Use the differential to approximate the expression. Then use a calculator to approximate the quantity, and give the absolute value of the difference in the two results to four decimal places.

53

Answers

Answer 1

9514 1404 393

Answer:

   0.0056

Step-by-step explanation:

  f(x) = √(49 +x)

  f'(x) = 1/(2√(49 +x))

A linear approximation of f(x) expanded about x=0 is ...

  f(x) ≈ f(0) + f'(0)x = 7 +x/(2·7)

Then for √53, we have x=4

  f(4) ≈ 7 +4/14 = 7 2/7 . . . . . approximate √53 using differentials

__

The calculator value of √53 is about 7.280110, so the difference in results is ...

  approx - actual ≈ 7.285714 -7.280110 = 0.005604 ≈ 0.0056


Related Questions

HELP ASAP!!!!!!
Thank you so much

Answers

x_1=-1x2=7y1=1y2=7m:n=3:5

We know

[tex]\boxed{\sf P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]

[tex]\\ \sf\longmapsto p(x,y)=\left(\dfrac{3(7)+5(-1)}{3+5},\dfrac{3(7)+5(1)}{3+5}\right)[/tex]

[tex]\\ \sf\longmapsto p(x,y)=\left(\dfrac{21-5}{8},\dfrac{21+5}{8}\right)[/tex]

[tex]\\ \sf\longmapsto p(x,y)=\left(\dfrac{16}{8},\dfrac{26}{8}\right)[/tex]

[tex]\\ \sf\longmapsto p(x,y)=\left(2,\dfrac{13}{4}\right)[/tex]

m:n=3:5

We know

[tex]\boxed{\sf M(x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]

[tex]\\ \sf\longmapsto M(x,y)=\left(\dfrac{3(7)+5(-1)}{3+5},\dfrac{3(7)+5(1)}{3+5}\right)[/tex]

[tex]\\ \sf\longmapsto M(x,y)=\left(\dfrac{21-5}{8},\dfrac{21+5}{8}\right)[/tex]

[tex]\\ \sf\longmapsto M(x,y)=\left(\dfrac{16}{8},\dfrac{26}{8}\right)[/tex]

[tex]\\ \sf\longmapsto M(x,y)=\left(2,\dfrac{13}{4}\right)[/tex]

the line that passes through the point (-4, 2) and has a
What is the equation of
slope of
2?

Answers

Answer:

y = 2x + 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2 , then

y = 2x + c ← is the partial equation

To find c substitute (- 4, 2 ) into the partial equation

2 = - 8 + c ⇒ c = 2 + 8 = 10

y = 2x + 10 ← equation of line

What is a1
of the arithmetic sequence for which a3=126
and a64=3,725
a
64
=
3
,
725
?

Answers

In an arithmetic sequence, every pair of consecutive terms differs by a fixed number c, so that the n-th term [tex]a_n[/tex] is given recursively by

[tex]a_n=a_{n-1}+c[/tex]

Then for n ≥ 2, we have

[tex]a_2=a_1+c[/tex]

[tex]a_3=a_2+c = (a_1+c)+c = a_1 + 2c[/tex]

[tex]a_4=a_3+c = (a_1 + 2c) + c = a_1 + 3c[/tex]

and so on, up to

[tex]a_n=a_1+(n-1)c[/tex]

Given that [tex]a_3=126[/tex] and [tex]a_{64}=3725[/tex], we can solve for [tex]a_1[/tex]:

[tex]\begin{cases}a_1+2c=126\\a_1+63c=3725\end{cases}[/tex]

[tex]\implies(a_1+63c)-(a_1+2c)=3725-126[/tex]

[tex]\implies 61c = 3599[/tex]

[tex]\implies c=59[/tex]

[tex]\implies a_1+2\times59=126[/tex]

[tex]\implies a_1+118 = 126[/tex]

[tex]\implies \boxed{a_1=8}[/tex]

Select the correct answer. Which graph represents this inequality? y ≥ 4x − 3

Answers

Step-by-step explanation:

You didn't put the graph, but you can compare between your graphs and the picture.

Brainliest please

The graph that represents this inequality y ≥ 4x − 3 is attached below.

