Answer: The value of k for which one root of the quadratic equation kx2 - 14x + 8 = 0 is six times the other is k = 3.
Let's look into the solution step by step.

Explanation:

Given: A quadratic equation, kx2 - 14x + 8 = 0

Let the two zeros of the equation be α and β.

According to the given question, if one of the roots is α the other root will be 6α.

Thus, β = 6α

Hence, the two zeros are α and 6α.

We know that for a given quadratic equation ax2 + bx + c = 0

The sum of the zeros is expressed as,

α + β = - b / a

The product of the zeros is expressed as,

αβ = c / a

For the given quadratic equation kx2 - 14x + 8 = 0,

a = k, b = -14, c = 8

The sum of the zeros is:

α + 6α = 14 / k [Since the two zeros are α and 6α]

⇒ 7α = 14 / k

⇒ α = 2 / k --------------- (1)

The product of the zeros is:

⇒ α × 6α = 8 / k [Since the two zeros are α and 6α]

⇒ 6α 2 = 8 / k

⇒ 6 (2 / k)2 = 8 / k [From (1)]

⇒ 6 × (4 / k) = 8

⇒ k = 24 / 8

⇒ k = 3

6 0

3 years ago

Making handcrafted pottery usually takes two major steps:wheel throwing and firing. The time of wheel throwing and thetime of fi

levacccp [35]

Answer:

a) $P(R$

And we can find this probability using the normal standard table or excel and we got:

$P(z$

b) $P(R>110)=P(\frac{R-\mu}{\sigma}>\frac{110-\mu}{\sigma})=P(Z>\frac{110-100}{3.606})=P(Z>2.774)$

And we can find this probability using the complement rule and the normal standard table or excel and we got:

$P(z>2.774)=1-P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the time for the step 1 and Y the time for the step 2, we define the random variable R= X+Y for the total time and the distribution for R assuming independence between X and Y is:

$R \sim N(40+60 = 100,\sqrt{2^2 +3^2}= 3.606 s)$