Daniela and Jack are hiking a steady incline. They use their GPS device to determine their elevation every 15 minutes. At 15 minutes and 30 minutes they were at elevations of 10,300 and 10,900 feet, respectively. Write an equation expressing their elevation in relation to time.

Answers

Answer 1

Answer:

[tex]h=40t+9700[/tex]

where the elevation, h, is in feet and time, t, is in minutes.

Step-by-step explanation:

At the time, [tex]t_1=15[/tex] min, the elevation, [tex]h_1= 10,300[/tex] feet and

at the time [tex]t_2= 30[/tex] min, the elevation, [tex]h_2=10,900[/tex] feet.

As they are hiking a steady incline, so the change in the elevation with respect to time will be constant.

So, there will be a linear relationship between the elevation and the time.

Let [tex]h[/tex] be the elevation at any time instant [tex]t[/tex], so the linear relation among these quantities is

[tex]h=mt+C_0\;\cdots(i)[/tex]

where [tex]m[/tex] is the rate of change of elevation with respect to time and [tex]C_0[/tex] is constant.

The change in the elevation, [tex]\Delta h=h_2-h_1= 10,900-10,300=600[/tex] feet.

and the change in time, [tex]\Delta t=t_2-1_1=30-15=15[/tex] min.

So, change in the elevation in unit time,

[tex]m=\frac{\Delat h}{\Delta t}=\frac{600}{15}=40[/tex] feet/min.

Now, from equation (i)

[tex]h=40t+C_0[/tex]

As the elevation, [tex]h=h_1[/tex] at time [tex]t=t_1[/tex], so

[tex]10,300=40\times15+C_0[/tex]

[tex]\Rightarrow C_0=9700[/tex]

Hence, the required equation is

[tex]h=40t+9700[/tex]

where the elevation, [tex]h[/tex], is in feet and time, [tex]t[/tex], is in minutes.


Related Questions

You want to buy some songs and you have a specific budget. A new song costs $0.99 and a classical song costs $0.65. Which expression would represent the total you would spend on buying these types of songs?
1.64N
1.64
0.99N + 0.65C
N + C

Answers

0.99N + 0.65C

It shows the individual price multiplied by the amount of each that you are buying, added together to get the total amount you would be spending

Answer:

0.99N + 0.65C

Step-by-step explanation:

Use calculator to find the values of the following,correct to 3decimal places:

1. Cot 61,4

Answers

No such thing as cot (61,4). I think you meant to say cot (61.4°). See the difference?

So, cot (61.4°) is approximately -0.139844.

Rounded to 3 decimal places we get -0.140.


[tex] - 5 {u}^{4} \times ( {u}^{4} )[/tex]
PLEASE HELP ME

Answers

it equals to - 5u to the power of 8

Under a dilation, the point (2, 6) is moved to (6, 18).

What is the scale factor of the dilation?

Answers

Answer:

The correct answer is 3

Hope this help :)

Answer:

3

Step-by-step explanation:

What is the maximum number of solutions each of the following systems could have?
Two distinct concentric circles:
Two distinct parabolas:
Aline and a circle:
A parabola and a circle:

Answers

Answer:

0

2

2

4

Step-by-step explanation:

Answers for entire assignment:

--> Page 1: 0 , 2 , 2 , 4

Page 2: D

Page 3: B

Page 4: Parabola , Line , A , B , C , 1 , -11 , 56

Page 5: Last one

Page 6: B , D , F , H

Page 7:

Use substitution to write the equation

–16t2 + 56t = –16t2 + 156t – 248.

Simplify and solve for t, which is 2.48 s.

Substitute 2.48 for t into either equation to get h = 40.5 ft.

--> 40.5 ft.

Jayda needs more than 2.25 pounds of meat for a recipe. Which of the following amounts is greater than 2.25 pounds?
2.205 pounds
2.502 pounds
2.2 pounds
2.25 pounds plz help

Answers

Answer:

2.502

Step-by-step explanation:

not needed

Which statement about 1.23 ÷ 0.15 is true?

Answers

Answer:

8.2

Step-by-step explanation:

1.23 ÷ 0.15 = 8.2

A box of laundry detergent contains 16.5 oz of product. What is the maximum number of loads that can be washed if each load requires a minimum of 3/4 oz of detergent?
A) 22 loads
B) 16.5 loads
C) 10 loads
D) 50 loads
E) 18 loads​

Answers

Answer:

A

Step-by-step explanation:

Find the measure of angle PKL​

Answers

The measure of PKL is: 108°

Which theorem or postulate justifies this statement?

