Graph this function.
f(t) = -1/3x + 8

Answer:

Step-by-step explanation:

Given this quadratic expression.

x² – 10x + c = 0

We are to find the value c that will make the expression a perfect square'

Using the completing the square method

Add the square of the half of coefficient of x

Coefficient of x = -10

Half of -10 = 1/2(-10) = -5

Square of -5 = (-5)^2 = 25

Hence the value of c to complete the expression is 25

Answer:

Step-by-step explanation:

(a) [tex]\int x^n e^{5x^4+1} \ dx[/tex]

Suppose [tex]5x^4 + 1 = f[/tex]

by differentiation;

[tex]\implies \ 20 x^3 dx = df --- (1)[/tex]

Suppose n = 3

Then, the integral

[tex]I = \int x^ 3 e^{5x^4 + 1} \ dx[/tex]

[tex]= \int e^f \ \dfrac{df}{20}[/tex]

[tex]= \dfrac{1}{20} \int e^f \ dt[/tex]

[tex]= \dfrac{1}{20} e^f + C[/tex]

recall that [tex]f = 5x^4 + 1[/tex]

Then;

[tex]\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}[/tex]

(b) [tex]\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx[/tex]

suppose; [tex]\dfrac{1}{x^3} = f[/tex]

[tex]x^3 = f[/tex]

[tex]\implies -3x^{-4} \ dx = df[/tex]

[tex]\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df[/tex]

If n = u, then the integration is:

[tex]I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx[/tex]

[tex]= \int -\dfrac{1}{3} \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \int \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \ sin \ f + C[/tex]

Since;  [tex]x^3 = f[/tex]

Then;

[tex]\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}[/tex]

(c) [tex]\int \dfrac{x+n}{x^2 + 8x -4} \ dx[/tex]

Suppose  [tex]x^2 + 8x - 4 = f[/tex]

Then, by differentiation of both sides

[tex](2x + 8) \ dx = df[/tex]

[tex](x + 4) \ dx = \dfrac{1}{2} \ df[/tex]

Suppose n = 4 in integration, then:

[tex]I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx[/tex]

By substitution;

[tex]I = \int \dfrac{1}{2}\dfrac{1}{f} \ df[/tex]

[tex]= \dfrac{1}{2} \ \ { In |f|} + C[/tex]

[tex]\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}[/tex]

The suitable substitutions of n are 3,4,4 respectively.

The process of finding integrals is called integration.

a)[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

Suppose

[tex]5x^4+1 =t\\20x^3 dx =dt[/tex]

So, we need n=3 for easy integration.

[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

[tex]I = \frac{1}{20} \int\limits {e^{t} } \, dt[/tex]

[tex]I=\frac{e^{t} }{20}[/tex]

[tex]I = e^{5x^{4}+1 }/20 +c[/tex]

b)Similarly for [tex]f(x) = \int\limits\frac{cos(\frac{1}{x^3} )}{x^n} \, dx[/tex]

n=4 is needed for easy integration.

I = [tex]\frac{-1}{3} sin(\frac{1}{x^3} ) +c[/tex]

c)For [tex]f(x) = \int\limits \frac{x+n}{x^{2} +8x-4} \, dx[/tex]

n=4 is needed for easy integration.

[tex]I = \frac{1}{2} log(x^{2} +8x-4)[/tex]

Hence, the suitable substitutions of n are 3,4,4 respectively.

To get more about integration visit:

https://brainly.com/question/2633548





Answer: It's the third one down

Step-by-step explanation:

Answer:

you have to put -160 over -16 then divide and your answer will be 10

so x=10. I hope this helps :)

Answer:

These two corners are [tex]\sqrt{13}[/tex] units apart.

Step-by-step explanation:

Distance between two points:

Suppose we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Approximately how far apart are the two corners?

We have to find the distance between the points (-5,-2) and (-8-3). So

[tex]D = \sqrt{(5-(-8))^2+(-2-(-3))^2} = \sqrt{13}[/tex]

These two corners are [tex]\sqrt{13}[/tex] units apart.

Answer:

im sure its D.)

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm not sure about number 3, but I have the answer for number. The answer is 1:32.

3: 69

3/69

Then we reduce the fraction to the lowest term

3/69 = 1/32

1:32

Just divide 96/3 and you can see that one bus can hold 32 students

Answer: 1324.12 sq. cm.

Step-by-step explanation:

A=2πrh+2πr2

A = 2π x 8.2 x 17.5 + 2π x 8.2^2

A = 2π x 143.50 + 2π x 67.24

A= 1324.12

Hi.. U should do like this

4/5 mile in 50 min

X mile in 60 min

X=5/4 mile

Answer:

5 milesss

:)))

Answer:

Hey

Step-by-step explanation:

Write the fraction in simplest form

[tex] - \frac{29}{18} [/tex]

[tex] \frac{8}{9} - \frac{5}{2} [/tex]

Find the difference between 8/9 and 5/-2

[tex] \frac{8}{9} - \frac{5}{2} [/tex]

[tex] \frac{8 \times 2}{9 \times 2} - \frac{5 \times 9}{2 \times 9} [/tex]

[tex] \frac{16}{18} - \frac{45}{18} [/tex]

[tex] \frac{16 - 45}{18} [/tex]

[tex] \frac{ - 29}{18} [/tex]

[tex] - \frac{29}{18} [/tex]

Answer:

The correct answer is,

[tex] {8x}^{6y {}^{5} } [/tex]

Answer:

carios has greater angle

Step-by-step explanation:

hope this helps

Answer: Total cost would be 10,320

Step-by-step explanation: Hope this helps

Answer:

weird questions but...

