin{gathered} cot\text{ }x=\frac{1}{tan\text{ }x} \\ cot240=\frac{1}{tan240} \\ tan240=\sqrt{3} \\  \\ Hence, \\ cot240=\frac{1}{\sqrt{3}} \\  \\ Rationalizing\text{ the denominator;} \\ cot240=\frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\  \\ Thus, \\ cot240^0=\frac{\sqrt{3}}{3} \end{gathered}

5 0
1 year ago
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