Bruno leaves Ms. Crabbe's office to return to the gym. As he moves 450 meters in 2 minutes, what is his velocity? Be sure to write out your units of measurements for distance, time,

Answer:

[tex]\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)}=1[/tex]

Step-by-step explanation:

We are given:

[tex]\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)[/tex]

And we want to evaluate it using L'Hopital's Rule.

First, using direct substitution, we will acquire:

[tex]=(1-1)^\ln(1)}=0^0[/tex]

Which is indeterminate.

In order to apply L'Hopital's Rule, we first need to manipulate the expression. We will let:

[tex]y=(x-1)^\ln(x)[/tex]

By taking the natural log of both sides:

[tex]\ln(y)=\ln(x)\ln(x-1)[/tex]

And by taking the limit as x approaches 1 from the right of both functions:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)=\lim_{x\to 1^+}\ln(x)\ln(x-1)[/tex]

Rewrite:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{\ln(x-1)}{\ln(x)^{-1}}[/tex]

Using direct substitution on the right will result in 0/0. Hence, we can now apply L'Hopital's Rule:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{1/(x-1)}{-\ln(x)^{-2}(1/x)}[/tex]

Simplify:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{1/(x-1)}{-\ln(x)^{-2}(1/x)}\Big(\frac{-x\ln(x)^2}{-x\ln(x)^2}\Big)[/tex]

Simplify:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}-\frac{x\ln(x)^2}{x-1}[/tex]

Now, by using direct substitution, we will acquire:

[tex]\displaystyle \Rightarrow -\frac{1\ln(1)^2}{1-1}=\frac{0}{0}[/tex]

Hence, we will apply L'Hopital's Rule once more. Utilize the product rule:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}-(\ln(x)^2+2x\ln(x))[/tex]

Finally, direct substitution yields:

[tex]\Rightarrow -(\ln(1)^2+2(1)\ln(1))=-(0+0)=0[/tex]

Thus:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)=0[/tex]

By the Composite Function Property for limits:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)=\ln( \lim_{x\to 1^+}y)=0[/tex]

Raising both sides to e produces:

[tex]\displaystyle e^{\ln \lim_{x\to 1^+}y}=e^0[/tex]

Therefore:

[tex]\displaystyle \lim_{x\to 1^+}y=1[/tex]

Substitution:

[tex]\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)}=1[/tex]

Answer:

[tex]x > \frac{1}{4} [/tex]

Step-by-step explanation:

[tex]12x - 5 > - 2[/tex]

Lets add +5 in both the sides.

[tex] = > 12x - 5 + 5 > - 2 + 5[/tex]

[tex] = > 12x > 3[/tex]

Now lets divide 12 on both the sides.

[tex] = > \frac{12x}{12} > \frac{3}{12} [/tex]

[tex] = > x > \frac{1}{4} [/tex]

Answer:

The dimensions are:

Length = 5m and Width = 4m

Or

Length = 4m and Width = 5m

Step-by-step explanation:

A rectangular dining room has an area of 20 square meters. It's perimeter is 18 meters. What are the dimensions of the dining room?

Area of a rectangle = Length × Width

= LW = 20 m²

Perimeter of a rectangle =

2L + 2W = 18 m

Hence:

LW = 20...... Equation 1

L = 20/W

2L + 2W = 18 ...... Equation 2

We substitute

20/W for L in Equation 2

2(20/W) + 2W = 18

40/W + 2W = 18

Multiply through by W

40 + 2W² = 18W

2W² - 18W + 40 = 0

2W² - 10W - 8W + 40 = 0

(2W - 8 )(W - 5) = 0

2W - 8 = 0

2W = 8 , W = 8/2 = 4m

W - 5 = 0

W = 5m

W = 4m or 5 m

Solving for L

When W = 5 m

L = 20/W

L = 20/5

L = 4m

When W = 4m

L = 20/W

L = 20/4

L = 5m

Therefore, the dimensions are:

Length = 5m and Width = 4m

Or

Length = 4m and Width = 5m

Answer:

a=4

Step-by-step explanation:

8=3a-4

12=3a

a=4

uh i did this wrong so uh just ignore what i said

Answer:

82°

Step-by-step explanation:

Angle C and B equal the measure of angle A so,

143 - 61 = 82

Angle B is 82°

Hey there!

