Need help with this problem, doesn't make sense to me.

Answer:

See below ~

Step-by-step explanation:

Problem 9

Problem 10

Answer: h'(1)=6/5

-1.5

Step-by-step explanation:

Answer:

9,9

Step-by-step explanation:

0 - -9 = 9

9 is the first number

10 - 1 = 9 (subtracting the biggest number by the lowest number tells the difference between two numbers.)

9 is also the second number.

Answer:

[tex]\displaystyle \lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} = \boxed{ \frac{34}{23} }[/tex]

General Formulas and Concepts:
Calculus

Limits

Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Property [Multiplied Constant]:
[tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]

Limit Property [Multiplication]:
[tex]\displaystyle \lim_{x \to c} f(x)g(x) = \lim_{x \to c} f(x) \lim_{x \to c} g(x)[/tex]

Step-by-step explanation:

*Note:

The problem is too big to fit all work. I will assume that you know how to do basic algebra and calculus.

Step 1: Define

Identify given limit.

[tex]\displaystyle \lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}}[/tex]

Step 2: Find Limit (Algebriaclly)

Rationalize the function and apply basic limit techniques listed under "Calculus":

[tex]\displaystyle\begin{aligned}\lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = \lim_{x \to 2} - \frac{17(x - 2)}{\big( \sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5} \big) \big( \sqrt{x + 7} + 3 \sqrt{2x - 3} \big)} \\& = -17 \lim_{x \to 2} \frac{1}{\sqrt{x + 7} + 3 \sqrt{2x - 3}} \lim_{x \to 2} \frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}}\end{aligned}[/tex]

[tex]\displaystyle\begin{aligned}\lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = - \frac{17}{6} \lim_{x \to 2} \frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} \\\end{aligned}[/tex]

Let's now focus on just the rationalization of the function within the limit:

[tex]\displaystyle\begin{aligned}\frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = \frac{(x - 2) \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] }{\Big( \sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5} \Big) \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] } \\& = - \frac{1}{23} \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] \\\end{aligned}[/tex]

Substitute in the simplified function and continue:

[tex]\displaystyle\begin{aligned}\lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = - \frac{17}{6} \lim_{x \to 2} \frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} \\& = \frac{17}{138} \lim_{x \to 2} \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] \\& = \frac{17}{138} (12) \\& = \boxed{ \frac{34}{23} } \\\end{aligned}[/tex]

∴ we have evaluated the following limit without L' Hopital's Rule.

Step 3: Geometrical Interpretation

We can also graph the given function and approximate the limit. Please refer to the attachment for visualization.

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Learn more about limits: https://brainly.com/question/27593180

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

Unit: Limits

Answer:

  34/23

Step-by-step explanation:

The limit can be evaluated by simplifying the expression in such a way as to cancel the offending zeros.

__

Define the following (to help keep the algebra cleaner):

  [tex]a=\sqrt{x+7},\ b=3\sqrt{2x-3}\\\\c=\sqrt[3]{x+6}.\ d=2\sqrt[3]{3x-5}[/tex]

Then the desired limit is ...

  [tex]\displaystyle \lim_{x\to 2}\dfrac{a-b}{c-d}[/tex]

We observe that ...

  [tex](a-b)(a+b)=\underline{a^2-b^2}=(x+7)-(3^2(2x-3))=-17x+34=\underline{-17(x-2)}\\\\(c-d)(c^2+cd+d^2)=\underline{c^3-d^3}=(x+6)-(2^3(3x-5))=-23x+46=\underline{-23(x-2)}\\\\\displaystyle\lim_{x\to2}{(a+b)}=3+3=6\\\\\lim_{x\to2}{(c^2+cd+d^2)}=4+4+4=12[/tex]

In the following expression, the factors (x-2) cancel, so, our limit is ...

