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2 years ago

Consider this polynomial, where a is an unknown real number.

Mathematics

1 answer:

DENIUS [597]2 years ago

8 0

Answer:

Step-by-step explanation:

Correct steps to find the value of 'a' should be,

Braulio's synthetic division should be,

-1 | 1 5 a -3 11

1 4 (a - 4) (1 - a) (a + 10)

Here remainder is (a + 10).

So (a + 10) = 17 ⇒ a = 7

Braulio Incorrectly found a value of 'a' because he should have used (-1) instead of 1.

Zahra's calculation by remainder theorem should be,

p(x) = x⁴ + 5x³ + ax² - 3x + 11

p(-1) = (-1)⁴ + 5(-1)³ + a(-1)² - 3(-1) + 11

= 1 - 5 + a + 3 + 11

= (a + 10)

Since, remainder of the solution is 17,

(a + 10) = 17 ⇒ a = 7

Zahra incorrectly found the value of 'a' because she incorrectly solved the powers to (-1).

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A drinks company use 76.8 kg of sugar in April .How much sugar the day use each day?

Strike441 [17]

Answer:

2.56 kgs

Step-by-step explanation:

76.8kg ÷ 30 days = 2.56 kgs

4 0

2 years ago

Read 2 more answers

World poultry production was 77.2 million tons in the year 2004 and increasing at a continuous rate of 1.6% per year. Assume tha

dezoksy [38]

Answer:

A) $P(t)=77.2\cdot e^{0.016t}$

B) 89.157 million tons.

C) In year 2017.

Step-by-step explanation:

We have been given that world poultry production was 77.2 million tons in the year 2004 and increasing at a continuous rate of 1.6% per year.

A). We know that a continuous growth function is in form $y=a\cdot e^{kx}$ , where,

a = Initial value,

k = Growth rate in decimal form.

$1.6\%=\frac{1.6}{100}=0.016$

Upon substituting our given values, we will get:

$P(t)=77.2\cdot e^{0.016t}$

Therefore, our required function would be $P(t)=77.2\cdot e^{0.016t}$ , where, P represents world poultry production, in million tons, as a function of the number of years, t, since 2004.

B) To find the world poultry production in the year 2013, we will substitute $t=2013-2004=9$ in above formula as:

$P(9)=77.2\cdot e^{0.016(9)}$

$P(9)=77.2\cdot e^{0.144}$

$P(9)=77.2\cdot 1.1548841085249135$

$P(9)=89.1570531781\approx 89.157$

Therefore, the world poultry production in the year 2013 would be 89.157 million tons.

C) To find the number of years it will take for world poultry production to be over 95 million tons, we will equate our function with 95 as:

$95=77.2\cdot e^{0.016t}$

Divide both sides by 77.2:

$1.2305699481865285=e^{0.016t}$

Take natural log of both sides:

$\text{ln}(1.2305699481865285)=\text{ln}(e^{0.016t})$

$\text{ln}(1.2305699481865285)=0.016t\text{ln}(e)$

$0.20747743456981035=0.016t*1$

Divide both sides by 0.016:

$t=12.9673396606$

$t\approx 13$

Therefore, 13 years after in 2017 world poultry production goes over 95 million tons.

4 0

2 years ago

Consider the graph of the linear function h(x) = –x + 5. Which could you change to move the graph down 3 units?

KATRIN_1 [288]

The +5 because that's the y value on the graph

8 0

2 years ago

Read 2 more answers

Which product is positive?

Virty [35]

Answer:

(Negative two-fifths) (Negative StartFraction 8 over 9 EndFraction) (one-third) (StartFraction 2 over 7 EndFraction)

Step-by-step explanation:

(Negative two-fifths) (Negative StartFraction 8 over 9 EndFraction) (one-third) (StartFraction 2 over 7 EndFraction) = (-2/5)(-8/9)(1/3)(2/7)

Let's take the fraction and eliminate the negative sign because negative multiply negative= positive

(-2/5)(-8/9)(1/3)(2/7)= 32/945

4 0

2 years ago

Read 2 more answers

a barangay has 1000 individuals and its population doubles every 60 years. Give an exponential model for the barangay's populati

sdas [7]

Answer:

P(t) = 1000e^(0.01155)t

Step-by-step explanation:

Let the population of barangay be expressed according to the exponential formula;

P(t) = P0e^kt

P(t) is the population of the country after t years

P0 is the initial population

t is the time

If barangay has 1000 initially, this means that P0 = 1000

If the population doubles after 60years then;

at t = 60, P(t) = 2P0

Substitute into the formula

2P0 = P0e^k(60)

2 = e^60k

Apply ln to both sides

ln2 = lne^60k

ln2 = 60k

k = ln2/60

k = 0.01155

Substitute k = 0.01155 and P0 into the expression

P(t) = 1000e^(0.01155)t

Hence an exponential model for barangay's population is

P(t) = 1000e^(0.01155)t

7 0

2 years ago