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wolverine [178]
3 years ago
10

A ball is thrown vertically upward with an initial velocity of 48 feet per second. The distance s​ (in feet) of the ball from th

e ground after t seconds is s = 48 t -16 t ^2. ​(a) At what time t will the ball strike the​ ground? ​(b) For what time t is the ball more than 32 feet above the​ ground?

Mathematics
1 answer:
ra1l [238]3 years ago
5 0
Hello,

s=48t-16t²

a)
s=0==>16t(3-t)=0==>t=0 or t=3

b)
s>32==>48t-16t²>32===>16(t²-3t+2)<0
Δ=9-8=1
==>16(t-1)(t-2)<0

==>1<t<2 (negative between the roots)

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Consider the parabola r​(t)equalsleft angle at squared plus 1 comma t right angle​, for minusinfinityless thantless thaninfinity
kodGreya [7K]

Given:-   r(t)=< at^2+1,t>  ; -\infty < t< \infty , where a is any positive real number.

Consider the helix parabolic equation :  

                                              r(t)=< at^2+1,t>

now, take the derivatives we get;

                                            r{}'(t)=

As, we know that two vectors are orthogonal if their dot product is zero.

Here,  r(t) and r{}'(t)  are orthogonal i.e,   r\cdot r{}'=0

Therefore, we have ,

                                  < at^2+1,t>\cdot < 2at,1>=0

< at^2+1,t>\cdot < 2at,1>=

                                              =2a^2t^3+2at+t

2a^2t^3+2at+t=0

take t common in above equation we get,

t\cdot \left (2a^2t^2+2a+1\right )=0

⇒t=0 or 2a^2t^2+2a+1=0

To find the solution for t;

take 2a^2t^2+2a+1=0

The numberD = b^2 -4ac determined from the coefficients of the equation ax^2 + bx + c = 0.

The determinant D=0-4(2a^2)(2a+1)=-8a^2\cdot(2a+1)

Since, for any positive value of a determinant is negative.

Therefore, there is no solution.

The only solution, we have t=0.

Hence, we have only one points on the parabola  r(t)=< at^2+1,t> i.e <1,0>




                                               




6 0
3 years ago
In your own words, explain to me what is absolute value? Make sure to talk about the definition of it, how you find it, and how
Tom [10]

Answer:

It's a function that associates a real number x with a positive real number using the flowing definition: If the number is not negative (so either positive or 0) the absolute value is x. If x is negative, the absolute value is -x.

This means that to find the absolute value of x you must first determine if x is negative or not, and if it is, multiply it by -1. If it isn't, leave it as it is.

Since the absolute value is a function (of a given number), you can't just plot that number in the number line but the function (so in this case absolute value must be taken first.

The absolute value of x is never negative, so given the absolute value of x we can't determinate if x was positive or negative (if x =/ 0) before the absolute value was taken.

4 0
2 years ago
WORTH 100 POINTS NEED DONE ASAP WRONG ANSWERS WILL BE REPORTED THANK YOUUU
zysi [14]

Answer:

3.

1.x=√(15²-12²)=√81=9

2.x=√(6²+6²)=6√2

3.c=√(√19²-√7²)=√(19-7)=√12

Step-by-step explanation:

4.h=10

a=b=x

we have

by using Pythagoras law

h²=x²+x²

100=2x²

x²=50

x=√50=5√2

both legs =5√2

7 0
3 years ago
Jose purchased 4/9 pound of peanut and 7/11 pounds of raisins find the total weight of his purchase
azamat

Answer:

The total weight of his purchase is 1.08 pounds

Step-by-step explanation:

To find the total weight of his purchase, we sum the weight of each of his purchases.

He purchased:

4/9 pound of peanut.

7/11 pounds of raisins

Total:

The least common multiple between 9 and 11 is 99.

Then

\frac{4}{9} + \frac{7}{11} = \frac{11*4 + 9*7}{99} = \frac{107}{99} = 1.08

The total weight of his purchase is 1.08 pounds

8 0
3 years ago
Find the value of x. Round your answer to the nearest tenth.
Crazy boy [7]
<h2>The value of x "option A) 12.5" is required answer.</h2>

Step-by-step explanation:

In given figure,

Base (b) = 11 and Angle = 28°

To find, the value of x = ?

We know that,

\cos A=\dfrac{b}{h}

Where, h is the hypotaneous = x

⇒ \cos 28=\dfrac{11}{x}

⇒ x=\dfrac{11}{\cos 28}

The value of \cos 28 = 0.8829

⇒ x = \dfrac{11}{0.8829}

⇒ x = 12.458

⇒ x ≈ 12.5

∴ The value of x ≈ 12.5

Thus, the value of x "option A) 12.5" is required answer.

7 0
3 years ago
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