MATHEMATICS HIGH SCHOOL

Which function has the smallest minimum y-value?fx) = 2 sin (3x + π) − 2
g(x) = (x − 3)2 − 1
h(x) >
x y
−2 3
−1 −2
0 −5
1 −6
2 −5
3 −2
4 3

Answers

Answer 1
Answer:

Answer:

The smallest minimum is attained by the function:

h(x)

Step-by-step explanation:

We are asked to find which function has smallest minimum value:

We have:

  • f(x)=2 sin (3x+π)-2

We know that the minimum value of sine function is -1 and the maximum value of sine function is 1.

So, when sine function will have minimum value -1 then the function f(x) also has minimum value as -4.

( since 2×(-1)-2=-2-2= -4 )

  • g(x)=(x-3)^2-1

As this function is a quadratic function and we know that:

(x-3)^2≥0 for all x.

so,

(x-3)^2-1≥ -1.

Hence, the minimum value of g(x) is -1.

  • Also we are given a set of values of function h(x) as:

   h(x) =y

x       y

−2      3

−1     −2

0     − 5

1     −6

2      −5

3      −2

4        3

Clearly from the table we could see that h(x) receives -6 as the minimum value.

Hence, the smallest minimum is attained by the function h(x).
Answer 2
Answer: The minimum value of sine is negative one, so f(x) has minimum -2-2=4.  The square function has minimum 0, so g(x) has minimum 0-1=-1. 
h(x) has minimum -6 when x=1, so it has the smallest minimum.

Related Questions

Given: x - 5 > -10. Choose the solution set. {x | x R, x < -15} {x | x R, x > -5} {x | x R, x < 5} {x | x R, x > 15}
Do you add them both together or multiply or do u put an equal sign between them? what is the sum of  and
Prove: AABStepStatementReasonGiven1ABCD is a parallelogramABCDSelect a Reason!!2ABN
How to simplify the expression -(-19)?
In the United States, 13 out of every 20 cans are recycled. What percent of cans are recycled?

How would you find the real solution, by using the quadratic formula.
x^2-4x+2=0

Answers

x^2-4x+2=0 \n \na=1 \n b=-4 \n c=2 \n b^2-4ac=(-4)^2-4 * 1 * 2=16-8=8 \n \nx=(-b \pm √(b^2-4ac))/(2a)=(-(-4) \pm √(8))/(2 * 1)=(4 \pm √(4 * 2))/(2)=(4 \pm 2√(2))/(2)=(2(2 \pm √(2)))/(2)=2 \pm √(2) \n\boxed{x=2-√(2) \hbox{ or } x=2+√(2)}
x^2-4x+2=0\nx^2-4x+4-2=0\n(x-2)^2=2\nx-2=\sqrt2 \vee x-2=-\sqrt2\nx=2+\sqrt2 \vee x=2-\sqrt2

CAN SOMEONE HELP ME ASAP? The density of a certain material is such that it weighs 7 ounces for every 2.5 gallons of volume. Express this density in tons per cubic meter. Round your answer to the nearest hundredth.

Answers

Answer: Density = 0.23 tons per cubic meter.

Step-by-step explanation:

Formula : Density=(Mass(in \ ton))/(Volume (in\ m^3))

1 ton = 32000 ounces

⇒ 1 ounce = 0.00003125 ton

⇒  7 ounces = 7(0.00003125)=  0.00021875 ton

1 gallon = 0.00378541 cubic meter

2.5 gallons = 0.009475 cubic meter

Density= (0.00021875)/(0.009475)\text{ tons per cubic meter}

(21875)/(94750)\text{ tons per cubic meter}\approx0.23\text{ tons per cubic meter}

Hence, Density = 0.23 tons per cubic meter.

Answer:

0.02 tons per cubic meter

Step-by-step explanation:

Can someone please help me and look over this and answer this?I have a huge E.A and this make up my whole grade please help.

Answers

1. (Species\ A)/(Species\ B) = ((3x^(2)y)^(2))/(6(xy)^(3)) = (3x^(4)y^(2))/(6x^(3)y^(3)) = (x)/(2y)

2. (Species\ C)/(Species\ D) = \frac{20√(xy)}{4\sqrt{x^(2)y}} = (5)/(√(x)) = (5)/(√(x)) * (√(x))/(√(x)) = \frac{5√(x)}{\sqrt{x^(2)}} = (5√(x))/(x)

the population of masterton was 23 000 in 2012. Assume that Masterton population increases at a rate of 2% per year. Write an equation to model the population of masterton (y) based on number of years since 2012(x)

Answers

So, let's first focus on the first year:

the population then would be: 23000* (100+2)%

100% is the old population the 2% is the incease, so in total it's 102%, or 1.02 - the same number written differently.

So it will be 23000*1.02

After two years it will be 23000*1.02*1.02, and so on

so after x years it will be:

y=23000*1.02^(z)

Need help with this. Show your steps so I could check my work and my answer.

Answers

Answer:

25

Step-by-step explanation:

The angle at C is 90 degrees, and BCD is a right triangle, so we can applythe Pythagorean theorem here -- 60²+m²=65², so 65²-60²=m²=625. The possible values for m are 25 and -25, and since m can't be negative, 25 is our answer as 25 is the square root of 625

The sales tax rate is 8%. Estimate the tax on a jacket that costs $69.95.

Answers

Answer:

8% is the same as (.08)x69.95=.556 or .56 ( because of rounding )

so .56 plus 69.95= $70.51


Step-by-step explanation:
Add 8% and 69.95 and then add 69.95 again to that answer and ta da!
Other Questions
Sams coordinates are (2,4) and the theaters coordinates are (5,-2.5) on a grid each unit represents 1 kilometer. Describe Sam's location relative to the theater.
how can you write the expression 2 − (p 6) in words? a two minus the sum of p and six b two added to the difference of p and six c the difference of two and p times six d the sum of two and p added to six
Find the value of xx = Classify the triangle : acute isosceles triangle acute isosceles triangle acute scalene triangle acute scalene triangle obtuse isosceles triangle obtuse isosceles triangle obtuse scalene triangle obtuse scalene triangle right isosceles triangle right isosceles triangle right scalene triangle right scalene triangle equiangular equilateral triangle
The main tank at an aquarium is a cylinder with diameter 203 ft and height 25 ft. Using 3.14 for pi, find the volume of the tank to the nearest cubic foot.