Two trucks leave a warehouse at the same time. One travels north at an average speed of 58miles per hour, and the other travels south at an average speed of 64miles per hour. After how many hours will the two trucks be 488 miles apart?

Answer:

0

Step-by-step explanation:

We are looking for the directional derivative of f at P in the direction of PQ.

First we compute

[tex]\nabla f=\langle yz\cos(xy),zx\cos(xy),\sin(xy)\rangle\\\nabla f(0,0,2) =\langle 0,0,0\rangle[/tex]

But if we dot any vector to the zero vector we always get 0. So the rate of change is zero.

After setting [tex]u=\sqrt{1+e^{2x}}[/tex], partially solving for x in terms of u gives

[tex]u = sqrt{1+e^{2x}} \implies u^2 = 1 + e^{2x} \implies e^{2x} = u^2 - 1[/tex]

Then taking differentials, you get

[tex]2 e^{2x} \,\mathrm dx = 2u \, \mathrm du \implies \mathrm dx = \dfrac{u}{u^2-1}\,\mathrm du[/tex]

Replacing everything in the original integral then gives

[tex]\displaystyle \int \frac9{\sqrt{1+e^{2x}}}\,\mathrm dx = \int \frac9u \times \frac u{u^2-1}\,\mathrm du = 9 \int \frac{\mathrm du}{u^2-1}[/tex]

Split up the integrand into partial fractions:

[tex]\dfrac1{u^2-1} = \dfrac a{u-1} + \dfrac b{u+1} \\\\ 1 = a(u+1) + b(u-1) = (a+b)u + a-b \\\\ \implies \begin{cases}a+b=0\\a-b=1\end{cases} \implies a=\dfrac12,b=-\dfrac12[/tex]

so that

[tex]\displaystyle 9 \int \frac{\mathrm du}{u^2-1} = \frac92 \int \left(\frac1{u-1} - \frac1{u+1}\right) \,\mathrm du \\\\ = \frac92 \left(\ln|u-1| - \ln|u+1|\right) + C \\\\ = \frac92 \ln\left|\frac{u-1}{u+1}\right| + C \\\\ = \frac92 \ln\left(\frac{\sqrt{1+e^{2x}}-1}{\sqrt{1+e^{2x}}+1}\right) + C[/tex]

Answer:

87/54 = m

Step-by-step explanation:

-11/6 + m = -2/9

Here is one way to solve this:

First, we can remove the fractions. We can do this by multiplying both sides by both denominators.

multiply both sides by 6

-11 + 6m = -12/9

multiply both sides by 9

-99 + 54m = -12

add 99 to both sides to isolate the m and its coefficient

-12+99= 54m

87 = 54m

divide both sides by 54 to isolate m

87/54 = m

Answer:

-y+5

Step-by-step explanation:

3/4 (8y +12) = 3y - 15

3(2y+3)=3y-15

2y+3=y-5

-(2y-3)=y-5

2y-3=y-5/-1

2y-3=-y+5

Answer: -19

Step-by-step explanation:

Given equation

(3/4) (8y + 12) = 3y - 15

Divide (3/4) on both sides

(REMEMBER division of fraction can be converted to multiplication by using the reciprocal of the fraction)

(3/4) (8y + 12) ÷ (3/4) = (3y - 15) ÷ (3/4)

(3/4) (8y + 12) × (4/3) = (3y - 15) × (4/3)

8y + 12 = 4y - 20

Subtract 4y on both sides

8y + 12 - 4y = 4y - 20 - 4y

4y + 12 = -20

Subtract 12 on both sides

4y + 12 - 12 = -20 - 12

4y = -32

Divide 4 on both sides

4y / 4 = -32 / 4

y = -8

Evaluate the expression basing on the [y] value

 2y - 3 ⇔ Given expression

=2(-8) - 3 ⇔ Substitute values into the expression

=-16 - 3 ⇔ Simplify by multiplication

=[tex]\boxed{-19}[/tex] ⇔ Simplify by subtraction

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

all steps are in picture

Answer:

3x - 6y - 74

Step-by-step explanation:

Given

3(5x - 2y) + 2(4x - 37) ← distribute parenthesis

= 15x - 6y + 8x - 74 ← collect like terms

= 23x - 6y - 74

Answer:

Distribute

3

(

5

−

2

)

