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Shalnov [3]
3 years ago
7

A large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 96 feet per second. T

he function h(t) = 96 t − 16 t 2 gives the height of the falling debris above the ground, in feet, t seconds after the explosion. A) Use the given function to find the height of the debris 2 second(s) after the explosion: Answer: After 2 second(s), the height is 112 Incorrect feet.
Mathematics
1 answer:
Vladimir [108]3 years ago
5 0

Answer:

the height after 2 seconds will be 128 feet

Step-by-step explanation:

Data provided in the question:

Initial velocity = 96 feet per second

The function of height of falling debris above the ground is given as:

h(t) = 96t - 16t²

A) To find height after time t = 2 seconds

substituting the value of time in the above function, we get

h(t) = 96 × 2 - 16 × 2²

or

h(t) = 192 - 16 × 4

or

h(t) = 192 - 64

or

h(t) = 128 feet

Hence,

the height after 2 seconds will be 128 feet

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The radius of a cylinder is 3x - 2 cm. The height of the cylinder is x + 3 cm. What is the surface area of the cylinder? Use the
Anestetic [448]
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= 2 pi (9x^2 - 12x + 4 + 3x^2 + 7x - 6

= 2pi(12x^2 - 5x - 2)

Its D
7 0
3 years ago
If f(x) =x-3 then find f^-1 (x)
Pepsi [2]

Answer:   x+3

The original function tells us to subtract 3 from the input x.

The inverse function will do the exact opposite: it adds 3 to the input x.

4 0
3 years ago
Suppose the expected tensile strength of type-A steel is 103 ksi and the standard deviation of tensile strength is 7 ksi. For ty
ExtremeBDS [4]

Answer:

a

i So  the approximate distribution of \= X is \mu_{\= X} =103 and  \sigma_{\= X} = 0.783

ii So the approximate distribution of \= Y is \mu_{\= Y} =105 and  \sigma_{\= Y} = 0.645

b

 the approximate distribution of  \=X  - \= Y is E (\= X - \= Y)  = -2 and  \sigma_{\= X  - \=Y}=1.029

Here we can see that the mean of the approximate distribution is negative which tell us that this negative value of the  data for  \=X  - \= Y sample   are more and their frequency occurrence is higher than the positive values  

c

the value of  P(-1 \le \=X - \= Y  \le 1) is = -0.1639    

Step-by-step explanation:

From the question we are given that

       The expected tensile strength of the type A steel is  \mu_A = 103 ksi

        The standard deviation of type A steel is  \sigma_A = 7ksi

         The expected tensile strength of the type B steel is \mu_B = 105\ ksi

            The standard deviation of type B steel is  \sigma_B = 5 \ ksi

Also the assumptions are

       Let \= X be the sample average tensile strength of a random sample of 80 type-A specimens

Here n_a =80

      Let \= Y be  the sample average tensile strength of a random sample of 60 type-B specimens.

  Here n_b = 60

Let the sampling distribution of the mean be

             \mu _ {\= X} = \mu

                   =103

 Let the sampling distribution of the standard deviation be

               \sigma _{\= X} = \frac{\sigma }{\sqrt{n_a} }

                     = \frac{7}{\sqrt{80} }

                    =0.783

So What this mean is that the approximate distribution of \= X is \mu_{\= X} =103 and  \sigma_{\= X} = 0.783

For \= Y

 The sampling distribution of the sample mean is

               \mu_{\= Y} = \mu

                    = 105

  The sampling distribution of the standard deviation is

               \sigma _{\= Y} = \frac{\sigma }{\sqrt{n_b} }

                    = \frac{5}{\sqrt{60} }

                    = 0.645

So What this mean is that the approximate distribution of \= Y is \mu_{\= Y} =105 and  \sigma_{\= Y} = 0.645                      

Now to obtain the approximate distribution for \=X  - \= Y

               E (\= X - \= Y) = E (\= X) - E(\= Y)

                                =  \mu_{\= X} - \mu_{\= Y}

                                = 103 -105

                                = -2

The standard deviation of \=X  - \= Y is

               \sigma_{\= X  - \=Y} = \sqrt{\sigma_{\= X}^2 - \sigma_{\= Y}^2}

                         = \sqrt{(0.783)^2 + (0.645)^2}

                         =1.029

Now to find the value of  P(-1 \le \=X - \= Y  \le 1)

  Let us assume that F = \= X - \= Y

    P(-1 \le F \le 1) = P [\frac{-1 -E (F)}{\sigma_F} \le Z \le  \frac{1-E(F)}{\sigma_F} ]

                             = P[\frac{-1-(-2)}{1.029}  \le  Z \le  \frac{1-(-2)}{1.029} ]

                             =  P[0.972 \le Z \le 2.95]

                             = P(Z \le 0.972) - P(Z \le 2.95)

Using the z-table to obtain their z-score

                             = 0.8345 - 0.9984

                             = -0.1639

                   

3 0
3 years ago
Extra points
weqwewe [10]

Answer:

Sale tax rate = 7.5%

Step-by-step explanation:

The book cost $12.95

If you take 12.95 x 0.075 = 0.97125

Round the answerto the hundredth (0.97)

Add the tax, 12.95 + 0.97 = 13.92

5 0
3 years ago
28/29 and 30 plz short explanation thanks
zzz [600]

Integers are numbers like ...-3, -2, -1, 0, 1, 2, 3... and so on. So, according to this definition, let's solve this problem:


28. We know that the product of three integers is -3. So, the statement states that we have three factor, so:


a.b.c = -3


The possible values of the factors are:

  • Factors are: 3, 1 and -1 in which case:

(3)(1)(-1) = -3

  • Factors are: -3, 1 and 1 in which case:

(-3)(1)(1) = -3


29. In this problem we know two nonzero integers, that is, they cannot be equal to zero. Thus, they must have different sign, that is, one of them must be positive and the other negative. For instance:


  • -9 and 2

(-9)(2) = -18, So -18 is less than -9 and 2


Another example:


  • 1 and -8

(1)(-8) = -8, So -8 is equal to -8 and -8 is less than 1.


30. The sign of the product of two integers with the same sign is positive, that is:


(+)(+) = (+) and

(-)(-) = (+)


So, the sign of the product of three integers with the same sign are two options:

  • <u>Option 1.</u> The three integers are positive in which case:

(+)(+)(+) = (+), So the sign of the product is positive


  • <u>Option 2.</u> The three integers are negative in which case:

(-)(-)(-) = (-), So the sign of the product is negative.


This option two gives us that result because:


(-)(-) = (+) and (+)(-) = (-)

5 0
3 years ago
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