∠8≅∠10

alternate interior angles theorem
corresponding angles postulate
alternate exterior angles theorem
vertical angles theorem
linear pair postulate

The figure shows parallel line segments G N and F H rising slowly from left to right with segment G N above segment F H. Line segment K L falls steeply from left to right, first intersecting segment G N and then segment F H. Line segment M J rises steeply from left to right, first intersecting both segment F H and segment K L at their point of intersection and then intersecting segment G N. The 4 angles at the intersection of segments G N and K L are numbered from 1 through 4 in a clockwise direction with angle 1 above segment G N and to the left of segment K L. The 4 angles at the intersection of segments G N and J M are numbered from 5 through 8 in a clockwise direction with angle 5 above segment G N and to the left of segment J M. The 6 angles at the intersection of segments F H, K L, and J M are numbered from 9 through 14 in a clockwise direction with angle 9 above segment F H, to the right of segment K L, and to the left of segment J M.

Answers

Answer:  heres the answer, i just finished the quiz

What is the value of x that makes the equation
3x - 4= 15 + 2x true?
You may show your work either by drawing on the
sketch pad

Answers

Answer:

[tex]\boxed {x = 19}[/tex]

Step-by-step explanation:

Solve for the value of [tex]x[/tex]:

[tex]3x - 4 = 15 + 2x[/tex]

-Take [tex]2x[/tex] and subtract it from [tex]3x[/tex]:

[tex]3x - 4 - 2x = 15 + 2x - 2x[/tex]

[tex]x - 4 = 15[/tex]

-Add [tex]4[/tex] to both sides:

[tex]x - 4 + 4 = 15 + 4[/tex]

[tex]\boxed {x = 19}[/tex]

So, the value of [tex]x[/tex] is [tex]19[/tex].

The age (in years) of 10 students practicipating in an english drama are 10, 6,8,19,12,8,10,18,19,15 find the median age of the particapating ​

Answers

Answer:

11

Step-by-step explanation:

First, list the numbers from least to greatest.

6, 8, 8, 10, 10, 12, 15, 18, 19, 19

find the middle term. There are ten terms, therefore there are 2 middle terms. You will add them togetehr and divide by two.

10+12=22/2=11

3.41 - 1.74
Show your work

Answers

Answer:

1.67

Step-by-step explanation:

3.41

1.74

1.67

1. Make 1, 11 (make 4, 3)

2. Subtract 11 and 4, you get 7

3. Make 3, 13 (make 3,2)

4. Subtract 13 and 7, you get 6

5. Subtract 2 and 1, you get 1

6. You answer is 1.67

Kayla has a puppy that weighs 5 pounds. Kayla's brother Manuel has a puppy that is 65 times the weight of Kayla's puppy. Which statement about the weight of Manuel's puppy is true?

Answers

is there a list of statements? if not i would reason that if
Kayla’s puppy’s weight=k
and we know k=5 (pounds)
and Manuel’s puppy’s weight=m
then your equation would be something like 5*65=m
which means that m=325

34 students in Mr.Jones math class passes the final exam.There are 40 students in his class total.what percent of students passed?

Answers

34/40 which is 85% if that helps

-.8x+40-8x-35 simplified

Answers

The answer I got is -16x + 5

I need to turn this in in 2 hours please hurry

please at least show me how to set it up. I want to do the work myself for #1

and for 2 and 3 please check my work

Answers

Answer:

  2) 162°, 72°, 108°

  3) 144°, 54°, 126°

Step-by-step explanation:

1) Multiply the equation by 2sin(θ) to get an equation that looks like ...

   sin(θ) = <some numerical expression>

Use your knowledge of the sines of special angles to find two angles that have this sine value. (The attached table along with the relations discussed below will get you there.)

____

2, 3) You need to review the meaning of "supplement".

It is true that ...

  sin(θ) = sin(θ+360°),

but it is also true that ...

  sin(θ) = sin(180°-θ) . . . . the supplement of the angle

This latter relation is the one applicable to this question.

__

Similarly, it is true that ...

  cos(θ) = -cos(θ+180°),

but it is also true that ...

  cos(θ) = -cos(180°-θ) . . . . the supplement of the angle

As above, it is this latter relation that applies to problems 2 and 3.


-2/3y-3/4=5
What is the answer i need to show my work please

Answers

Answer:

y=  -69/8  (negative 69 over 8)

Step-by-step explanation:

First, you have to simplify both sides of the equation:

[tex]-2/3y+ -3/4 =5[/tex]

Second, add 3/4 to both sides:

-2/3y +-3/4 + 3/4=5 +3/4

-2/3y= 23/4

Next, multiply both sides by 3/(-2) (3 over -2)

(3/-2)*(-2/3y)= (3/-2) * (23/4)

y= -69/8

What is 9/4 - 7/10 subtracting fractions

Answers

Answer:

31/20

Step-by-step explanation:

write all numerators above the LCD 20

45-14/20

subtract the numbers

31/20

Answer:

31/20

Step-by-step explanation:

The gum of two number is 37. Find the number if
lone number is 1 more than twice the other.

