All categories

2 years ago

Determine the range of this function

Mathematics

1 answer:

hodyreva [135]2 years ago

6 0

The answer is b) {y|y≤5}

You might be interested in

The area of a rectangular wall of a barn is 85 square feet. Its length is 12 feet longer than the width. Find the length and wid

MaRussiya [10]

Answer:

Length = 17 feet, Width = 5 feet

Step-by-step explanation:

Given:

The area of a rectangular wall of a barn is 85 square feet.

Its length is 12 feet longer than the width.

Question asked:

Find the length and width of the wall of the barn.

Solution:

Let width of a rectangular wall of a barn = $x$

<u>As length is 12 feet longer than the width.</u>

Length of a rectangular wall of a barn = $12+x$

As we know:

$Area\ of\ rectangle=length\times breadth$

$85=(12+x)x\\\\85=12x+x^{2} \\$

Subtracting both sides by 85

$x^{2} +12x-85=0\\x^{2} +17x-5x-85=0\\Taking\ common\\x+(x+17)-5x(x+17)=0\\(x+17)(x-5)=0\\x+17=0, x-5=0\\x=-17,x=5$

As width can never be in negative, hence width of a rectangular wall of a barn = $x$ = 5 feet

Length of a rectangular wall of a barn = $12+x=12+5=17\ feet$

Therefore, length and width of the wall of the barn is 17 feet and 5 feet respectively.

4 0

3 years ago

Primitive function for:<br><br> 1. f(x)=4e2x+e−x, sådan att F(0)=2

Free_Kalibri [48]

The primitive function for $f(x) = 4e^{2x} + e^{-x}$ is given by it's indefinite integral.

To calculate it, recall:

$\frac{d}{dx}e^{ax}=ae^{ax}$

$\int c f(x)dx = c\int f(x)dx$

Let's begin

$\int 4e^{2x}+e^{-x}dx \\4\int e^{2x}dx+ \int e^{-x}dx\\4\frac{e^{2x}}{2}+\frac{e^{-x}}{-1} + c\\$

$F(x) = 2e^{2x}-e^{-x} +c$

To find the costant, we just need to use the fact that $F(0)=2$

$F(0) = 2 \\4e^{0}+e^{0} + c =2\\5+c =2\\c=-3$

Therefore,

$\boxed{F(x) = 2e^{2x} - e^{-x} -3 }$

6 0

2 years ago

What is the equation of the line through (1, 6) and (0, 2)?

ASHA 777 [7]

Answer:

y = 4x + 2

Step-by-step explanation:

y = mx + b

m is the slope

b is the y-intercept

6 0

2 years ago

A group of students were asked if they carry a credit card. The responses are listed in

Stels [109]

Part of the question is missing

3 0

3 years ago

Given the functions, f(x) = x2 + 2 and g(x) = 4x - 1, perform the indicated operation. When applicable, state the domain restric

icang [17]

I hope this helps you

7 0

2 years ago