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bekas [8.4K]
3 years ago
14

Crickets can jump with a vertical velocity of up to 14 ft/s. Which equation models the height of such a jump, in feet, after t s

econds? h(t) = –16t2 + v0t + h0
h(t) = –16t2 + v0t + 14

h(t) = –16t2 + 14t

h(t) = –16t2 + 14t + 14
Mathematics
2 answers:
Natasha_Volkova [10]3 years ago
8 0
Acceleration is simplified by assuming it is the constant -g

a=-g  we integrate this with respect to time to get v...

v=-gt+C  where C is the initial velocity in this case 14ft/s so

v=-gt+14  integrate again to get the height function

h=(-gt^2)/2 +14t +C  we are not given an initial height so C is 0

h(t)=14t-gt^2/2   letting g=32 and neatening up a bit...

h(t)=14t-16t^2
Vlada [557]3 years ago
4 0

Answer:

Option 3. h(t) = -16t² + 14t

Step-by-step explanation:

As we know the formula of motion under gravity is

h = ut - (1/2)gt²

Here h is the height covered by the cricket with vertical velocity u and (-g) is the gravitational pull downwards.

Since the value of g = 9.8 mt/sec²

It can be written in feet as g = 32 feet/sec²

Vertical velocity of the crickets u = 14 ft/sec

Now by putting these values in the formula

h = 14t - (1/2)×32×t²

h = 14t - 16t²

we can rewrite this equation in the form of function

h(t) = -16t² + 14t

So the answer is Option 3. h(t) = -16t² + 14t

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Answer:

after sprouting it lived for 100 days

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A random sample of n = 45 observations from a quantitative population produced a mean x = 2.5 and a standard deviation s = 0.26.
oee [108]

Answer:

P-value (t=2.58) = 0.0066.

Note: as we are using the sample standard deviation, a t-statistic is appropiate instead os a z-statistic.

As the P-value (0.0066) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the population mean μ exceeds 2.4.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the population mean μ exceeds 2.4.

Then, the null and alternative hypothesis are:

H_0: \mu=2.4\\\\H_a:\mu> 2.4

The significance level is 0.05.

The sample has a size n=45.

The sample mean is M=2.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.26.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.26}{\sqrt{45}}=0.0388

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.5-2.4}{0.0388}=\dfrac{0.1}{0.0388}=2.58

The degrees of freedom for this sample size are:

df=n-1=45-1=44

This test is a right-tailed test, with 44 degrees of freedom and t=2.58, so the P-value for this test is calculated as (using a t-table):

P-value=P(t>2.5801)=0.0066

As the P-value (0.0066) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the population mean μ exceeds 2.4.

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3 years ago
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fiasKO [112]
C is the correct answer
4 0
3 years ago
Mr. Musah withdrew some money from the bank. He gave ½ of it to his son and ⅓ to his daughter. if he had GH¢ 500.00 left, how mu
Savatey [412]

Answer:

GH 3000.00

Step-by-step explanation:

1/2 + 1/3 = 5/6

   6/6-5/6=1/6

  6/6 X 500.00 X6/1

 GH 3000.00

5 0
3 years ago
A square on a coordinate plane has the points A(0, 0), B(0, 5), C(5, 5) and D(5, 0). If Square ABCD is rotated about the origin
Georgia [21]

Answer:

B. 5 units

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Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, dilation, rotation or translation.

If a point X(x,y) is rotated about the origin 180 degrees clockwise the new point is at X'(-x, -y).

If the square with vertices at A(0, 0), B(0, 5), C(5, 5) and D(5, 0) is rotated about the origin 180 degrees clockwise the new points are at A'(0, 0), B'(0, -5), C'(-5, -5), D'(-5, 0)

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|XY|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Hence:

|A'B'|=\sqrt{(0-0)^2+(-5-0)^2} =5

3 0
3 years ago
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