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Using a linear approximation, the estimated cube root of 217 is  6.00925.

Given that the number is,

The cube root of 217

Now, for the cube root of 217 using a linear approximation, use differentials.

So, the derivative of the function [tex]f(x) = x^{(1/3)[/tex] at a known point.

Taking the derivative of [tex]f(x) = x^{(1/3)[/tex], we get:

[tex]f'(x) = (\dfrac{1}{3} )x^{-2/3[/tex]

Now, we can choose a point near 217 to evaluate the linear approximation.

Let's use x = 216, which is a perfect cube.

Substituting x = 216 into the derivative, we get:

[tex]f'(216) = (\dfrac{1}{3} )(216)^{-2/3[/tex]

            [tex]= 0.00925[/tex]

Next, use the linear approximation formula:

Δy ≈ f'(a)Δx

Since our known point is a = 216 and we want to estimate the cube root of 217,

since 217 - 216 = 1

Hence, Δx = 1

Δy ≈ f'(216)

Δx ≈ 0.00925 × 1

      ≈ 0.00925

Finally, add this linear approximation to the known value at the known point to get our estimate:

Estimated cube root of 217 ;

f(216) + Δy = 6 + 0.00925

                 = 6.00925

Therefore, the estimated cube root of 217 is 6.00925.

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Answer - It’s 31.56

Step-by-step explanation: You just do regular multiplication and then add  the decimal point

Answer:

I don't really understand the question

Step-by-step explanation:

c

Answer:

Following are the response to the given choice.

Step-by-step explanation:

Please find the complete question in the attached file.

Subjective opinion = Question of opinion.

Therefore this requires only just opinion and we don't have to do any actual calculations.

Does this seem like a great number of girls, a little number of girls, or a decent number of girls to you but if 1,300 babies were born, 5 of whom were females?

This is a small number of beautiful gals, in my honest opinion. We anticipate boys and girls to be produced about the very same frequency, thus I expect some half of them to be females if there are 1 300 newborns. You should have roughly 650 girls if 50% of the infants are girls, but now we only have five. That appears to me to be considerably low. which is your own opinion.

Answer: You will never reach a sum of 2. You would need infinitely many terms to sum up.

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

Explanation:

We have this sequence

1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ...

which is geometric with the following properties

Notice how we multiply each term by 1/2 to get the next term. Eg: (1/4)*(1/2) = 1/8 or (1/16)*(1/2) = 1/32.

Since r = 0.5 is between -1 and 1, i.e. -1 < r < 1 is true, this means that adding infinite terms of this form will get us to approach some finite sum which we'll call S. This is because the new terms added on get smaller and smaller.

That infinite sum is

S = a/(1-r)

S = 1/(1-0.5)

S = 1/0.5

S = 2

So if we keep going with that pattern 1+1/2+1/4+... and do so forever, then we'll reach a sum of 2. However, we cannot go on forever since it's asking when we'll reach that specific sum. In other words, your teacher wants finitely many terms to be added.

In short, we'll never actually reach the sum 2 itself. We'll just get closer and closer.

Here's a list of partial sums

We can see that we're getting closer to 2, but we'll never actually get there. We'd need to add infinitely many terms to get to exactly 2.

Answer:

[tex]\displaystyle V = \frac{6561 \pi}{2}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Shell Method:                                                                                                         [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 9

Step 2: Identify

Find other information from graph.

See attachment.

Bounds of Integration: [0, 9]

Step 3: Find Volume

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e

Answer:

A. TRUE

Step-by-step explanation:

To determine if two triangles are congruent, we need to establish the facts that the three angles and three side lengths of one is congruent to corresponding angles and side lengths of the other triangle.

The diagram given only tells us the angle measure of the two triangles which are congruent to each other. The side length wasn't given. Therefore, the triangles may not be congruent.

Answer:

(-5,2)

Step-by-step explanation:

A function is a relation where each y-value has a unique x-value. That means that x's can never repeat. Therefore, to solve find the ordered pair that does not have the same x-value as one of the points on the graph. The x-values currently represented on the graph are -4, -2, 2, 3. So, the only coordinate pair that does not repeat an x-value is the last option, (-5, 2).

Answer:

They can buy up to 240 drinks.

Step-by-step explanation:

Let x = number of drinks

The price of 1 drink is 75¢ = $0.75

The price of x drinks is 0.75x

The store gives a discount of $100.

The rice of x drinks is

0.75x - 100

The total price of the drinks must be less than or equal to $80.

0.75x - 100 ≤ 80

Add 100 to both sides.

0.75x ≤ 180

Divide both sides by 0.75

x ≤ 240

Answer: They can buy up to 240 drinks.

9514 1404 393

Answer:

Step-by-step explanation:

Rewriting the equations to make x the subject, we have ...

  x = y² -1 . . . . . [eq1]

  x = 1 - y . . . . . .[eq2]

At the points of intersection, the difference will be zero.

  y² -1 -(1 -y) = 0

  y² +y -2 = 0

  (y -1)(y +2) = 0

The y-coordinates of points A and B are 1 and -2.

The corresponding x-coordinates are ...

  x = 1 -{1, -2} = {1 -1, 1+2} = {0, 3}

Then A = (0, 1) and B = (3, -2).

__

A differential of area can be written ...

  (x2 -x1)dy = ((1 -y) -(y² -1))dy = (2 -y -y²)dy

Integrating this over the interval y = [-2, 1] gives the area.

  [tex]\displaystyle A=\int_{-2}^1(2-y-y^2)\,dy=\left.(2y-\dfrac{1}{2}y^2-\dfrac{1}{3}y^3)\right|_{-2}^1\\\\=\left(2-\dfrac{1}{2}-\dfrac{1}{3}\right)-\left(2(-2)-\dfrac{(-2)^2}{2}-\dfrac{(-2)^3}{3}\right)=\dfrac{7}{6}+4+2-\dfrac{8}{3}\\\\=\boxed{4.5}[/tex]

The area of the shaded region is 4.5 square units.

Answer:

RM 1200 kalau ada gambar cuba insert

Answer:

42%

Step-by-step explanation:

to find percentages, you move the decimal point twice to the right

Answer:

69.6

Step-by-step explanation:

sin 55 = x / 85

0.8191520443 = x / 85

x = 69.6

Answer:

1/2 or 50-50

Step-by-step explanation:

1/4 +1/4 = 1/2 or 50-50

Answer:

[tex]z + 4 = 15 \\ z + 4 - 4 = 15 \\ z = 15 - 4 \\ z = 11[/tex]

z>11

Answer:

24% or 0.24

Step-by-step explanation:

100% or 1 minus 76% or 0.76. That makes 24% or 0.24.

To answer the question you should prob just put in 0.24.

Answer:

The program in Java is as follows:

import java.util.*;

public class PyTheorem{

   public static void main(String [] args){

       Random rNum = new Random();

       int a = rNum.nextInt(17) + 5;

       int b = rNum.nextInt(17) + 5;

       System.out.println("a: "+a);

       System.out.println("b: "+b);

       double hyp = Math.sqrt(Math.pow(a,2)+Math.pow(b,2));

       System.out.print("Hypotenuse: "+hyp);

   }}

Step-by-step explanation:

This generates random number for a

       int a = rNum.nextInt(17) + 5;

This generates random number for b

       int b = rNum.nextInt(17) + 5;

Print a

       System.out.println("a: "+a);

Print b

       System.out.println("b: "+b);

Calculate the hypotenuse

       double hyp = Math.sqrt(Math.pow(a,2)+Math.pow(b,2));

Print the calculated hypotenuse

       System.out.print("Hypotenuse: "+hyp);

Answer:

-00

OKAY

OKAY

OK

OK

DGSOTSITS6EUEYEYTITUTUTIT

Answer:

[tex]{19}C_1=19[/tex]

Step-by-step explanation:

We need to find the value of [tex]{19}C_1[/tex].

C stands for combination.

The formula of combination is as follows :

[tex]nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Here,

n = 19 and r = 1

So,

[tex]nC_r=\dfrac{19!}{1!(19-1)!}\\\\nC_r=\dfrac{19!}{1!\times 18!}\\\\nC_r=\dfrac{19\times 18!}{1!\times 18!}\\\\nC_r=19[/tex]

So, the value of [tex]{19}C_1[/tex] is 19.

Answer:

Your answer will be 19C1 =19

Answer:

60 marbles in total

Step-by-step explanation:

Find how many marbles there are in total by dividing 42 by 0.7:

42/0.7

= 60

So, there are 60 marbles in total

Answer:

Grey's Anatomy

Step-by-step explanation:

Answer:

[tex]A=603.18\ cm^2[/tex]

Step-by-step explanation:

The length of a blade, r = 24 cm

The sweeping angle is 120°.

We need to find the total area cleaned at one sweep of the blade. The area of sector is given by :

[tex]A=\dfrac{\theta}{360}\times \pi r^2[/tex]

[tex]A=\dfrac{120}{360}\times \pi \times 24^2\\\\=603.18\ cm^2[/tex]

So, the total area cleaned at one sweep of the blade is [tex]603.18\ cm^2[/tex].

The probability of winning at least one prize is 0.40951.

Probability is the likelihood that an event will occur.

The following information can be deduced:

P = probability of winning = 1/10

q = probability of not winning = 1- (1/10) = 9/10

x = no. of winning

then, p (x ≥ 1) = 1 - p (x < 1)

= 1 - p (x=0)

= 1 - ⁵C₀ (1/10)^⁰ (9/10)^(5-0)

= 1 - (1) (1) (9/10)^5

=  1 - (9/10)^5

= 1 - 0.59049

= 0.40951

Therefore, the probability is 0.40951.

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Answer:

D is the correct answer.

Step-by-step explanation:

You can get every y value by multiplying the x value by 3/2. This value never changes and there are no extra limitations.

Answer:

Step-by-step explanation:

we are given  the angles ∠5 , ∠4 , ∠3 , but with one variable,  "X"  :)

also we are told ∠AOC is bisected by OB , meaning that ∠1 = ∠2

and the EC is perpendicular to OD ,  so ∠4+∠5=90°

since we are given ∠4 & ∠5,  lets use that to solve for "X"

:)

90= x-6 + 2x+4

90= 3x -2

92 =3x

30[tex]\frac{2}{3}[/tex] ° = x

30.6666666666666666 ° = x

Answer:

y=0

Step-by-step explanation:

1. Make variable y as subject for the first equation, which is y= -2x +10

2. substitute the first eq to the second one

3. x - (-2x+10) -5=0

4. solve x, which x = 5

5. substitute in eq 1 which is y= -2x +10

6. solve the eq, the possible solution is y=0

Answer:

∠L = 25°

Step-by-step explanation:

Two sides are equal. so , it is an isosceles triangle.

Angles opposite to equal sides are equal.

∠L =  25

Incurring a budget surplus and allowing that surplus to accumulate as idle Treasury balances. Then the correct option is B.

A span of transitory negative growth marked by a drop in Income in four quarters.

The negative effects of a recession would be reduced by the fiscal policy decision will be

Incurring a budget surplus and allowing that surplus to accumulate as idle Treasury balances

Then the correct option is B.

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Answer:

The probability that you get an even card or a spade is P = 0.596

Step-by-step explanation:

In a deck of 52 cards, all the cards have the exact same probability of being drawn.

So, the probability of drawing an even card of a spade, will be equal to the quotient between the number of even cards and spades, and the total number of cards (52).

First, let's found the number of even cards and spades.

There are 13 spades.

For each set, the even cards are:

{2. 4, 6, 8, 10}

(not counting the queen as a "12")

Then for each set, there are 6 even cards.

(there are four sets but we already counted the 6 even cards from the spade set, so we ignore that set)

Then there are 3 sets with 6 even cards each, there are:

3*6 = 18 even cards

So we have:

13 spades + 18 even cards = 31 cards that meet the condition.

The probability is then:

P = 31/52 = 0.596

The probability that you get an even card or a spade is P = 0.596

(C)

Step-by-step explanation:

The sum of angles a and b is 180°, which make the two supplementary angles.