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3 years ago

Evaluate the piecewise function at the given values of the independent variable.

Mathematics

1 answer:

lutik1710 [3]3 years ago

7 0

Answer:

a) f(-1) = 1

b) f(0) = 6

c) f(2) = 8

Step-by-step explanation:

If x is lesser than 0, we have that:

f(x) = 4x + 5

Otherwhise

f(x) = x + 6

(a) f(-1)

Here x = -1.

-1 is lesser than 0

Then

f(x) = 4x + 5

f(-1) = 4*(-1) + 5 = -4 + 5 = 1

(b) f(0)

Here x = 0

When x equals 0

f(x) = x + 6

Then

f(0) = 0 + 6 = 6

(c) f(2)

Here x = 2

When x = 2

f(x) = x + 6

Then

f(2) = 2 + 6 = 8

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two mountain bikers leave from the same parking lot and head in opposite directions on two different trails. the first rider goe

sveta [45]

Applying the required rule or theorem, it can be concluded that the second biker is farther from the parking lot. The distance of the bikers to the parking lot are:

i. First biker = 17.0 km

ii. Second biker = 20.22 km

The path of travel of both bikers would form a triangle. Applying the Pythagoras theorem to the path of the first biker would give his distance from the starting point. While applying the cosine rule to the path of second rider would gives his distance to the starting point.

Thus,

a. To determine the distance of the first biker from the parking lot.

Let the required distance be represented by x. Applying the Pythagoras theorem, we have:

$hyp^{2}$ = $adj 1^{2}$ + $adj 2^{2}$

$x^{2}$ = $8^{2}$ + $15^{2}$

= 64 + 225

= 289

x = $\sqrt{289}$

= 17

x = 17 km

Thus, the first biker is 17.0 km from the starting point.

b. To determine the distance of the second biker from the parking lot.

Let the required distance be represented by x. So that applying the cosine rule, we have:

$c^{2}$ = $a^{2}$ + $b^{2}$ - 2ab Cos θ

$x^{2}$ = $8^{2}$ + $15^{2}$ - 2(15*8) Cos (180 - 20)

= 64 + 225 - 240 Cos 160

= 289 - 240 * -0.5

$x^{2}$ = 289 + 120

= 409

x = $\sqrt{409}$

= 20.2237

x = 20.22 km

Thus, the second biker is 20.22 km from the starting point.

Therefore, the second biker is farther from the parking lot.

A sketch of the path of travel for the two bikers is attached for more clarifications.

Visit: brainly.com/question/22699651

7 0

2 years ago

Which expression is equivalent to 4 square root 6 divided by 3 root 2?

saw5 [17]

Answer:

$\sqrt[12]{55296}$ /2

Step-by-step explanation:

$\sqrt[4]{6}$ / $\sqrt[3]{2}$ =1.2422

$\sqrt[12]{27}$ /2=0.66 <-- not matching with the top expression.

$\sqrt[4]{24}$ /2=1.11<--not matching with the top expression.

$\sqrt[12]{55296}$ /2=1.2422<-- matches!!

$\sqrt[12]{177147}$ /3=0.91<-- not matching with the top expression.

5 0

3 years ago

Is the point (−7,1) a solution to the inequality y<0.5x+9? yes or no

pshichka [43]

(-7,1) is a solution to the inequality y<0.5x+9

4 0

4 years ago

List all subsets of ta, b, c, d, e) containing a but not containing b

fomenos

Answer:

(a), (a,c), (a,d), (a,e), (a,c,d), (a,c,e), (a,d,e), (a,c,d,e)

Step-by-step explanation:

We are given the set (a,b,c,d,e).

Total number of subsets of the above set are $2^5$ = 32

Subsets:

(a,b,c,d,e)

(a), (b), (c), (d), (e)

(a,b), (a,c), (a,d), (a,e), (b,c), (b,d), (b,e), (c,d), (c,e), (d,e)

(a,b,c), (a,b,d), (a,b,e), (a,c,d), (a,c,e), (a,d,e), ( b,c,d), (b,c,e), (b,d,e), (c,d,e)

(a,b,c,d), (a,b,c,e), (a,b,d,e), (a,c,d,e), (b,c,d,e)

Subset having a but not b :

(a), (a,c), (a,d), (a,e), (a,c,d), (a,c,e), (a,d,e), (a,c,d,e)

7 0

4 years ago

Admission for a movie is $8 for children and $12 for adults. On a certain day, 3200 people attend the movie theater and $33,040

Nezavi [6.7K]

Let us assume the number of children attending the movie = x
Let us also assume the number of adults attending the movie = y
Cost of admission for a children in the movie = $8
Cost of admission of an adult in the movie = $12
Number of people going to the movie on a certain day = 3200
Total amount collected from the movie theater = $33040
Then
x + y = 3200
And
8x + 12y = 33040
2x + 3y = 8260
Let us first take the equation
x + y = 3200
x = 3200 - y
Now we will put the value of x in the equation
2x + 3y = 8260
2(3200 - y) + 3y = 8260
6400 - 2y + 3y = 8260
y = 8260 - 6400
= 1860
Now we will put the value of y from the above deduction in the equation
x + y = 3200
x + 1860 = 3200
x = 3200 - 1860
= 1340
So the number of children going to the movie theater is 1340 and the number of adults going to the movie theater is 1860.

5 0

3 years ago