May I have 4 cups of water please?

Answer:

deciliter of water

Step-by-step explanation:

a unit of capacity equal to 1/10 of a liter.

Answer:

2?

Step-by-step explanation:

Answer:8,5 recirpoal is 5,8

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

4.50 × 10 =45!

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.

.

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.

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.

Answer:

$15

Step-by-step explanation:

$4.50 time 3 = $13.50 (9 lbs)

$4.50 divided by 3 = $1.50 (1 lb)

$1.50 plus $13.50 = $15

Answer:

Amount contributed by Oscar = $8

Step-by-step explanation:

Given that:

Amount spent on gift = $36

Amount contributed by Moriah = $12

Let,

x be the amount contributed by each of them.

Thus,

Gift total = Contribution of all

36 = x+x+x+12

36 = 3x+12

3x+12 = 36

3x=36-12

3x=24

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{24}{3}\\x=8[/tex]

Hence,

Amount contributed by Oscar = $8

Answer:

8 is the number

Step-by-step explanation:

I don't know why it took me so long to figure it out, 4 x 8 = 32 32 + 15 = 47

It probably took me a really long time because I am tired, and I am not using a calculator.

Answer:

[tex](-4, 1) \: and \: (-4,7)[/tex]

Step-by-step explanation:

[tex]the \: shortest \: distance \: between \: two \: points \: can \: be \: used \: here \to \\ were : d = \sqrt{ (x_{2} -x_{1} ) {}^{2} + (y_{2} -y_{1} ) {}^{2} } \\checking \: for \: the \: pair \to \: (-4, 1) \: and \: (-4,7) \\ d = \sqrt{ (( - 4)-( - 4)) {}^{2} + (7 -1 ) {}^{2} } \\ d = \sqrt{ (- 4 + 4) {}^{2} + (6) {}^{2} } \\ d = \sqrt{ (0) {}^{2} + (6) {}^{2} } \\ d = \sqrt{ (6) {}^{2} } \\ \underline{ \boxed{d = 6}}[/tex]

Answer: x > - 18

Step-by-step explanation:

Step-by-step explanation:

Sum of interior angles in a polygon

= 180°(n - 2), where n is the number of sides.

Hence a convex polygon with 6 sides

=> 180°(6 - 2) = 720°.

Answer:

The answer is 154.8 ml

Step-by-step explanation:

In this question, the amount of pure acid is 18% of the total solution, that is, 18% of 860 milliliters. So

0.18*860 = 154.8 ml

The answer is 154.8 ml

Answer:

quadrant 3

Step-by-step explanation:

Answer:

a smart person is not me clearly lol

Step-by-step explanation:

Answer:

[tex]\mathrm{No\: solutions}[/tex]

Step-by-step explanation:

Since Connor has worked 12 hours walking dogs, he's earned [tex]12\cdot 8 = \$96[/tex] from walking dogs. He still needs to earn [tex]\$160-\$96=\$64[/tex]. As stated in the problem, he makes $12 an hour landscaping, therefore the minimum number of whole hours he must work to fulfill his requirements is [tex]\lceil{ \frac{64}{12} \rceil = 6\: \mathrm{hours}[/tex]. However, the problem states he can only work a maximum of 15 hours. He would have to work [tex]12+6=18[/tex] to fulfill his requirements and therefore he will not be able to meet his requirements with the restrictions given.

Answer:

a) The z-score for a backyard structure costing $2300 is -0.57.

b) The z-score for a backyard structure costing $4900 is 1.29

c) A backyard structure costing $2300 costs 0.57 standard deviations below the mean, while a backyard structure costing $4900 costs 1.29 standard deviations above the mean. Since both are within 2 standard deviations of the mean, none is an outlier.

d) Since this combination costs more than 2 standard deviations from the mean, yes, it should be considered an outlier.

Step-by-step explanation:

Z-score:

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

If the z-score is more than two standard deviations from the mean(lesser than -2 or more than 2), the score X is considered an outlier.

In this question, we have that:

[tex]\mu = 3100, \sigma = 1400[/tex]

a. What is the z-score for a backyard structure costing $2300?

We have to find Z when [tex]X = 2300[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2300 - 3100}{1400}[/tex]

[tex]Z = -0.57[/tex]

The z-score for a backyard structure costing $2300 is -0.57.

b. What is the z-score for a backyard structure costing $4900?

We have to find Z when [tex]X = 2300[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{4900 - 3100}{1400}[/tex]

[tex]Z = 1.29[/tex]

The z-score for a backyard structure costing $4900 is 1.29

c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.

A backyard structure costing $2300 costs 0.57 standard deviations below the mean, while a backyard structure costing $4900 costs 1.29 standard deviations above the mean. Since both are within 2 standard deviations of the mean, none is an outlier.

d. If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier?

We have to find the z-score when X = 13000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13000 - 3100}{1400}[/tex]

[tex]Z = 7.07[/tex]

Since this combination costs more than 2 standard deviations from the mean, yes, it should be considered an outlier.

Answer:

Slope of a line passing through ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2} , y_{2}[/tex]) is given by:

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

Now,

Slope of line L, (m) = [tex]\frac{-3-(-1)}{-2-2}[/tex] = 0.5

Slope of line M, (n) = [tex]\frac{-1-1}{W-1}[/tex] = [tex]\frac{-2}{W-1}[/tex]

If the lines L and M are parallel to each other,

m = n

or, 0.5 = [tex]\frac{-2}{W-1}[/tex]

or, 0.5 (W - 1) = -2

or, W - 1 = -4

or, W = -3

Therefore the required value of W is -3.