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2 years ago

(6Q) Find the domain and range.

Mathematics

1 answer:

Rudik [331]2 years ago

8 0

Answer: Option a.

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

We have the function $f(x) = 2x + cosx$

Note that f(x) is the sum of two continuous functions $h(x) = 2x$ and $g(x) = cosx$

The domain and range of h(x) are all real numbers

The domain of g(x) is all real numbers. The range of g(x) is [-1, 1]

Then the domain of $f(x) = h(x) + g(x)$ will be the intersection of the domains of the function $h(x) = 2x$ and the function $g(x) = cosx$ .

Therefore the domain of f(x) are all real numbers. x ∈ (-∞, ∞)

The range of f(x) will be equal to the union of the range of g(x) and h(x)

Therefore the range will be all real numbers f(x) ∈ (-∞, ∞)

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A coordinate map of the local grocery store is shown below. Hot dogs are located at the point (6,4) Mustard is located at the po

deff fn [24]

The distance between the 2 locations = 7 units

Step-by-step explanation:

Step 1:

Given,

Location of Hot dogs = (6,4)

Location of Mustard = (6,-3)

We need to find the distance between the two locations

Step 2:

Since the x coordinates of both the location are the same , they lie in the same line.

The first location is 4 units above the x axis and the second location is 3 units below the x axis.

Hence the distance between the 2 locations 4-(-3) = 7 units

Step 3 :

Answer :

The distance between the 2 locations = 7 units

8 0

3 years ago

LCM of 294 and 1260

Alex Ar [27]

Answer:

8820

Step-by-step explanation:

Prime factorization of 294,

→ 2 × 3 × 7 × 7

Prime factorization of 1260,

→ 2 × 2 × 3 × 3 × 5 × 7

LCM of 294 and 1260,

→ 2 × 2 × 3 × 3 × 5 × 7 × 7

→ 8820

Hence, the LCM is 8820.

4 0

1 year ago

PLEASE ANSWR DUE BY 11:59 P.M TODAY 50 POINTS

hoa [83]

Answer:

1) 1/4

3) 1/12

4) 5/6

Step-by-step explanation:

1) P(Red) = 1/4

4 options out of which 1 is red

Black --> Black, White, Yellow

Green --> Black, White, Yellow

Red --> Black, White, Yellow

White --> Black, White, Yellow

First 4 branches for buttons.

From each of these 4 branches, make 3 further branches for ribbons

3) In the tree diagram, there are

12 (4×3 = 12) equally likely outcomes

Out of which 1 is (Black, Black)

So, P(Black & Black) = 1/12

4) out of the 12 outcomes, only 2 have same colour of bottom ribbon:

(Black, Black) & (White,White).

Other 10 have different colours.

P(different) = 10/12 = 5/6

5 0

3 years ago

-3x -4>8 solve it pls

Aleks04 [339]

Answer:

see picture

Step-by-step explanation:

6 0

2 years ago

The total profit Upper P (x )(in thousands of dollars) from the sale of x hundred thousand pillows is approximated by Upper P

Schach [20]

Answer:

x=12 maximizes the profit function.

Step-by-step explanation:

We are given that the profit is $P(x) = -x^3+15x^2+72x-200$ for $x\geq 5$

To find x that maximizes P, we will find the derivative of P(x) and find x such that P'(x) =0. Recall that the derivative of a function of the form $x^k$ is $kx^{k-1}$ , and that the derivative of a constant is zero. Then, by using the properties of derivatives, we get (the details of the calculation is omitted).

$P'(x) =-3x^2+30x+72$ .

We want to solve $P'(x) = 0$ . By dividing the equation by -3, we get

$x^2-10x-24=0=(x-12)(x+2)$

So we have that x=12 and x=-2 are solutions. In this case, we are only considering x greater than o equals 0. So, we take x=12.

We will check that x=12 is a maximum of P.

To do so, we will use the second derivative criteria, which is as follows. Given a function f whose first and second derivative exist, a point x is a maximum if $f''(x)$ . In our case,

$P''(x) = -6x+30$

Note that $P''(12) = -42$ . So x=12 is a maximum of P.

6 0

3 years ago