Answers

Answer:

a = 25

b = 12

Step-by-step explanation:

Hi there !

a + b = 37

a = 2b + 1

replace a

(2b + 1) + b = 37

3b = 37 - 1

3b = 36

b = 36 : 3

b = 12

a = 2×12 + 1

a = 24 + 1

a = 25

a + b = 37

25 + 12 = 37

37 = 37 (true)

Good luck !

I need help. . . . . . . . .

Answers

Answer:

61, C

Step-by-step explanation:

So, congruent means all the same. The question is just saying that 3 lines intersect at one point and form 6 angle. The 6 angles are not all the same. Given that, what is the smallest possible largest angle. Obviously, if all angles could be congruent, then, it would be 6 60° angles. However, they aren't. So, to minimize the largest angle, we can just make 1 angle 61° and another 59°. Therefore, the answer should be C which is 61° as you would have the 6 angles being:

59°, 60°, 60°, 60°, 60°, and 61°.

What is the inverse of this trigonometric function?

y = sinx
y = cosx
y = arcsinx
y = arccosx

Answers

Answer:

D

Step-by-step explanation:

edge

The inverse of this trigonometric function is y = arccosx. Then the correct answer is option D.

What is a trigonometric function?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.

The given graph is represented by the function y = cosx. The inverse function will be y = arccosx.

Hence, the correct answer is option D.

To know more about trigonometric functions follow

https://brainly.com/question/1143565

#SPJ2

A calling plan charges $0.10 per minute and a monthly fee of $5.99. How many minutes can a customer talk if
they want the bill to equal $37.99?

Answers

Answer:

320 mins

Step-by-step explanation:

Answer:

320 minutes

Step-by-step explanation:

37.99-5.99= 32

32/.10 = 320 minutes

pls answer i need answer fast

Answers

Answer:

-24

Step-by-step explanation:

Given expression:

      3z (2y - 4)²

  z = -2 and y = 3

To solve this problem, simply substitute:

       3z (2y - 4)² = 3(-2){2(3) - 4}²

                           = -6(6-4)²

                           = -6 (2)²

                          = -6 x 4

                          = -24

Answer:

The answer is -24

Luis purchased a laptop computer that was marked down by 2/5 of the original price. How much does Luis pay if the laptop was originally $550.00?​

Answers

Answer:

$330

Step-by-step explanation:

Start by dividing the original price by five, then multiply by 3. You do that because he paid 3/5 of the original price. Hope this helps!

Answer:

$220

Step-by-step explanation:

Markdown is the percentage decrease

2/5 is written as .4 in decimal form (40%)   [tex]\frac{2}{5} times 20=\frac{40}{100}[/tex]

So when you multiply the number with the markdown percent, you get

550 times .4 = $220

A 16-ounce can of carrots for $1.29 OR a 20-ounce can of carrots for $1.49

Answers

Answer: 20 ounce

Step-by-step explanation: 1.29/16=0.080625 1.49/20=0.0745

Answer:

20 ounce, its 20 cents more and it has more carrot.

Step-by-step explanation:

Alexander is a stockbroker. He earns 13 percent commission each week. Last week, he sold $5,400 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011?

Answers

Answer:

($5,400) * 0.13 = $702 * 52 weeks = $36,000

Step-by-step explanation:

Please help me!! Please explain and I’m pretty sure the answer needs to have < and > signs or >_ and <_ with “_” under < and >.



(For other ppl who search this)
4. Jim makes 8.50 an hour. Each week, 26% of his total pay is deducted for taxes. How many hours does Jim have to work if he wants his take-home pay to be AT LEAST $300 per week? Write and solve an inequality for this situation.

Answers

Answer:

Jim has to work 48 hours to earn at least $300 per week.

Step-by-step explanation:

Jim makes 8.50 per hour

so in x hours he makes 8.5x

26% is deducted for taxes

so his take home pay is 8.5x(1 - .26) = 8.5x(.74) = 6.29x

To make > = $300 Jim must work enough hours so that

6.29x >= 300

x >= 17.49

Find the midpoint of the segment with the following endpoints.
(-1,-5) and (8, -2)

Answers

To Find :-

The midpoint of the like segment having (-1,5) and (8,-2) as their endpoints.

Solution :-

Midpoint formula :-

[tex] \bf \left( \dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2} \right)[/tex]

Here ,

x1 = -1

x2 = 8

y1 = 5

y2 = -2

[tex] \longrightarrow \dfrac{ - 1 + 8}{2} ,\dfrac{5 + - 2}{2} [/tex]

[tex] \longrightarrow \dfrac{ 7}{2 },\dfrac{7}{2} [/tex]

10.) What is 99 as a fraction?

Answers

Answer:

Step-by-step explanation:

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