Step By Step:

Well so we know that 12 is about half of an 25. So what we are gonna do is to buy 3 of 12$ and 2 of 25$.

3x12=36 and 2x25=50.

With adding those two last numbers, you’ll get $86.

Graph would be down below.

Hope it helps :D

The fractional form is 7/10.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

We have to divide 7 by 10.

The common factor for 7 and 10

7 = 7 x 1

and, 10= 2 x 5 x 1

so, there is only one factor common is 1.

Thus, the fraction is 7/10.

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Answer:

3√3−x=3√2x

Graph each side of the equation. The solution is the x-value of the point of intersection.

x≈0.46567646

image of graph

Step-by-step explanation:

Hope it is helpful.....

Answer:

x=7

Step-by-step explanation:

∠STP=∠SWT+∠TSW(exterrior ∠ of Δ)

15x=7x+1+7x+6

x=7

Answer:

13

Step-by-step explanation:

Given data

flat amount =$10

let the number of dogs walked be x

and let the money earned be y

y= 10+5x

for y= 75

let us find x

75= 10+5x

75-10= 5x

65= 5x

divide both sides by 5

x= 65/5

x=13

Hence the number of dogs is 13

Answer:

he added the dimensions of the rectangle. He used the wrong formula. the formula he used was length + breadth. He should have multiplied by 2

6x + 8y +8

Step-by-step explanation:

Perimeter of a rectangle = 2 x (L + B)

L = length

b = breadth

2 (3x + 4y + 4. ) = 6x + 8y +8

Answer:

eight hundred seventy-five thousand six hundred eighty-seven

hope this helps :)

Answer:

Explanation:

(-6 + 3i) + (6 + 4i)

-6 + 6 = 0

3i + 4i = 7i

Answer:

t=0.08

Step-by-step explanation:

see attached kindly

Answer:

la eneria es muy importante

Answer:

A. {–8, –2, 18}

Step-by-step explanation:

y = 5x − 2

x = −1.2 ----> y = 5(−1.2) − 2 = −6 − 2 = −8

x = 0 -----> y = 5(0) − 2 = 0 − 2 = −2

x = 4 -----> y = 5(4) − 2 = 20 − 2 = 18

Answer:

you add 40+45

Step-by-step explanation:

40+45=85

then you subtract 180 - 85 = 95

then divide x into 95 that will give you x=95

Answer:ugh is there an picture maybe i can understand it better?

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

Answer:

12 because u use the other shapes to reference your measurements.

Answer:

d 5 tan theta

Step-by-step explanation:

5 sin theta x 1/cos theta

5 (sin theta/cos theta)

5 tan theta

Answer:

Output equals imput minus 6

Step-by-step explanation:

First, we know that -2 is 1 of the Imputs.

Then we know 8 is the second Output

8 - (-2) so that means it would be minus 6 Imput.

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Output equals input times 4 is the function rule from the values in the table.

Looking at the values in the table, we can identify the function rule by analyzing the relationship between the input and output values.

The output values are obtained by applying specific operations to the input values.

Let's examine each statement and see which one matches the given input-output pairs:

Output equals input times -4:

When we multiply the input values by -4, we get the following output values:

[tex]-2 \times -4 = 8[/tex]

[tex]0 \times -4 = 0[/tex]

[tex]1 \times -4 = -4[/tex]

[tex]3 \times -4 = -12[/tex]

This function rule matches the given input-output pairs.

Therefore, the function rule that matches the values in the table is "Output equals input times -4."

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Answer:

x = 3

Step-by-step explanation:

Answer: x = 3

Step-by-step explanation:

Answer:

can you show us the graph

Answer:

i cant help you with this sorry

Step-by-step explanation: