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3 years ago

14

The graph of a quadratic function is shown above.

1 answer:

OleMash [197]3 years ago

6 0

Answer:

0 real zeros
2 complex zeros

Step-by-step explanation:

The "fundamental theorem of algebra" says a polynomial of degree n will have n zeros. If the polynomial has real coefficients, the complex zeros will appear in conjugate pairs.

The graph of this quadratic (degree = 2) does not cross the x-axis, so there are no real values of x that make y=0. That means the two zeros are both complex.

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Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.

$I(5)=x^5e^x-5I(4)$

$I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)$

$I(5)=(x-5)x^4e^x+20(x^3e^x-3I(2))=(x^2-5x+20)x^3e^x-60I(2)$

$I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)$

$I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))$

Finally,

$I(0)=\displaystyle\int e^x\,\mathrm dx=e^x+C$

so we end up with

$I(5)=(x^4-5x^3+20x^2-60x+120)xe^x-120e^x+C$

$I(5)=(x^5-5x^4+20x^3-60x^2+120x-120)e^x+C$

and the antiderivative is

$\displaystyle\int2x^5e^x\,\mathrm dx=(2x^5-10x^4+40x^3-120x^2+240x-240)e^x+C$

8 0

3 years ago

Sally has 71 peppermints. Bernard has p fewer peppermints than Sally. Write an expression that shows how many peppermints Bernar

satela [25.4K]

an expression is:

y = 71 - p

4 0

1 year ago

Read 2 more answers

If y varies inversely as x and } = 3 when x = 4, then y

Andrews [41]

Answer:

FALSE

Step-by-step explanation:

If y varies inversely as x., this is expressed as;

y = k/x

k is the proportionality constant

when y = 3 and x = 4

3 = k/4

k = 3 * 4

k = 12

when x = 15;

y = k/x

y =12/15

y = 4/5

Hence y is not equal to 12 when x = 15.

The correct answer is FALSE

5 0

2 years ago

Help please thank you!

Liula [17]

97 rounds up to 100
78 rounds up to 80
100x80= 8,000
estimate=8,000

97x78=7,566
product=7,566

7 0

2 years ago

Read 2 more answers

H is between points Q and R. QH=23 and HR=12. What is the length of QR

PSYCHO15rus [73]

Answer:

35

Step-by-step explanation:

Given:

GH = 23

HR = 12

Required:

Length big QR

SOLUTION:

Since H is a point in between points Q and R, points Q, H, R are collinear.

QH = 23

HR = 12

QH + HR = QR (segment addition postulate)

23 + 12 = QR (substitution)

35 = QR

Therefore, the length of QR is 35

3 0

3 years ago