What is a solution set to an inequality or an equation?

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

We are given that the inequality is;

y ≥ 4x − 3

The slope of the inequality is 4.

The equation of the red line is y = 4x − 3  

The shading is above the line and the line is solid, that means  y is greater than or equal 4x − 3

The graph of this inequality y ≥ 4x − 3 is attached below.

Learn more about inequalities here:

https://brainly.com/question/27425770

#SPJ2

Find the x- and y-intercepts of the following line: 4x − 3y = 12

Answers

Answer:

x-intercept: (3,0)

y-intercept: (0,-4)

Step-by-step explanation:

To find the x and y-intercepts, we first need to understand what they are. X and y-intercepts are points on the line that passes through the x-axis and y-axis. When a point is an x-intercept, it passes through the x-axis. This means the x-coordinate is an integer, while the y-coordinate is always 0. This can be denoted by (x,0). When a point is a y-intercept, it passes through the y-axis. This means the y-coordinate is an integer, while the x-coordinate is always 0. This can be denoted by (0,y).

Now that we know what x and y-intercepts are, we can plug in x=0 and y=0 to find the intercepts.

x-intercept

4x-3y=12            [plug in y=0]

4x-3(0)=12          [multiply]

4x-0=12              [add both sides by 0]

4x=12                 [divide both sides by 4]

x=3

---------------------------------------------------------------------------------------------------------

y-intercept

4x-3y=12            [plug in x=0]

4(0)-3y=12         [multiply]

0-3y=12             [subtract both sides by 0]

-3y=12               [divide both sides by -3]

y=-4

Therefore, the x-intercept is (3,0) and y-intercept is (0,-4).

Work out 45% of $200.00

Answers

Answer:

If you are using a calculator, simply enter 45÷100×200 which will give you 90 as the answer.

Mark me brainliest plz.

First you change 45% to decimal form (move the decimal two places to the left) which gives .45

Then, you multiply .45 x $200.00

Your answer is $90

A professor, transferred from Toronto to New York, needs to sell his house in Toronto quickly. Someone has offered to buy his house for $220,000, but the offer expires at the end of the week. The professor does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with his realtor, the professor believes the price he will get by leaving the house on the market for another month is uniformly distributed between $210,000 and $235,000. If he leaves the house on the market for another month, what is the probability that he will get at least $225,000 for the house

Answers

Sorry I’m not sure but others might know

URGENT HELP

The gradient of the tangent to the curve y = ax + bx^3 at the point (2, -4) is 6.
Determine the unknowns a and b.
a=?
b=?

Answers

Answer:

a = -6

b = 1

Step-by-step explanation:

The gradient of the tangent to the curve y = ax + bx^3, will be:

dy/dx = a + 3bx²

at (2, -4)

dy/dx = a+3b(2)²

dy/dx = a+12b

Since the gradient at the point is 6, then;

a+12b = 6 ....1

Substitute x = 2 and  y = -4 into the original expression

-4 = 2a + 8b

a + 4b = -2 ...2

a+12b = 6 ....1

Subtract

4b - 12b = -2-6

-8b = -8

b = -8/-8

b = 1

Substitute b = 1 into equation 1

Recall from 1 that a+12b = 6

a+12(1) = 6

a = 6 - 12

a = -6

Hence a = -6, b = 1

What is the best interpretation of the y-intercept of the line

Answers

Answer:

vertical line

Step-by-step explanation:

because horizontal means horizon which goes left to right across a board

Hi there!

The y-intercept of a line represents its initial value. On a graph, the y-intercept would represent the value of y when the line crosses the y-axis.

For example, if an equation were to model the amount of money someone had in their bank account overtime starting from the day they opened their account, the y-intercept would represent the original amount of money they had.

I hope this helps!

a gym class has 10 boys and 12 girls. how many ways can a team of 6 be selected if the team must have the same number of boys and girls

Answers

Answer:

The number of ways of selecting the team is 26,400 ways.

Step-by-step explanation:

Given;

total number boys in the gym, b = 10 boys

total number of girls in the gym, g = 12 girls

number of team to be selected, n = 6

If there must equal number of boys and girls in the team, then the team must consist of 3 boys and 3 girls.

