Mel slides down waterslide A, and Victor slides down waterslide B. After 2 seconds, Mel was 50 feet in the air, and after 5 seconds, she was 35 feet in the air. After 1 second, Victor was 60 feet in the air, and after 4 seconds, he was 50 feet in the air. Who was descending at a faster rate?

Mel: (2, 50) and (5, 35)

Victor: (1, 60) and (4, 50)

Mel’s rate of change is _. That means that her height in the air decreases _ feet every second.


Victor’s rate of change is _. That means that his height in the air decreases _ feet every second.

Answer:

[tex](\ln(5), 19-5\ln(5))[/tex]

Step-by-step explanation:

The line can be represented as y=5x-8, so the slope of the line is 5.

The derivative of the curve is:

[tex]\frac{d}{dx} [9+2e^x-5x]\\=\frac{d}{dx} [9]+\frac{d}{dx} [2e^x]-\frac{d}{dx} [5x]\\=2e^x-5\\[/tex]

We need to set that equal to 5 to find the x coordinate of our desired point

[tex]2e^x-5=5\\2e^x=10\\e^x=5\\x=\ln(5)[/tex]

Now, just plug in x in the curve to solve for y:

[tex]9+2e^{\ln(5) } -5\ln(5) = y\\9+10-5\ln(5)=y\\19-5\ln(5)=y[/tex]

Line 5x y = 8 has a slope of 5. This means that the tangent line that runs parallel to this line must also have a slope of 5.

To solve this equation

dy/dx = 2ex 5 is the derivative of the function y = 9 + 2ex 5x. Consequently, 2ex 5 is equal to the slope of the tangent line at any location.

When we set the slope of the tangent line to 5, we obtain:

2ex − 5 = 5

2ex = 10

e^x = 5

Taking the natural logarithm of both sides, we get:

ln(e^x) = ln(5)

x = ln(5)

Therefore, ln(5) is the x-coordinate of the crossing point.

We can enter this value of x into the original function to determine the y-coordinate:

y = 9 + 2e^(ln(5)) − 5(ln(5))

y = 9 + 10 − 5ln(5)

y = 15 − 5ln(5)

As a result, the intersection is at (ln(5), 15 5ln(5)).

To sum up, (ln(5), 15 5ln(5)) is the point on the curve y = 9 + 2ex 5x where the tangent line is parallel to the line 5x y = 8.

Learn more about tangent line here

https://brainly.com/question/33610482

#SPJ3

Answer:

What does the random variable for a binomial experiment of n trials measure? The random variable measures the number of successes out of n trials. ... A binomial experiment requires that the probability of success be the same for each trial. In an experiment, there are n independent trials.

Step-by-step explanation:

Answer: (with explanation) (ANSWER AT THE BOTTOM)

et P = number of hours that the plumber worked.

let H = number of hours that the helper worked.

since the plumber worked 3 more hours than the helper, the equation for hours worked is

P = H + 3

-----

since the plumber earned 28 dollars per hour and the helper earned 15 dollars per hour, the equation for amount of money each made is the number of hours each worked times the dollars per hour each earned.

this equation is

(28*P) + (15*H) = 213 dollars

-----

both get the same answer.

-----

-----

substitute for P in the money equation since P is the same as H + 3.

equation becomes

(28*(H+3)) + (15*H) = 213

solve for H.

28*H + 28*3 + 15*H = 213

43*H + 84 = 213

43*H = 129

H = 3

-----

if H = 3, then P = 6 because P = H + 3.

-----

6*28 + 3*15 = 213 so your answer is

now to find the amount each earn by themselves, we just have to multiply by 6 or 3 by their hourly earning.

let's do the Plumber first

28x6=168

now the helper

15x3=45

---------

now to check if that was the right answer, let's add them up...

168+45=213

so, our answer is right.

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

Answer:

mark other guy brainly, his answer is right, and he truly deserves it, he got expert verified

Step-by-step explanation:

Answer:

75 onces 15 eggs and I dont know for the brown sugar

Step-by-step explanation:

Answer:

point-slope form: [tex]y-1=\frac{-2}{3}(x+6)[/tex]

y-intercept form: [tex]y=\frac{-2}{3}x-3[/tex]

Step-by-step explanation:

hope this helps :)

Answer:

(i) 88°

(ii) 23°

Step-by-step explanation:

See the picture below.

The numbers added in red are the angle measures. The numbers added in black are the order in which each angle measure was written.

