Please help test due in 30 mins!

A is true but f(x) is wrong need help

MrRissso [65]

Answer:

f(x)=-18x^2

Step-by-step explanation:

Given:

1+Integral(f(t)/t^6, t=a..x)=6x^-3

Let's get rid of integral by differentiating both sides.

Using fundamental of calculus and power rule(integration):

0+f(x)/x^6=-18x^-4

Additive Identity property applied:

f(x)/x^6=-18x^-4

Multiply both sides by x^6:

f(x)=-18x^-4×x^6

Power rule (exponents) applied"

f(x)=-18x^2

Check:

1+Integral(-18t^2/t^6, t=a..x)=6x^-3

1+Integral(-18t^-4, t=a..x)=6x^-3

1+(-18t^-3/-3, t=a..x)=6x^-3

1+(6t^-3, t=a..x)=6x^-3

That looks great since those powers are the same on both side after integration.

Plug in limits:

1+(6x^-3-6a^-3)=6x^-3

We need 1-6a^-3=0 so that the equation holds true for all x.

Subtract 1 on both sides:

-6a^-3=-1

Divide both sides by-6:

a^-3=1/6

Raise both sides to -1/3 power:

a=(1/6)^(-1/3)

Negative exponent just refers to reciprocal of our base:

a=6^(1/3)

3 0

3 years ago

Dimitri wrote the equations y = 3x and y = x + 3.

STALIN [3.7K]

Answer:

(12,-1)

Step-by-step explanation:

just be nice and dont call no one an idiot

6 0

3 years ago

g red bell pepper seeds germinates 85% of the time. planted 25 seeds. What is the probability that 20 or more germinate

bixtya [17]

Answer:

$P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)$

And replacing using the mass function we got:

$P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156$

$P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211$

$P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217$

$P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161$

$P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759$

$P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172$

And adding the values we got:

$P(X\geq 20) = 0.8381$

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=25, p=0.85)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We want to find the following probability:

$P(X\geq 20)= P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)$

And replacing using the mass function we got:

$P(X=20)=(25C20)(0.85)^{20} (1-0.85)^{25-20}=0.156$

$P(X=21)=(25C21)(0.85)^{21} (1-0.85)^{25-21}=0.211$

$P(X=22)=(25C22)(0.85)^{22} (1-0.85)^{25-22}=0.217$

$P(X=23)=(25C23)(0.85)^{23} (1-0.85)^{25-23}=0.161$

$P(X=24)=(25C24)(0.85)^{24} (1-0.85)^{25-24}=0.0759$

$P(X=25)=(25C25)(0.85)^{25} (1-0.85)^{25-25}=0.0172$

And adding the values we got:

$P(X\geq 20) = 0.8381$

7 0

3 years ago

Last season he scored 179 touchdowns. This season he scored 253 touchdowns.

nydimaria [60]

Given,
Previous Season touchdowns scores = 179
Current Season touchdowns scores = 253
Here,
Increased touchdowns scores = 253 - 179 = 74
Now,
Percent increment = (increased/previous)*100 = (74/179)*100 = 41.34%
Hence, the required answer is 41% ( nearest round off percent)

5 0

3 years ago

Hey hey hey. help pls

Firdavs [7]

Answer:

Emma spend 8 hours in homework in a week and Jared spends 16 hours in homework in 2 weeks.

Step-by-step explanation:

Two quantities P and Q are said to be in PROPORTION if and only if for all values of P and q, we get:

$\frac{P}{Q} = k$

Here, k : PROPORTIONALITY CONSTANT

Case: 1

5 hour piano practice in 1 week.

So, the piano practice in 2 weeks( 1 x 2) = 2 x 5 = 10 hours

But here, it is given to be 12 hours in 2 weeks.

Hence, NOT PROPORTIONAL.

Case 2:

70 words in 60 seconds.

So, the words typed in 210 seconds ( 60 x 3.5) = 70 x 3.5 = 240 words

But here, it is given to be 280 words in 210 seconds.

Hence, NOT PROPORTIONAL.

Case: 3

8 hour homework in 1 week.

So, the homework done in 2 weeks( 1 x 2) = 2 x 8 = 16 hours

It is given to be 16 hours in 2 weeks.

Hence, PROPORTIONAL.

Case: 4

15 miles in 78 minutes.

So, the distance covered in 102 minutes (78 x 1.3) = 15 x 1.3 = 19.6 miles

But here, it is given to be 17 miles in 102 minutes.

Hence, NOT PROPORTIONAL.

Case: 5

18 miles in 45 minutes.

So, the distance covered in 55 minutes (45 x 1.2) = 18 x 1.2 = 21.6 miles

But here, it is given to be 22 miles in 55 minutes.

Hence, NOT PROPORTIONAL.

Hence, the only proportional case is Emma spend 8 hours in homework in a week and Jared spends 16 hours in homework in 2 weeks.

6 0

3 years ago

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