+

2

(

4

−

3

7

)

{\color{#c92786}{3(5x-2y)}}+2(4x-37)

3(5x−2y)+2(4x−37)

1

5

−

6

+

2

(

4

−

3

7

)

{\color{#c92786}{15x-6y}}+2(4x-37)

15x−6y+2(4x−37)

2

Distribute

1

5

−

6

+

2

(

4

−

3

7

)

15x-6y+{\color{#c92786}{2(4x-37)}}

15x−6y+2(4x−37)

1

5

−

6

+

8

−

7

4

15x-6y+{\color{#c92786}{8x-74}}

15x−6y+8x−74

3

Combine like terms

1

5

−

6

+

8

−

7

4

15x−6y+8x−74

2

3

−

6

−

7

423x}}-6y-74

23x−6y−74

Solution

2

3

−

6

−

7

4

Step-by-step explanation:

whats the full question?

Answer:

AB slope= 4/5

CD slope= - 5/4

Step-by-step explanation:

AB: (0,-1) (5,3)

Slope= (3- -1)/(5-0) = 4/5

CD: (2,3) (6,-2)

CD slope= (-2-3)/(6-2) = -5/4

Answer:

answer is -20

BODMAS

So we do addition First, then subtraction so 7+15 = 22

2- 22= -20

Answer:

Part A. [tex]h=\frac{V}{\pi r^2}[/tex]

Part B. h= 4cm

Step-by-step explanation:

Answer:

13.8

Step-by-step explanation:

His dive once he hits the water and goes below the surface water line is in the same direction as his dive off the platform. That's very important when you start to consider direction. So you add. Be sure and read this paragraph again.

Dive = platform + under the surface

Dive = 10 + 3.8

Dive = 13.8

Answer:

7 > 24/4

Step-by-step explanation:

7 _ 24/4

Simplify 24/4

24/4 = 6

7 is greater than 6

7 > 24/4

7 is greater than the fraction 24/4 so we use the ">" symbol between them. Hence, the complete equation is 7 > 24/4.

Comparison of two numbers involves determining the relationship between them. Here are a few possible outcomes when comparing two numbers:

1: If the first number is greater than the second number, we can say that the first number is "greater than" or "larger than" the second number.

2: If the first number is less than the second number, we can say that the first number is "smaller than" or "less than" the second number.

3: If the first number is equal to the second number, we can say that the numbers are "equal" to each other.

The given numbers are:

7 and 24/4

To compare these numbers,

Convert the fraction 24/4 into the simplest form

Therefore,

[tex]\frac{24}{4} = 6[/tex]

Now since 7 is greater than 6 so we use ">" between them.

Hence,

The complete equation will be 7 > 24/4.

To learn more about the fraction visit:

https://brainly.com/question/5454147

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Answer:

Step-by-step explanation:

-13x + 7y - (12x +10y)

= - 13x + 7y - 12x - 10y

= - 13x - 12x + 7y - 10y

= - 25x - 3y (Ans)

Answer:

8%

Step-by-step explanation:

(2376-2200):2200x100%=8%

Answer:

-22

Step-by-step explanation:

-18 + (-4) = -18 - 4 = -22

Answer:

He got $25 in change.

Step-by-step explanation:

Suppose the balance amount is x.

The cost of 3 pants is 3 × 25 = 75

John paid = $ 100

x = 100 – 75

x =  25

Answer:25

Step-by-step explanation:

25×3=75 then you subtract 100-75=25

Answer:

2 one

Step-by-step explanation:

well if u go the other way for it to go right it is mf

Here, we are given that a room is painted by A, B and C so here three of them have done the work. So, we'll add all these fractions and assume the total work as 1 after that we will substract all the added ones from 1

Let us assume the room completely painted be 1

Now,

A has done 1/3, B has done 1/4 and C has done 1/5 work of the remaining

So, let us add them

Getting the L.C.M. The L.C.M of 3,4,5 is 60

Hence, 47/60 room has been painted

Remaining to paint

Total is assumed as 1

Work done = 47/60

Fraction of room needs to painted = 1 - 47/60

13/60 of the room needs to be painted, OPTION C IS CORRECT

Yes, there is. It's 14. Hope this helps.

