Jimmy thought he had purchased 7
folders, but he had only purchased 6.
What was his percent error?

Hello :D

The answer is 0.08

I hope this helps :)

Using the Newton method, the next estimate of the height after one iteration is: h = 0.1474m.

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

The Newton's method to find a solution [tex]x[/tex] of a function [tex]f(x)[/tex] is given by:

[tex]x_{n+1} = x_n - \frac{f(x_n)}{f^{\prime}(x_n)}[/tex]

In which n+1 is the next iteration.

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

In the context of this problem, the height is:

[tex]h_{n+1} = h_n - \frac{V(h_n)}{V^{\prime}(h_n)}[/tex]

Thus, for the first iteration:

[tex]h_1 = h_0 - \frac{V(h_0)}{V^{\prime}(h_0)}[/tex]

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

The function, and its derivative, are:

[tex]V(h) = \frac{3r \pi h^2 - \pi h^3}{3}[/tex]

The radius is [tex]r = 3[/tex], thus:

[tex]V(h) = \frac{9\pi h^2 - \pi h^3}{3}[/tex]

[tex]V^{\prime}(h) = \frac{18\pi h - 3\pi h^2}{3}[/tex]

Simplifying by 3:

[tex]V^{\prime}(h) = \pi(6h - h^2)[/tex]

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

The initial estimate is [tex]h_0 = 0.3[/tex], thus:

[tex]V(0.3) = \frac{9\pi (0.3)^2 - \pi (0.3)^3}{3} = 0.82[/tex]

[tex]V^{\prime}(0.3) = \pi[6(0.3) - (0.3)^2] = 5.3721[/tex]

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

The estimate, after 1 iteration, is:

[tex]h_1 = h_0 - \frac{V(h_0)}{V^{\prime}(h_0)}[/tex]

[tex]h_1 = 0.3 - \frac{0.82}{5.3721}[/tex]

[tex]h_1 = 0.1474[/tex]

The estimate of the height after one iteration is of h = 0.1474m.

A similar problem is given at https://brainly.com/question/17031314

9514 1404 393

Explanation:

If you can't operate a calculator, perhaps you can do long division. The attachment shows the work for that.

__

  [tex]\dfrac{20}{8}=\dfrac{5\cdot4}{2\cdot4}=\dfrac{5}{2}\\\\=\dfrac{5\cdot5}{2\cdot5}=\dfrac{25}{10}=2.5[/tex]

We assume that you know dividing by 10 moves the decimal point one place left.

[tex]\\ \sf\longmapsto 5x+5+4x-5=180[/tex]

[tex]\\ \sf\longmapsto 5x+4x+5-5=180[/tex]

[tex]\\ \sf\longmapsto 9x=180[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{180}{9}[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]

Step-by-step explanation:

hope this helps u ✌️✌️

Make mister as brainliest

Answer: 5

Step-by-step explanation:

2 pizzas ten slices eatch, so 20 slices. 20 slices devided by 4 is five. :)

Lets find f(n) formula

[tex]\boxed{\sf f(n)=\dfrac{1680}{n}}[/tex]

Now

[tex]\\ \sf\longmapsto f(10)=\dfrac{1680}{10}=168[/tex]

[tex]\\ \sf\longmapsto f(12)=\dfrac{1680}{12}=140[/tex]

[tex]\\ \sf\longmapsto f(16)=\dfrac{1680}{16}=105[/tex]

[tex]\\ \sf\longmapsto f(14)=\dfrac{1680}{14}=120[/tex]

Answer:

-31+(-42)= -31-42 = -73

38+(-43)= 38-43 = -5

(-) - (-) = +

(-)+(-) = +

(-)+(+) = -

Answers:

The value of x is exact. The y value is approximate.

==================================================

Explanation:

Let's subtract the equations straight down.

After doing those three sets of subtractions, we have the new equation -22x = 0. This solves to x = 0 after dividing both sides by -22.

Plug this x value into any of the two original equations to solve for y

9x + 7y = 48

9(0) + 7y = 48

7y = 48

y = 48/7

y = 6.857 approximately

y = 6.9

Answer:

256

Step-by-step explanation:

1,4,16,64,256

As 4 is being multiplied in each case.

Answer:

Step-by-step explanation:

187 divided by 7 is 6.5

Answer: 29

Step-by-step explanation:

174 = dividend

6 = divisor

The divisor (6) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top Multiply the divisor by the result in the previous step (6 x 0 = 0) and write that answer below the dividend. Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.

Move down the 2nd digit of the dividend (7) like this:

0

6 ⟌ 1 7 4

- 0

1 7

Multiply the divisor by the result in the previous step (6 x 2 = 12) and write that answer at the bottom:

0 2

6 ⟌ 1 7 4

- 0

1 7

1 2

Subtract the result in the previous step from the number written above it. (17 - 12 = 5) and write the answer at the bottom.

0 2

6 ⟌ 1 7 4

- 0

1 7

- 1 2

5

Move down the last digit of the dividend (4) like this:

0 2

6 ⟌ 1 7 4

- 0

1 7

- 1 2

5 4

Multiply the divisor by the result in the previous step (6 x 9 = 54) and write the answer at the bottom:

0 2 9

6 ⟌ 1 7 4

- 0

1 7

- 1 2

5 4

5 4

Subtract the result in the previous step from the number written above it. (54 - 54 = 0) and write the answer at the bottom.

0 2 9

6 ⟌ 1 7 4

- 0

1 7

- 1 2

5 4

- 5 4

0

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 174 divided by 6 calculated using Long Division is:

29

0 Remainder

Its long but your welcome :)

Answer:

9.3

Step-by-step explanation:

Answer:

6+[25=(-0.9)]

6+[-22.5]

-16.5

Step-by-step explanation:

the answe of this question will be -16.5

(a) Concerning the coefficients of the equation for the volume of the eggplant ( [tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex]), the units of the coefficients with values [tex]3.53 \times 10^{-2}[/tex] and 2 are cubic feet and [tex]\frac{1}{h^{2}}[/tex], respectively.

(b) Regarding the determination of the coefficients by linear regression, the scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.

(c) After the solicitation of the European distributor of the film, the new formula is [tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex], where volume is in cubic meters and time is in seconds.

Note - The statement reports typing mistakes. We present the correct statement below:

The climatic moment in the film "The Eggplant that Ate New Jersey" comes when the brilliant young scientist announces his discovery of the equation for the volume of the eggplant: [tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex], where [tex]t[/tex] is the time in hours from the moment the vampire injected the eggplant with a solution prepared from the blood of the beautiful dental hygienist.

(a) What are the units of [tex]3.53\times 10^{-2}[/tex] and [tex]2[/tex]?

(b) The scientist obtained the formula by measuring [tex]V[/tex] and [tex]t[/tex] and determining the coefficients by linear regression. What would he have plotted versus what on what kind of coordinates? What would he have obtained as the slope and intercept of his plot?

(c) The European distributor of the film insists that the formula must be given for the volume in cubic meters ([tex]m^{3}[/tex]) as a function of time, in seconds. Derive the formula.

(a) In this exercise, we must make use of principles for dimensional analysis. We know that the equation for the volume of the eggplant is represented by:

[tex]V(ft^{3}) = 3.53\times 10^{-2}\cdot e^{2\cdot t^{2}}[/tex] (1)

Dimensionally speaking, we have the following case:

[tex][L]^{3} = [A]\cdot e^{[B]\cdot [t]^{2}}[/tex] (2)

By direct inspection and some algebraic handling, we conclude that:

[tex][A] = [L]^{3}[/tex]

[tex][B] = [t]^{-2}[/tex]

Therefore, the units of [tex]3.53 \times 10^{-2}[/tex] and 2 are cubic feet and [tex]\frac{1}{h^{2}}[/tex], respectively.

(b) The curve fit for the exponential expression used by the scientist is of the form:

[tex]V = A\cdot e^{B\cdot t^{2}}[/tex] (3)

If we apply logarithms on both sides of the expression above, then we have the following form:

[tex]\ln V = \ln A\cdot e^{B\cdot t^{2}}[/tex]

[tex]\ln V = \ln A + B\cdot t^{2}[/tex] (4)

The scientist must plot the square of time versus the natural logarithm of the volume and he would have obtained that the intercept is the natural logarithm of constant A and the slope is constant B.

(c) An hour equals 3600 seconds and a cubic feet equals 0.028 cubic meters. Hence, we can adapt (1) to fulfill the requirements of the European film distributor by using the following conversions:

[tex]t' = 3600\cdot t[/tex] (5)

[tex]V' = 0.028\cdot V[/tex] (6)

Where:

By applying (5) and (6) in (1), we have the resulting formula:

[tex]V' = 0.028\cdot [3.53\times 10^{-2}\cdot e^{2\cdot \left(\frac{t'}{3600} \right)^{2}}][/tex]

[tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex]

The new formula is [tex]V' = 9.884\times 10^{-4}\cdot e^{1.543\times 10^{-7}\cdot t'^{2}}[/tex], where volume is in cubic meters and time is in seconds.

We kindly invite to check this question on exponential functions: https://brainly.com/question/2456547

After a small online search, I've found that the volume equation is:

[tex]V[ft^3] = 3.53 \cdot10^{-2} \cdot exp(2 \cdot t^2)[/tex]

a) We want to see what are the units of the first factor:

[tex]3.53 \cdot10^{-2}[/tex]

You can see that the volume is in cube feet, and the only part in the equation that can have units is this one, so the units of this factor should be cube feet.

b) On the vertical coordinate he would see the volume and on the horizontal coordinate he would see the time.

The graph of this function is an increasing exponential function, that grows slow at the beginning and then grows faster.

c) Remember that the term with the units is:

[tex]3.53 \cdot10^{-2}[/tex]

So we should write this as:

[tex]3.53 \cdot10^{-2} ft^3[/tex]

Now we know that:

[tex]1m^3 = 35.3 ft^3\\\\1 = \frac{1 m^3}{35.3 ft^3}[/tex]

Now we can multiply our measure by this to get:

[tex]3.53 \cdot10^{-2} ft^3 = ( \frac{1 m^3}{35.3 ft^3})*(3.53 \cdot10^{-2} ft^3) = 0.1 m^3[/tex]

Then the equation is:

[tex]V = 0.1m^3\cdot exp(2 \cdot t^2)[/tex]

If you want to learn more you can read:

https://brainly.com/question/172096

Answer:

$70.399.62

Step-by-step explanation:

To find the final amount, we have to use the compound interest formula

A = P(1 + r/n)ⁿˣ

A = Final amount

P = Starting amount (65,000)

r = rate (0.02)

n = time applied (4 since it's quarterly, meaning 4 times every year)

x = years (4)

Our equation will look like this

A = 65,000(1 + 0.02/4)¹⁶

You should use a calculator to plug to solve 65,000(1 + 0.02/4)¹⁶

A = 70,399.62483294155

Answer:

82.6

Step-by-step explanation:

First you add 53 and 29 which equals 82 then you do 4 plus 2 which equals 6 and so the answer is 82.6

Answer:

2x3xX you solve this with 1 linear 2 nonlinear 3 nonlinear 4linear 5linear 6 nonlinear

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

multiply each number by 40

ex:

.10x40=40

Answer:d

Step-by-step explanation:

Answer: 10n^2 - 10

Step-by-step explanation:

(5n - 5)(2+2n) becomes (5n-5)(2n+2)

= (5n)(2n) + (5n)(2) + (-5)(2n) + (-5)(2)

= 10n^2 - 10

Answer:

(4, 14) is on the given line

Step-by-step explanation:

We can use the points given in the answer choices to see if the point is on the line. If both sides are equal, then it is.

Option 1:

16 = 4(4) - 2

16 = 16 - 2

16 = 14

FALSE

Option 2:

13 = 4(4) - 2

13 = 16 - 2

13 = 14

FALSE

Option 3:

14 = 4(4) - 2

14 = 16 - 2

14 = 14

TRUE

Option 4:

10 = 4(4) - 2

10 = 16 - 2

10 = 14

FALSE

Best of Luck!

