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3 years ago

What is the range of this function?

Mathematics

1 answer:

Rzqust [24]3 years ago

5 0

Greetings.

The range is the set of y-value.

The range starts from the minimum point to maximum point.

Our minimum point starts at 0 and maximum point starts less than infinity.

Therefore the range is 0<=y<+inf

However, we do not often write that, although it is right.

Therefore we write as y≥0

Thus, the answer is B choice.

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Verify identity: <br><br> (sec(x)-csc(x))/(sec(x)+csc(x))=(tan(x)-1)/(tan(x)+1)

Nikitich [7]

So hmmm let's do the left-hand-side first

$\bf \cfrac{sec(x)-csc(x)}{sec(x)+csc(x)}\implies \cfrac{\frac{1}{cos(x)}-\frac{1}{sin(x)}}{\frac{1}{cos(x)}+\frac{1}{sin(x)}}\implies 
\cfrac{\frac{sin(x)-cos(x)}{cos(x)sin(x)}}{\frac{sin(x)+cos(x)}{cos(x)sin(x)}}
\\\\\\
\cfrac{sin(x)-cos(x)}{cos(x)sin(x)}\cdot \cfrac{cos(x)sin(x)}{sin(x)+cos(x)}\implies \boxed{\cfrac{sin(x)-cos(x)}{sin(x)+cos(x)}}$

now, let's do the right-hand-side then

$\bf \cfrac{tan(x)-1}{tan(x)+1}\implies \cfrac{\frac{sin(x)}{cos(x)}-1}{\frac{sin(x)}{cos(x)}+1}\implies \cfrac{\frac{sin(x)-cos(x)}{cos(x)}}{\frac{sin(x)+cos(x)}{cos(x)}}
\\\\\\
\cfrac{sin(x)-cos(x)}{cos(x)}\cdot \cfrac{cos(x)}{sin(x)+cos(x)}\implies \boxed{\cfrac{sin(x)-cos(x)}{sin(x)+cos(x)}}$

7 0

3 years ago

A bakery has the following pricing for large orders of cupcakes. The first 100 cupcakes of any order

Taya2010 [7]

A piecewise function is a function that behaves differently in different intervals of its domain.

The answers are:

f(x) = x*$2.00 if 0 ≤ x ≤ 100

f(x) = x*$1.75 if 100 < x ≤ 250

f(x) = x*$1.25 if x > 250.

b) $306.25

The given information is:

The first 100 cupcakes cost $2.00 each.

If the order is between 100 and 250 cupcakes, the cost is $1.75 each.

If the order is more than 250 cupcakes, the cost is $1.25 each.

a) Now we want to write the piecewise function, this will be:

f(x) = x*$2.00 if 0 ≤ x ≤ 100

f(x) = x*$1.75 if 100 < x ≤ 250

f(x) = x*$1.25 if x > 250.

Above you can see the piecewise function, when you want to evaluate it, the first thing you need to do is to find at which interval the input belongs.

b) If you order 175 cupcakes you have x = 175.

This belongs to the second interval ( 100 < x ≤ 250) then we will use the second part of the function:

f(175) = 175*$1.75 = $306.25

If you want to learn more, you can read:

brainly.com/question/12561612

8 0

3 years ago

HELPPPPPPPPPPPPPPPPPPPPP

77julia77 [94]

Answer:

ill guess -2 for u

Step-by-step explanation:

5 0

2 years ago

5cosx -2sin(x/2) +7=0<br>Help me to find x step by step<br>pls

miskamm [114]

Answer:

x = 180

Step-by-step explanation:

First, you need to know

1. Double-angle formula:

cos(2x) = $cos^{2}x - sin^{2}x$

2. Pythagorean identity:

$cos^{2}x + sin^{2}x = 1$

Back to your problem, replacing the variable by the above:

$5cosx-sin\frac{x}{2}+7 = 0$

$5(cos^{2}\frac{x}{2}-sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0$ By Double-angle formula

$5(1 - 2sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0$ By Pythagorean identity

Given $y = \frac{x}{2}$

$5(1-2sin^{2}y) - 2siny + 7 = 0$

$10sin^{2}y+2siny-12=0$

$5sin^{2}y+siny-6=0$

$(5siny + 6)(siny - 1)=0$ , we know -1 < sinx < 1, for every x ∈ R

$siny = 1, y =90$

$y = \frac{x}{2}$

$x = 180$

8 0

3 years ago

Abigail tosses a coin off a bridge into the stream below. The distance, in feet, the coin above the water is modeled by the equa

melomori [17]

Answer:

7 seconds

Step-by-step explanation:

Distance of the coin above the water is modeled by the equation

$y=-16x^2+96x+112$

where $x$ is time taken to cover the distance

Now equating with zero.

$0=-16x^2+96x+112\\\Rightarrow 16x^2-96x-112=0\\\Rightarrow x=\dfrac{-\left(-96\right)\pm \sqrt{\left(-96\right)^2-4\times \:16\left(-112\right)}}{2\times \:16}\\\Rightarrow x=7, -1$

So, time taken by the coin to hit the water is 7 seconds.

6 0

3 years ago