The functions j(x)=x−1 and k(x)=3x+1 intersect at:

Suppose that the functions s and t are defined for all real numbers x as follows.

jeka94

Answer:

$(s.t)(x) = 4x^2+24x^2\\(s-t)(x) = x+6-4x^2\\(s+t)(-3) = 39$

Step-by-step explanation:

Given functions are:

$s(x)= x+6\\t(x)= 4x^2$

We have to find:

(s.t)(x) => this means we have to multiply the two functions to get the result.

So,

$(s.t)(x) = s(x)*t(x)\\= (x+6)(4x^2)\\=4x^2.x+4x^2.6\\=4x^3+24x^2$

Also we have to find

(s-t)(x) => we have to subtract function t from function s

$(s-t)(x) = s(x) - t(x)\\= (x+6) - (4x^2)\\=x+6-4x^2$

Also we have to find,

(s+t)(-3) => first we have to find sum of both functions and then put -3 in place of x

$(s+t)(x) = s(x)+t(x)\\= x+6+4x^2$

Putting x = -3

$= -3+6+4(-3)^2\\=-3+6+4(9)\\=3+36\\=39$

Hence,

$(s.t)(x) = 4x^2+24x^2\\(s-t)(x) = x+6-4x^2\\(s+t)(-3) = 39$

8 0

3 years ago

How fast must a 56. 5 g tennis ball travel to have a de broglie wavelength equal to that of a photon of green light (5400 angstr

alexandr402 [8]

Answer:

Given:

Mass of the tennis ball=56.5 g

wavelength=5400 Angstroms

De-Broglie Wavelength = 5400 Angstrom.

= 5400 × 10⁻¹⁰ m.

Now, Using the Formula,

λ = h/mv

here,

h is the Planck's constant = 6.62 × 10⁻³⁴ J-s.

and v is the velocity of the tennis balls.

∴ 5400 × 10⁻¹⁰ = (6.62 × 10⁻³⁴)/ (0.054 × v)

⇒ 0.054v = (6.62 × 10⁻³⁴)/ (5400 × 10⁻¹⁰)

⇒ 0.054v = 0.0012 × 10⁻²⁴

⇒ v = 0.0012 × 10⁻²⁴/0.054

⇒ v = 0.023 × 10⁻²⁴ m/s.

Hence, the velocity of the tennis balls is 0.023 × 10⁻²⁴ m/s.

Learn more about average velocity here:

brainly.com/question/13372043

#SPJ4

8 0

2 years ago

18. A normal population has a mean of 80.0 and a standard deviation of 14.0. a. Compute the probability of a value between 75.0

mixer [17]

Answer:

a) 40.17% probability of a value between 75.0 and 90.0.

b) 35.94% probability of a value 75.0 or less.

c) 20.22% probability of a value between 55.0 and 70.0.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 80, \sigma = 14$