Answer:

above the sea level means height than the sea and below sea level means lower than sea height

[tex]\begin{array}{l}\begin{cases} \begin{array}{l}\sin \alpha =\frac{x}{12} \Leftrightarrow x=12\sin \alpha \end{array}\\\cos \alpha =\frac{y}{12} \Leftrightarrow y=12\cos \alpha \end{cases}\\\\\text{Thus,\ the\ area\ is}\\\\A=\frac{xy}{2} =\frac{12\sin \alpha \cdotp 12\cos \alpha }{2}\\\\\Longrightarrow A=72\sin \alpha \cos \alpha \end{array}[/tex]

D

a) The x-coordinates of the points A and B are [tex]x_{A} = 11[/tex] and [tex]x_{B} = -7[/tex].

b) The point of intersection of the tangents to the circle at A and B is [tex](x,y) = (2, 27)[/tex].

a) In this part we simplify the equation of the circle and solve for [tex]x[/tex] to determine the coordinates associated to the required points:

The coordinates of the two points so that circle intersects the x-axis, occurs when the following condition is met:

[tex]f(x, 0) = 0[/tex] (1)

Where [tex]f(x,y)[/tex] is in implicit form.

If we know that the equation of the circle is [tex]x^{2} + y^{2} - 4\cdot x + 6\cdot y - 77 = 0[/tex] and [tex]y = 0[/tex], then the reduced equation is:

[tex]x^{2} - 4\cdot x - 77 = 0[/tex] (2)

And we obtain the x-coordinates of the points by factoring (2):

[tex](x-11) \cdot (x + 7) = 0[/tex]

The x-coordinates of the points A and B are [tex]x_{A} = 11[/tex] and [tex]x_{B} = -7[/tex].

b) Lines are defined by both slope and intercept. Slope is defined by implicit differentiation and intercept is found by equation of the line.

Given that [tex]A(x,y) = (11, 0)[/tex] and [tex]B(x,y) = (-7, 0)[/tex], we determine line equations corresponding to each tangent line:

Slope

[tex]2\cdot x + 2\cdot y \cdot \dot y - 4 + 6\cdot \dot y = 0[/tex]

[tex](2\cdot y + 6)\cdot \dot y = 4 - 2\cdot x[/tex]

[tex]\dot y = \frac{2 - x}{y + 3}[/tex]

Point A

[tex]\dot y = \frac{2-11}{0 + 3}[/tex]

[tex]\dot y = -3[/tex]

Point B

[tex]\dot y = \frac{2-(-7)}{0 + 3}[/tex]

[tex]\dot y = 3[/tex]

Intercept

Point A ([tex]A(x,y) = (11, 0)[/tex], [tex]\dot y = -3[/tex])

[tex]b = y - m\cdot x[/tex]

[tex]b = 0 - (-3)\cdot (11)[/tex]

[tex]b = 33[/tex]

Point B ([tex]B(x,y) = (-7, 0)[/tex], [tex]\dot y = 3[/tex])

[tex]b = y - m\cdot x[/tex]

[tex]b = 0 - 3\cdot (-7)[/tex]

[tex]b = 21[/tex]

The equations of the lines tangent to the circle are:

[tex]y = -3\cdot x +33[/tex] (3)

[tex]y = 3\cdot x +21[/tex] (4)

The point of intersection is the solution of this system of linear equations:

[tex](x,y) = (2, 27)[/tex]

The point of intersection of the tangents to the circle at A and B is [tex](x,y) = (2, 27)[/tex].

We kindly invite you to see this question on circles: https://brainly.com/question/23988015

Work Shown:

L = d+9 = length along the horizontal

W = 10 feet = width along the vertical

P = 2(L+W) = perimeter of rectangle = 70 feet

70 = 2(d+9+10)

70/2 = d+19

35 = d+19

d+19 = 35

d = 35-19

d = 16

The deep end is 16 feet wide

Answer:

G) tan 60 = opp / adj = 30 / x

which equals

1.7321 = 30 / x

x = 30 / 1.7321

x = 17.3200161653

H)  secant = hyp / adj

secant 30 = 16 / x

1.1547 = 16 / x

x = 16 / 1.1547

x = 13.8564

Here's a good site for trig functions :  http://www.1728.org/trigcalc.htm

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

A. 6÷0.2=30

B. 0.6÷0.2=3

C. 60÷2=30

D. 600÷2=300

Answer:

Area =

[tex]\pi {r}^{2} [/tex]

=3.14×1.5^2

=3.14×2.25

=7.065

Hence the area of circle is 7.065.

Answer:

The equation would be 5-3x=7

Step-by-step explanation:

5 less than indicates subtraction, and 3 times a number indicates both values being multiplied with each other, so it's 3x. Hope that helped.