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2 years ago

find the equation of a cubic function whose graph passes through points (3,0) and (1,4) and is tangent to x-axis at the origin

Mathematics

1 answer:

Tomtit [17]2 years ago

3 0

Answer:

y = -2x^2(x - 3)

Step-by-step explanation:

Preliminary Remark

If a cubic is tangent to the x axis at 0,0

Then the equation must be related to y = a*x^2(x - h)

(3,0)

If the cubic goes through the point (3,0), then the equation will become

0 = a*3^2(3 - h)

0 = 9a (3 - h)

0 = 27a - 9ah

from which h = 3

From the second point, we get

4 = ax^2(x - 3)

4 = a(1)^2(1 - 3)

4 = a(-2)

a = 4 / - 2

a = -2

Answer

y = -2x^2(x - 3)

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J. Reexamine the sequence 20, 14, 8, 2, ... from the problem

DENIUS [597]

Answer:

The n th of the given sequence is $t_{n} = 26-6 n$

Step-by-step explanation:

Step 1 :-

Given sequence is 20,14,8,2,.......this sequence in arithmetic progression but this sequence is decreasing sequence.

given first term is 20 and difference is $d = second term- first term = 14-20=-6$

now the nth term of given sequence is

by using formula $t_{n}=a+(n-1)d$

$t_{n}= 20+(n-1)(-6)$

$t_{n}= 20-6 n+6$

final answer:-

$t_{n} = 26-6 n$

verification:-

$t_{n} = 26-6 n$

put n=1 we get first term is 20

put n=2 we get second term is 14

put n=3 we get third term is 8

put n=4 we get fourth term is 2

so the n th term of sequence is

$t_{n} = 26-6 n$

3 0

3 years ago

Write a polynomial equation of degree 4 in standard form that has the solutions i, −i, 1, −1.

Brut [27]

Answer:

x⁴ + 2 x² + 1

Step-by-step explanation:

given solution of the polynomial

i, −i, 1, −1.

equation of the polynomial will be equal to

=(x - i)(x + i)(x - 1)(x + 1)

= (x² + i x - i x - i²)(x² + x - x + 1)

=(x² - (-1))(x² + 1 )

= (x² + 1)(x² + 1)

= x⁴ + x² + x² + 1

= x⁴ + 2 x² + 1

hence, the required polynomial equation is x⁴ + 2 x² + 1

4 0

2 years ago

Josh Pruitt worked 48.75 hours.

leva [86]

For this case, as Josh worked more than 40 hours, he was able to receive a payment
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6 0

3 years ago

Which equation has a graph that passes through the points at (0,5) and (-3,-4)?

Roman55 [17]

Answer:

$y = 3x + 5$

Step-by-step explanation:

We are asked the equation of the graph which passes through the points at (0,5) and (-3,-4).

Now, we know that the equation of a straight line passing through the points ( $x_{1},y_{1}$ ) and ( $x_{2},y_{2}$ ) is given by

$\frac{y - y_{1}}{y_{1} - y_{2}} = \frac{x - x_{1}}{x_{1} - x_{2}}$ .

So, in our case ( $x_{1},y_{1}$ ) ≡ (0,5) and ( $x_{2},y_{2}$ ) ≡ (-3,-4)

Therefore, the equation of the straight line will be

$\frac{y - 5}{5 - (- 4)} = \frac{x - 0}{0 - (- 3)}$

⇒ $y - 5 = \frac{9}{3}x$

⇒ $y = 3x + 5$ (Answer)

4 0

3 years ago

Avocados cost $3 per pound. write and graph an equation in two variables that represents the cost of buying avocados.

mezya [45]

Answer:

y = 3x

Step-by-step explanation:

sorry cant do the graph

6 0

2 years ago