ABCD is a rhombus, so all sides are congruent.

Triangle BCD is isosceles with sides DC and BC congruent, so <DBC is congruent to <BDC. From the sum of the measures of the angles of a triangle, we get m<DCB. Opposite angles of a rhombus are congruent, so m<A = m<DCB. From the sum of the measures of the angles of a triangle and from isosceles triangle ADB we get m<ADB and m<ABD. From m<DBC and supplementary angles, we get m<CBE. From isosceles triangle BCE, we get m<BCE.

1/8; 0.2; 13/26; 3/5; 7/8; 1.09; 1.19; 1.5; 1.9

Answer:

x = 6/5

y = 2/5

Step-by-step explanation:

this is the answer i got please mark brainliest i really need it cuz i need 2 more

Answer:

Order is    1/2  < 5/6 < 5/4

Step-by-step explanation:

  1/2  = 0.5

  5/6 = 0.83

  5/4 = 1.25

      0.5 < 0.83 < 1.25

Just convert 'em to decimals....

½ = 0.5

⅚ = 0.83

5/4 = 1.25

# 1/2 < 5/6 < 5/4

Answer:

5+4+1=10

20000/10=2000

5x2000:4x2000:1x2000

10000:8000:2000

Answer:

B) 8

Step-by-step explanation:

Triangles MNC and RSC are similar because all 3 angles are the same, so the the ratio between each side should be the same.

If NC=12 and SC=6 then triangle MNC is scaled up by 2 from triangle RSC. This means each side of MNC is 2 times bigger than on RSC. So, sense RS=4, we can multiply that by 2 to get MN=8.

Answer:

A. <LKM = <LJN

Step-by-step explanation:

A. <JKM = <LJN is not congruent = will NOT prove

B. KM/JN = KL/ML is a valid proportion = will prove

C. JN || KM is congruent = will prove

D. KL/JL = ML/NL is a valid proportion = will prove

Answer:

$352

Step-by-step explanation:

One ticket costs $22, so 16 tickets would be 22 times 16.

Final Answer: $352

Answer:

7n+24 is greater than that 3n-4

Step-by-step explanation:

First Distributive Property

4(n+6)+3n

Combine like terms

4n +24+3n

7n+ 24

Explanation

7n+24 is greater than that 3n-4

Answer:

See below.

Step-by-step explanation:

The answer is D. M and O are congruent, but that is not an option, so the focus goes towards M and N. M and N are similar, but are not congruent.

-hope it helps

Answer:

M and N are similar but not congruent.

Step-by-step explanation:

Answer:22 hopes this helps

Step-by-step explanation:

so here the problem look at the numbers -8 and 14

8 is no long a a negative it’s positive

So now you got 8 + 14 = 22

Answer:

22 blocks

Step-by-step explanation:

just simply add 8 and 14 to get your answer :)

Answer:

[tex]7( - 7 + 6m) + 9[/tex]

Answer:

45

Step-by-step explanation:

The equation for area of a triangle is:

[tex]A=\frac{1}{2}*b*h[/tex]

Using the figure, we can determine the base is 15 since it is perpendicular to the height.

We can plug 6 (height) and 15 (base) into the equation to solve for the area...

[tex]A=\frac{1}{2}*6*15=\frac{1}{2}*90=\frac{80}{2}=45[/tex]

Answer:

12.9 or 12 9/10

Answer:

y=2x-10

2y=x-8

since the second equation equals 2y and the first is y that means the first equation times 2 equals the other one

4x-20=x-8

-x

3x-20=-8

+20

3x=12

x=4

then lets just plug it in

2y=4-8

simplefy

2y=-4

y=-2

(4,-2)

Hope This Helps!!!

Answer:

$23

Step by step explanation

Answer:

0.21% of 8,095.23=17

Step-by-step explanation:

17÷0.21%

17÷(0.21÷100)

(100×17)÷0.21

1700÷0.21

8,095.238095

ans is 8095.23

hope it helps

Answer:

-6 = negative 6

negative is on the left side of the number lines

6 left from the middle

If this helped, please consider picking this answer as the Brainliest Answer. Thank you!

Answer:

1 d

2 b

3 g

4 a

5 e

6 f

7 c

8 h

Please mark as Brainliest

Answer:

AV of -15 is 15.

AV of 16 is 16.

Step-by-step explanation:

It turns the number positive.