Number of ways of choosing 3 boys from the total of 10 = [tex]10_C_3[/tex]

Number of ways of choosing 3 girls from a total of 12 = [tex]12_C_3[/tex]

The number of ways of combining the two possibilities;

[tex]n = 10_C_3 \times 12_C_3\\\\n = \frac{10!}{7!3!} \ \times \ \frac{12!}{9!3!} \\\\n = \frac{10\times 9 \times 8}{3\times 2} \ \times \ \frac{12\times 11 \times 10}{3\times 2} \\\\n = 120 \times 220\\\\n = 26,400 \ ways[/tex]

Therefore, the number of ways of selecting the team is 26,400 ways.

whats 2 plus 2

*just trying to help someone get points* :)

Answers

Answer:4 ma boi

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

because I am god at meth and very smart

6
1
10 points
Find the probability that a randomly selected person's birthday is not in May. Ignore leap years.
31
334
31
365
334
365
11
2
3
12
Previous

Answers

Answer:

c. [tex]\frac{334}{365}[/tex]

Step-by-step explanation:

May has 31 days and a normal year is 365 days, so the probability is [tex]\frac{31}{365}[/tex]

The probability that isn't in May is: 1 - [tex]\frac{31}{365}[/tex] = [tex]\frac{334}{365}[/tex]

Use the procedures developed to find the general solution of the differential equation. (Let x be the independent variable.)

2y''' + 15y'' + 24y' + 11y= 0

Answers

Solution :

Given :

2y''' + 15y'' + 24y' + 11y= 0

Let x = independent variable

[tex](a_0D^n + a_1D^{n-1}+a_2D^{n-2} + ....+ a_n) y) = Q(x)[/tex]  is a differential equation.

If [tex]Q(x) \neq 0[/tex]

It is non homogeneous then,

The general solution  = complementary solution + particular integral

If Q(x) = 0

It is called the homogeneous then the general solution =  complementary solution.

2y''' + 15y'' + 24y' + 11y= 0

[tex]$(2D^3+15D^2+24D+11)y=0$[/tex]

Auxiliary equation,

[tex]$2m^3+15m^2+24m +11 = 0$[/tex]

-1  | 2    15    24     11

    | 0   -2    - 13    -11  

      2    13    11       0

∴ [tex]2m^2+13m+11=0[/tex]

The roots are

[tex]$=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]

[tex]$=\frac{-13\pm \sqrt{13^2-4(11)(2)}}{2(2)}$[/tex]

[tex]$=\frac{-13\pm9}{4}$[/tex]

[tex]$=-5.5, -1$[/tex]

So, [tex]m_1, m_2, m_3 = -1, -1, -5.5[/tex]

Then the general solution is :

[tex]$= (c_1+c_2 x)e^{-x} + c_3 \ e^{-5.5x}$[/tex]

 

.
you invested $
7000
7000
between two accounts payin 
6
%
6
%
and 
8
%
8
%
annual interet, respectively. if the total interest earned for the year was $
480
,
480
,
how much was invested at each rate

Answers

9514 1404 393

Answer:

$3000 at 8%$4000 at 6%

Step-by-step explanation:

Let x represent the amount invested at 8%. Then the total interest earned is ...

  0.06(7000 -x) +0.08x = 480

  420 +0.02x = 480 . . . . . . . . . eliminate parentheses

  0.02x = 60 . . . . . . . . . . subtract 420

  x = 60/0.02 = 3000 . . . . . divide by the coefficient of x

$3000 was invested at 8%; $4000 was invested at 6%.

Which diagram best shows how fraction bars can be used to evaluate One-half divided by one-fourth? A fraction bar labeled 1. Under the 1 are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing one-fourth. 2 one-fourths are circled. A fraction bar labeled one-fourth. Under the one-fourth are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing 1. 2 boxes containing 1 are circled. A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 8 boxes containing one-half. One box containing one-half is circled. A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 2 boxes containing one-half. One box containing one-half is circled.

Answers

Answer:

Step-by-step explanation:

The description is too ambiguous to reconstruct the diagram. You need to post the actual diagram.