  [tex]\displaystyle\lim_{x\to2}\dfrac{a-b}{c-d}=\lim_{x\to2}\dfrac{(a^2-b^2)(c^2+cd+d^2)}{(c^3-d^3)(a+b)}=\lim_{x\to2}\dfrac{-17(x-2)(12)}{-23(x-2)(6)}=\boxed{\dfrac{34}{23}}[/tex]

walking tour is $15

boat tour is $18

[tex]\huge\underline\mathsf \colorbox{cyan}{-1/2}[/tex]

Step-by-step explanation:

To find the value of f(3) we need to follow the below steps :

Step 1 : First plot the graph of f(x)

Step 2 : We need to find f(3) or the function value at x = 3 therefore, in the graph locate the point (3,0)

Step 3 : Draw a line parallel to Y-axis passing through the point (3,0) .

Step 4 : Now there exists two cases :

If the drawn line do not intersect the graph of f(x), then no value of f(3) exists for the given function of x

If the drawn line intersects the graph, then the intersection point is marked and a line parallel to x - axis is drawn passing through that marked or intersection point. And the line where it intersects the y - axis is our required value of f(3).

If this is wrong than I guess I wasn't smart enough :)

Answer:

12 times

Step-by-step explanation:

first, find out how much she makes weekly.

40 (hours per week she works * 30 ($ she will earn per hour)

40 * 30 = 1200 per week

for 52 weeks so multiply that by her weekly pay

multiply her weekly pay (1200) by the weeks she works annually (52)

52 * 1200 = 62,400

she makes just $62,400 (annually, before taxes) with her new employer

subtract how much more money she needs

62,400 - 63,300 = -900

she needs 900 dollars

divide by the money she makes on weekends (for dog sitting)

900/75 = 12

she will need to dog sit at least 12 times to make approx. $63,300 annually, before taxes.

hope this helps:)

-2.15

-2.154 should be your answer!! have a blessed day x

Answer:

1.36 centimeters

Step-by-step explanation:

Given,

side length ( a ) = 17 mm

To find : Perimeter of regular octagon ( in cm )

Octagon has 8 sides.

Perimeter of regular octagon

= 8 x a

= 8 x 17

= 136 mm

1 mm = 0.1 cm

136 mm

= 136 x 0.1

= 1.36 centimeters ( cm )

Hence,

Perimeter of regular octagon is 1.36 centimeters.

Answer:

13.6 cm

Step-by-step explanation:

17 mm = 1.7 cm

Perimeter of octagon

= 8 x 1.7 cm

= 13.6 cm

Answer:

Choice A

Step-by-step explanation:

<4 and <5 are alternate interior angles.

Answer:

angle 3 and 6

Step-by-step explanation:

They are on the other sides of eachother and are both in the interior.

Answer:

Aida did not correctly divide by the common factor to get (4 + 8).

Answer:

B). Aida did not correctly divide by the common factor to get (4 + 8).

Step-by-step explanation:

Aida applied the distributive property to write the equivalent expressions given as

15 + 21 = 3(4 + 8)

But Aida made a mistake.

Since to get the common factor of 15 and 21 she did not divide these numbers by 3 correctly.

In simple words by division of 3 in 15 and 21, we get 5 and 7 instead of 5 and 8.

Therefore, Aida did not correctly divide by the common factor to get (4 + 8). ⇒ option B is the correct answer.

He had bank fees $15 that were not in his check register.

The correct option is (B)

Balancing statement is a final statement of your income tax liability for a tax year. It is issued by Revenue when your income tax liability has been reviewed and it shows: your total income from all sources. tax reliefs and credits claimed. amounts of income tax

Balance in check register be,

=Initial Balance - ( Expense on Food Market + Frank's auto parts + Barber shop ) + Deposit

Initial Balance = 900

Expense on Food Market= 67.25

Frank's auto parts =36.80

Barber shop =15

Deposit =650.45

So,

Balance = 900 - (67.25 + 36.80 + 15) + 650.45

              = 1550.45-119.05

             = $1431.40

Balance on Account statement be,

=  Opening balance - ( checks amount on different dates ) + deposit - fees

= 900 - (67.25 + 36.80 + 15) + 650.45  - 15

= 1550.45-134.05

= $1416.40

As, the balances in bank statement and in checking register are not matched. This is because the fees $15 paid on 9/30 is not calculated by Jerry in his check register

thus,

= $1431.40 - $15.00 (Fees)

= $1416.40

Now the balance on account and checking statements matched.

