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pishuonlain [190]
3 years ago
11

When working through limit problems, why must you write the limit statement every time until you evaluate the equation?

Mathematics
1 answer:
Softa [21]3 years ago
8 0
Because that how it goes
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At the Howelton Hot Dog Happiness competition, Olaf eats five fewer than triple the hot dogs Alfred eats. Olaf eats 67 hot dogs.
viva [34]

Answer:

Alfred ate 24 hot dogs.

Step-by-step explanation:

Let the number of hot dog ate by Olafs be represented by b.

Since Olafs eats five fewer than triple the hot dogs Alfred eats, and Alfred ate a hot dogs. This can be expressed in a mathematical equation as follows;

b = 3a - 5

But Olafs eats 67 hot dogs, so that b = 67. Thus;

b = 3a - 5

67  = 3a - 5

67 + 5 = 3a

3a = 72

divide both sides by 3 to have;

a = \frac{72}{3}

a = 24

Alfred ate 24 hot dogs.

7 0
3 years ago
Find the area of the region enclosed by f(x) and the x axis for the given function over the specified u reevaluate f(x)=x^2+3x+4
lord [1]

Answer:

A = 68 unit^2

Step-by-step explanation:

Given:-

The piece-wise function f(x) is defined over an interval as follows:

                       f(x) =  { x^2+3x+4    , x < 3

                       f(x) =  { x^2+3x+4     , x≥3

                        Domain : [ -3 , 4 ]

Find:-

Find the area of the region enclosed by f(x) and the x axis

Solution:-

- The best way to tackle problems relating to piece-wise functions is to solve for each part individually and then combine the results.

- The first portion of function is valid over the interval [ -3 , 3 ]:      

                       f(x) = x^2+3x+4

- The area "A1" bounded by f(x) is given as:

                      A1 = \int\limits^a_b {f(x)} \, dx

Where,  The interval of the function { -3 , 3 ] = [ a , b ]:

                     A1 = \int\limits^a_b {x^2+3x+4} \, dx\\\\A1 = \frac{x^3}{3} + \frac{3x^2}{2} + 4x |\limits_-_3^3 \\\\A1 = \frac{3^3}{3} + \frac{3*3^2}{2} + 4*3 - \frac{-3^3}{3} - \frac{3(-3)^2}{2} - 4(-3)\\\\A1 = 9 + 13.5 +12 + 9-13.5+12\\\\A1 =42 unit^2

- Similarly for the other portion of piece-wise function covering the interval [3 , 4] :

                     f(x) = 4x+10

- The area "A2" bounded by f(x) is given as:

                      A2 = \int\limits^a_b {f(x)} \, dx

Where,  The interval of the function { 3 , 4 ] = [ a , b ]:

                     A2 = \int\limits^a_b {4x+10} \, dx\\\\A2 = 2x^2 + 10x |\limits_3^4 \\\\A2 = 2*(4)^2 + 10*4 - 2*(3)^2 - 10*3\\\\A2 = 32 + 40 - 18-30\\\\A2 =26 unit^2

- The total area "A" bounded by the piece-wise function over the entire domain [ -3 , 4 ] is given:

                     A = A1 + A2

                     A = 42 + 26

                     A = 68 unit^2

8 0
3 years ago
How do u solve xk = w - v for x
Wewaii [24]

Answer:

It is D

Step-by-step explanation:

You have to divide each side by k to get x by itself. So,

x=\frac{w-v}{k}

8 0
3 years ago
Read 2 more answers
A circular running track is 1/4 mile long. Jamie runs on this track, completing each lap in 1/20 of an hour. What is Jamie’s run
Grace [21]

Answer: The running speed of Elena is 5 miles/hour and this can be determined by using the formula of speed.

Step-by-step explanation:

A circular running track 1/4 is a mile long.

Elena runs on this track, completing each lap in 1/20 of an hour.

Speed formula is used to determine the speed of Elena. The formula of speed is given by:

   ----- (1)

where S is the speed, D is the distance and T is the time taken by Elena to run a circle.

Now, put the value of distance D and time T in the equation (1).

Speed = 5 miles/hour

Therefore, the running speed of Elena is 5 miles/hour.

For more information, refer to the link given below:

brainly.com/question/22610586

3 0
2 years ago
Hey I'm confused can someone help
lilavasa [31]
The answer is 95 based on the line
5 0
3 years ago
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