That diagram is just one way to view division by a fraction. An easier way: DIVIDING by a fraction is the same as MULTIPLYING by the upside-down fraction. For example,

(1/2) ÷ (1/4) = (1/2) × (4/1) = 2

That doesn’t help you answer this particular question, though.

Answer:

C

Step-by-step explanation:

The work done by a machine in 2 minutes is 480J. Calculate the power of the machine​

Answers

Answer:

I think the power is 4

Step-by-step explanation:

480J / 120 = 4

Put 2 mins into seconds which is 120 seconds

Sorry if it is wrong :)

Answer:

[tex]4\text{ watts}[/tex]

Step-by-step explanation:

In physics, the power of a machine is given by [tex]P=\frac{W}{\Delta t}[/tex], where [tex]W[/tex] is work in Joules and [tex]\Delta t[/tex] is time in seconds.

Convert 2 minutes into seconds:

2 minutes = 120 seconds.

Substitute [tex]W=480[/tex] and [tex]\Delta t=120[/tex] to solve for [tex]P[/tex]:

[tex]P=\frac{480}{120}=\boxed{4\text{ watts}}[/tex]

A humanities professor assigns letter grades on a test according to the following scheme.
A: Top 8% of scores
B: Scores below the top 8% and above the bottom 62%
C: Scores below the top 38% and above the bottom 18%
D: Scores below the top 82% and above the bottom 9%
E: Bottom 9% of scores Scores on the test are normally distributed with a mean of 67 and a standard deviation of 7.3.
Find the numerical limits for a C grade.

Answers

Answer:

The numerical limits for a C grade are 60.6 and 69.1.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Scores on the test are normally distributed with a mean of 67 and a standard deviation of 7.3.

This means that [tex]\mu = 67, \sigma = 7.3[/tex]

Find the numerical limits for a C grade.

Below the 100 - 38 = 62th percentile and above the 18th percentile.

18th percentile:

X when Z has a p-value of 0.18, so X when Z = -0.915.

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

[tex]-0.915 = \frac{X - 67}{7.3}[/tex]

[tex]X - 67 = -0.915*7[/tex]

[tex]X = 60.6[/tex]

62th percentile:

X when Z has a p-value of 0.62, so X when Z = 0.305.

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

[tex]0.305 = \frac{X - 67}{7.3}[/tex]

[tex]X - 67 = 0.305*7[/tex]

[tex]X = 69.1[/tex]

The numerical limits for a C grade are 60.6 and 69.1.

what is the area of this whole shape

Answers

Answer:

104 m²

Step-by-step explanation:

Area of the whole shape = area of the triangle + area of the rectangle

= ½*b*h + L*W

Where,

b = 8 m

h = 6 m

L = 10 m

W = 8 m

Plug in the values into the equation

Area of the whole shape = ½*8*6 + 10*8

= 24 + 80

= 104 m²

What is the numerical coefficient of the first term

Answers

Answer:

the number before the first variable (first term)

Step-by-step explanation:

this appears to be an incomplete question. The numerical coefficient of a term is the number before the variable.

the constant is the number without a variable.

The constant number without the verbal?

The thicknesses of 81 randomly selected aluminum sheets were found to have a variance of 3.23. Construct the 98% confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory. Round your answers to two decimal places

Answers

Answer:

The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.

Step-by-step explanation:

The confidence interval for population variance is given as below:

[tex][(n - 1)\times S^{2} / X^{2} \alpha/2, n-1 ] < \alpha < [(n- 1)\times S^{2} / X^{2} 1- \alpha/2, n- 1 ][/tex]

We are given

Confidence level = 98%

Sample size = n = 81

Degrees of freedom = n – 1 = 80

Sample Variance = S^2 = 3.23

[tex]X^{2}_{[\alpha/2, n - 1]} = 112.3288\\\X^{2} _{1 -\alpha/2,n- 1} = 53.5401[/tex]

(By using chi-square table)

[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]

[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]

2.3004 < σ^2 < 4.8263

Lower limit = 2.30

Upper limit = 4.83.

Please helpppppp me!!!!!!!!

