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3 years ago

Which function has the smallest minimum? (5 points)

Mathematics

1 answer:

Andrej [43]3 years ago

4 0

f(x) has the smallest minimum. The minimum value of f(x) is -3

The largest sin(x) can get is 1.
This applies to sin(2x-pi) as well. So f(x) is as small as -5*(1)+2 = -5+2 = -3.
You can see this each time the red curve bottoms out at y = -3.

The smallest that g(x) can get is y = -2 as shown at the vertex (3,-2)

The smallest that h(x) can get is y = 3 as shown by the point (1,3)

See the attachment for a visual comparison of the three functions.

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A diver dives from a 10m springboard. the equation f(t) = -4.9t² + 4t + 10 models her height above the pool at time t. When will

Gennadij [26K]

Answer:

At time t = 0.408 sec diver will be at maximum height

Step-by-step explanation:

We have given equation of the height $f(t)=-4.9t^2+4t+9$

We know that velocity is the rate of change of distance with respect to time

So $v=\frac{df(t)}{dt}=\frac{df(-4.9t^2+4t+10)}{dt}=-9.8t+4+0=-9.8t+4$

At maximum height velocity will be zero

So $-9.8t+4=0$

t = 0.408 sec

So at time t = 0.408 sec diver will be at maximum height

5 0

3 years ago

Y=2x+1<br> y=-x+4<br><br> It's a system of equation

MrRissso [65]

Since y=y. set the equations equal to each then solve
2x + 1 = -x + 4
+x +x
3x + 1 = 4
-1 -1
3x = 3
/3 /3
x = 1

8 0

3 years ago

Two surfers and statistics students collected data on the number of days on which surfers surfed in the last month for 30 longbo

Alisiya [41]

Answer:

Do not reject H0. The mean days surfed for longboarders is significantly larger than the mean days surfed for all shortboarders

Step-by-step explanation:

The null hypothesis is that the mean days surfed for all long boarders is larger than the mean days surfed for all short boarders

H0: μL > μs against the claim Ha: μL≤ μs

the alternate hypothesis is the mean days surfed for all long boarders isless or equal to the mean days surfed for all short boarders (because long boards can go out in many different surfing conditions)

The test statistic is

t= x1- x2/ √s1/n1+ s2/n2

1) Calculations

Longboards

Mean

ˉx=∑x/n=4+8+9+4+9+7+9+6+6+11+15+13+16+12+10+12+18+20+15+10+15+19+21+9+22+19+23+13+12+10/30

=377/30

=12.5667

Longboard Variance S2=[∑dx²-(∑dx)²/n]/n-1

=[831-(-13)²/30]/29

=831-5.6333/29

=825.3667/29

=28.4609

Shortboard Mean

ˉx=∑x/n=6+4+6+6+7+7+7+10+4+6+7+5+8+9+4+15+13+9+12+11+12+13+9+11+13+15+9+19+20+11/30

=288/30

=9.6

Shortboard Variance S2=[∑x²-(∑x)²/n]/n-1

=[ 3270-(288)2/30]/29

=3270-2764.8/29

=505.2/29

=17.4207

2) Putting values in the test statistic

t=|x1-x2|/√S²1/n1+S²2/n2

t =|12.5667-9.6|/√28.4609/30+17.4207/30

t =|2.9667|/√0.9487+0.5807

t=|2.9667|/√1.5294

t=|2.9667|/1.2367

t=2.3989

3) Degree of freedom =n1+n2-2=30+30-2=58

4) The critical region is t ≤ t(0.05) (58) =1.6716

5) Since the calculated t= 2.4 does not fall in the critical region t(0.05) (58) ≤ 1.6716 we do not reject H0.

The p-value is 0.008969. The result is significant at p <0 .05.

6 0

3 years ago

NEED HEELLLLPPPPPP!!

Tju [1.3M]

It looks equivalent.

Do the Pythagorean theorem on the triangle shown.
2.1^2-1.4^2

4.2-1.96=2.24

Sqrt of 2.24 is 1.496 or 1.5
Now multiply this by 2 to get the length of x

HOPE THIS HELPS

6 0

2 years ago

The school cafeteria offers three choices for the main course (peanut

Elena-2011 [213]

Answer: 18 different combinations

Step-by-step explanation: When finding out combinations, you just multiply all the numbers. In this case, it would be 3x2x3 which equals 18. Please mark brainliest <3

6 0

2 years ago