4,3,2,1,0,-1, -2, -3, -4,

Equation of a line can be given by :

y = mx + b

Let's find the slope of the line (m) :

[tex] \mathcal{ \hookrightarrow \: \dfrac{y_2 - y_1}{x_2 - x_1} }[/tex]

[tex] \mathcal{ \hookrightarrow \: \dfrac{ - 1 - ( - 7)}{0 - 5} }[/tex]

[tex] \hookrightarrow \: \dfrac{6}{ - 5} [/tex]

[tex] \hookrightarrow \: m = \dfrac{ - 6}{5} [/tex]

now let's solve for b :

[tex] \hookrightarrow \: y = mx + b[/tex]

Let's plug the values of x and y from the coordinates of a point .

[tex] \hookrightarrow \: - 7 = (\dfrac{ - 6}{5} \times 5) + b[/tex]

[tex] \hookrightarrow \: - 7 = - 6 + b[/tex]

[tex] \hookrightarrow \: b = - 1[/tex]

now, let's put the value of m (slope) and b (y-intercept) in the equation.

[tex] \hookrightarrow \: y = mx + b[/tex]

[tex] \boxed{ \boxed{\: y = \dfrac{ - 6}{5}x - 1 }}[/tex]

That's All, I hope it helped ya

Answer: - 29/8

Step-by-step explanation:

9 + 8c < - 20

8c < - 20 - 9

8c < - 29

c < - 29/8

Answer:

give this other guy or girl branliest

Step-by-step explanation:

Answer:

1. roughly symmetric

2. skewed to the right

3. greater than

Step-by-step explanation:

correct on edge 2021 :)

1. The distribution of fuel economy for Honda is roughly symmetric vand for Ford is skewed to the right. and 3. Fuel economy for Honda tends to be greater than the fuel economy for Ford.

Shape: The distribution of fuel economy for Honda is roughly symmetric vand for Ford is skewed to the right.

Outliers: There appears to be an outlier of 47 mpg for Honda. There appears to be an outlier of 40 mpg for Ford

Center: Fuel economy for Honda tends to be greater than the fuel economy for Ford.

Variability: Fuel economy for Honda varies about the same as the fuel economy for Ford.

Learn more about Fuel economy here;

https://brainly.com/question/24212851

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Answer:

scale factor = 3 : 11

Step-by-step explanation:

Given 2 similar figures with scale factor a : b , then

ratio of volumes = a³ : b³

Here

ratio of volumes = 27 : 1331 . so

scale factor = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{1331}[/tex] = 3 : 11

Answer:

3:11

Step-by-step explanation:

Answer:

125 p^3 g^3

Step-by-step explanation:

(5pg)^3

We know that (ab)^c = a^c * b^c

5^3 p^3 g^3

125 p^3 g^3

The answer is: 250 adult tickets were sold.

To be safe, prove that your answer is correct.

If there are 74 more student tickets than adult tickets, the amount of adult tickets must obviously be less.

Explanation:

74 more than 250, or 250+74 is 324.

250+324=574.

Now, you know the answer is correct. It satisfies all of the given conditions.

Also, note that the difference between the number of student tickets and adult tickets is 74.

So, there are 250 adult tickets and 324 student tickets.

9514 1404 393

Answer:

  g(f(4)) = 9

Step-by-step explanation:

Put the argument value where the variable is and do the arithmetic.

  g(f(4)) = g(4 -7) = g(-3) = (-3)^2

  g(f(4)) = 9

Answer: 3 1/2

Step-by-step explanation:

"Of" is the same as multiplication so,

2/3 × 21/4=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

2 × 2/13 × 4 = 42/12

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 42 and 12 using

GCF(4/2 , 1/2) = 6

4/2 ÷ 6 1/2 ÷ 6 = 7/2

The fraction

7/2

is the same as

7÷2

Convert to a mixed number using

long division for 7 ÷ 2 = 3R1, so

7/2 = 3 1/2

Therefore:

2/3 of 21/4 = 3 1/2

Hopefully, I Helped

Answer:

the answer is 150

Step-by-step explanation:

you will do cross multiplication where 3 will multiply 50 and 15 will multiply 10. u will get 150=150

Answer:

[tex]f(a) = 3a + 1 \\ Now,\: a = - 1 \\ f( - 1) = 3( - 1) + 1 \\ f( - 1) = - 3 + 1 \\ \boxed{ f( - 1) = - 2}[/tex]