Answers

Answer:

A --> y=cot(x)

Step-by-step explanation:

if you graph tan(x), it has a period of just PI, because tan(x) is just sin(x)/cos(), and cot(x) is the same because it is just sec(x)/csc(x).

Can someone help me with this problem

Answers

Answer:

3/11

Step-by-step explanation:

the answer is 9/110 zzzz

Open the graphing tool one last time. Compare the graphs of y=log (x-k) and y=log x+k in relation to their domain, range, and asymptotes. Describe what you see.

Answers

Answer:

sorry I don't know the answer

Answer:

For the equation y=log(x-k), the domain depends on the value of K. Sliding K moves the left bound of the domain interval. The range and the right end behavior stay the same. For the equation y=log x+k, the domain is fixed, starting at an x-value of 0. The vertical asymptote is also fixed. The range of the equation depends on K.

Step-by-step explanation:

3w2 – 21w = 0

Need some help.

Answers

Answer:

The solutions are w=0 ,7

Step-by-step explanation:

3w^2 – 21w = 0

Factor out 3w

3w(w-7) =0

Using the zero product property

3w=0  w-7=0

w =0    w=7

The solutions are w=0 ,7

5 = –6x2 + 24x
5 = –6(x2 – 4x)

inside the parentheses and
.
–19 = –6(x – 2)2
StartFraction 19 Over 6 EndFraction = (x – 2)2
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot = x – 2
The two solutions are
Plus or minus StartRoot StartFraction 19 Over 6 EndFraction EndRoot.

Answers

Answer:

x = 2 - sqrt(19/6)

x = 2 + sqrt(19/6)

Step-by-step explanation:

Answer:

add 4

subtract 24 from 5

2

Step-by-step explanation:

Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that three are women.

0.010

0.354

0.424

0.25

Answers

Answer:

B. 0.354

Step-by-step explanation:

Combination of 4 out of 5 + 7 = 12 is:

12C4 = 12!/8!4! = 495

Combination of 1 man and 3 women is:

5C1*7C3 = 5*7!/4!3! = 5*35 = 175

Required probability:

P(3W) = 175/495 ≈ 0.353

Correct choice is B

The sum of two binomials is 12x2 − 5x. If one of the binomials is x2 − 2x, the other binomial is:

1. 11x2 − 7x.
2. 12x2 − 3x.
3. 11x2 − 3x.
4. None of these choices are correct.

Answers

Answer:

C. 11x² - 3x

Step-by-step explanation:

(12x² - 5x) - (x² - 2x)

12x² - 5x - x² + 2x

12x - x² - 5x + 2x

11x² - 3x

distance between 4, -4 and -7, -4

Answers

Step-by-step explanation:

here's the answer to your question

Answer: Distance = 11

Step-by-step explanation:

Concept:

Here, we need to know the idea of the distance formula.

The distance formula is the formula, which is used to find the distance between any two points.

If you are still confused, please refer to the attachment below for a clear version of the formula.

Solve:

Find the distance between A and B, where:

A (4, -4)B (-7, -4)

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

[tex]Distance=\sqrt{(4+7)^2+(-4+4)^2}[/tex]

[tex]Distance=\sqrt{(11)^2+(0)^2}[/tex]

[tex]Distance=\sqrt{121+0}[/tex]

[tex]Distance=\sqrt{121}[/tex]

[tex]Distance=11[/tex]

Hope this helps!! :)

Please let me know if you have any questions

А _______ equation can be written in the form ax2 + bx+c=0 where a, b, and c are real numbers, and a is a nonzero number.

Fill in the blank.

A) quadratic
B) quartic
C) linear
D) cubic

Wrong answers WILL be reported. Thanks!

Answers

Answer:

A) quadratic

Step-by-step explanation:

ax2 + bx+c=0

Since the highest power of the equation is 2

A) quadratic -2

B) quartic- 4

C) linear- 1

D) cubic-3

A) quadratic because the highest power of the equation is 2

Which graph shows the solution to the given system of inequalities? [y<6x+1 y<-3.2x-4

Answers

Answer:

VERY NICE RACK U HAVE MAM

Step-by-step explanation:

Answer:

Its a

Step-by-step explanation:

found on another thing and im taking test

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