So, he had bank fees were not in Check Register.

Learn more about balancing statements here:

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Answer:

Option B {1,3,4,5}

Step-by-step explanation:

The domain of the function is nothing but the input of the given function

Therefore the domain of given function is

{1,3,4,5} Option B

Answer:

45 cubic units

Step-by-step explanation:

Vtotal = 1/2 (2.5*3) * 6 *2

where

2.5 is the base

3 is the height

6 is the length

2 is the number of prisms

Answer:

The correct answer is 90 cubic units which is Option A.

Hope this helps you!!

Please Mark me Brainleast friend!!

Answer:

2nd option

Step-by-step explanation:

the volume (V) of the prism is calculated as

V = Ah ( A is the area of the triangular face and h is its height )

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 30, h = 8 , then

A = [tex]\frac{1}{2}[/tex] × 30 × 8 = 15 × 8 = 120 in²

with h = 15 , then

V = 120 × 15 = 1800 in³

Answer:

  A = 90°

  B = 37°

  C = 53°

Step-by-step explanation:

Given three sides of a triangle, the Law of Cosines can be used to find the angles.

__

For angle A (the largest), we can use ...

  a² = b² +c² -2bc·cos(A)

Solving for A, we get ...

  A = arccos((b² +c² -a²)/(2bc)) = arccos((3² +4² -5²)/(2·3·4)) = arccos(0)

  A = 90°

We can use a similar equation for angle B:

  B = arccos((a² +c² -b²)/(2ac)) = arccos((25 +16 -9)/(2·5.4)) = arccos(4/5)

  B ≈ 37°

The sum of angles is 180°, so ...

  C = 180° -90° -37°

  C = 53°

Answer: y = 5x-3

Step-by-step explanation: Using y = mx+b, where m is the slope, and b is the y intercept, you just plug in 5 and -3.

Answer:

8y

Step-by-step explanation:

Answer: I think its D

Step-by-step explanation:

Answer:

Maximum value = 7, minimum value = 8

Step-by-step explanation:

Your answer is right !

As no table mentioned it can't be told which city accurately but you can find it by below precedence.

Find the city having temperature 10°F , that's the answer

Answer:

a

Step-by-step explanation:

We will solve these through graphical way .

Find some coordinates

And

Find some coordinates

Graph both

The intersection points are

Answer:

4.

Step-by-step explanation:

1) the rule:

h:2=8:h;

2) according to the rule:

h²=16; ⇒ h=4.

Answer:

28

Step-by-step explanation:

Since n = 3, you would times n (3) 4 times then add that to 3, then divide that by three, and there's your answer!

One Opposite side pair of a trapezoid has equal length

A is true

<J is supplement to <K

JK and LM are not paralle

<J is congruent to <M may be true

May not be

Answer:

A.  [tex]\sf \overline{KL}[/tex] is parallel to [tex]\sf \overline{JM}[/tex]

D.  ∠J is supplementary to ∠K

Step-by-step explanation:

Properties of a trapezoid:

Although the sides of the shape do not have any arrows to indicate that any are parallel, we know that a trapezoid has one pair of parallel sides, so:

When two angles sum to 180° they are called supplementary angles.

As the two angles that are on the same leg sum to 180° then:

Answer:

D

Step-by-step explanation:

3(25-(12))=39

3(13)=39

39=39

The correct statement regarding the measurements of the parallelogram is that the base is 9 and the height is 7, so the area is 9 (7) = 63 square units.

This is defined as a quadrilateral which has two pairs of parallel sides present and the area is base × height.

The base is 9 and the height is 7, when the points are plotted which results in the area being 63 square units hence option D was chosen.

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Answer:

No Solution

x = 1/2

x = -5

x = 1

No Solution