The height of a projectile fired upward is given by the formula
s = v0t − 16t2,
where s is the height in feet,
v0
is the initial velocity, and t is the time in seconds. Find the time for a projectile to reach a height of 96 ft if it has an initial velocity of 128 ft/s. Round to the nearest hundredth of a second.

Ans; 7× [2-6 { 1+66}] —> 7× [2 - 6 { 67} ] —> 7× [2-402] —> 7×[- 400] —> = – 2800

I hope I helped you ^_^

Hello there!

Previously, we learnt that to solve the equation, we have to isolate the sin, cos, tan, etc first.

First Question

The first question has sin both sides. Notice that if we move sin(theta) to left. We get:-

[tex] \displaystyle \large{2 {sin}^{2} \theta - sin \theta = 0}[/tex]

We can common factor out the expression.

[tex] \displaystyle \large{sin \theta(2sin \theta - 1) = 0}[/tex]

It is a trigonometric equation in quadraric pattern.

We consider both equations:-

First Equation

[tex] \displaystyle \large{sin \theta = 0}[/tex]

Remind that sin = y. When sin theta = 0. It means that it lies on the positive x-axis.

We know that 0 satisfies the equation, because sin(0) is 0.

Same goes for π as well, but 2π does not count because the interval is from 0 ≤ theta < 2π.

Hence:-

[tex] \displaystyle \large { \theta = 0,\pi}[/tex]

Second Equation

[tex] \displaystyle \large{2sin \theta - 1 = 0}[/tex]

First, as we learnt. We isolate sin.

[tex] \displaystyle \large{sin \theta = \frac{1}{2} }[/tex]

We know that, sin is positive in Quadrant 1 and 2.

As we learnt from previous question, we use π - (ref. angle) to find Q2 angle.

We know that sin(π/6) is 1/2. Hence π/6 is our reference angle. Since π/6 is in Q1, we only have to find Q2.

Find Quadrant 2

[tex] \displaystyle \large{\pi - \frac{\pi}{6} = \frac{6\pi}{6} - \frac{\pi}{6} } \\ \displaystyle \large{ \frac{5\pi}{6} }[/tex]

Hence:-

[tex] \displaystyle \large{ \theta = \frac{\pi}{6} , \frac{5\pi}{6} }[/tex]

Since both first and second equations are apart of same equation. Therefore, mix both theta from first and second.

Therefore, the solutions to the first question:-

[tex] \displaystyle \large \boxed{ \theta = 0,\pi, \frac{\pi}{6} , \frac{5\pi}{6} }[/tex]

Second Question

This one is a reciprocal of tan, also known as cot.

[tex] \displaystyle \large{cot3 \theta = 1}[/tex]

For this, I will turn cot to 1/tan.

[tex] \displaystyle \large{ \frac{1}{tan3 \theta} = 1}[/tex]

Multiply whole equation by tan3 theta, to get rid of the denominator.

[tex] \displaystyle \large{ \frac{1}{tan3 \theta} \times tan3 \theta = 1 \times tan3 \theta } \\ \displaystyle \large{ 1= tan3 \theta }[/tex]

We also learnt about how to deal with number beside theta.

We increase the interval, by multiplying with the number.

Since our interval is:-

[tex] \displaystyle \large{0 \leqslant \theta < 2\pi}[/tex]

Multiply the whole interval by 3.

[tex] \displaystyle \large{0 \times 3 \leqslant \theta \times 3 < 2\pi \times 3} \\ \displaystyle \large{0 \leqslant 3 \theta < 6\pi }[/tex]

We also know that tan is positive in Quadrant 1 and Quadrant 3.

and tan(π/4) is 1. Therefore, π/4 is our reference angle and our first theta value.

When we want to find Quadrant 3, we use π + (ref. angle).

Find Q3

[tex] \displaystyle \large{\pi + \frac{\pi}{4} } = \frac{5\pi}{4} [/tex]

Hence, our theta values are π/4 and 5π/4. But that is for [0,2π) interval. We want to find theta values over [0,6π) interval.

As we learnt previously, that we use theta + 2πk to find values that are in interval greater than 2π.

As for tangent, we use:-

[tex] \displaystyle \large{ \theta + \pi k = \theta}[/tex]

Because tan is basically a slope or line proportional graph. So it gives the same value every π period.

Now imagine a unit circle, and make sure to have some basic geometry knowledge. Know that when values addition by 180° or π would give a straight angle.

We aren't using k = 1 for this because we've already found Q3 angle.

Since we know Q1 and Q3 angle in [0,2π).

We can also use theta + 2πk if you want.

First Value or π/4

[tex] \displaystyle \large{ \frac{\pi}{4} + 2\pi = \frac{9\pi}{4} } \\ \displaystyle \large{ \frac{\pi}{4} + 4\pi = \frac{17\pi}{4} }[/tex]

Second Value or 5π/4

[tex] \displaystyle \large{ \frac{5\pi}{4} + 2\pi = \frac{13\pi}{4} } \\ \displaystyle \large{ \frac{5\pi}{4} + 4\pi = \frac{21\pi}{4} }[/tex]

Yes, I use theta + 2πk for finding other values.

Therefore:-

[tex] \displaystyle \large{3 \theta = \frac{\pi}{4} , \frac{5\pi}{4} , \frac{9\pi}{4}, \frac{17\pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} }[/tex]

Then we divide every values by 3.

[tex] \displaystyle \large \boxed{\theta = \frac{\pi}{12} , \frac{5\pi}{12} , \frac{9\pi}{12}, \frac{17\pi}{12} , \frac{13\pi}{12} , \frac{21\pi}{12} }[/tex]

Let me know if you have any questions!

A sample of size n taken from a normally distributed population with mean µ and standard deviation σ has a sample mean of µ and standard deviation of σ/√n.

So the sample mean would still be 180.1, while the sample standard deviation would be 100/√94 ≈ 10.31.

Answer:slope 2/3

Y-int 6

Step-by-step explanation:

Answer: 1360 ways.

Step-by-step explanation:

Number of men = 11

Number of women = 8

Total members = 8 + 11 = 19

Firstly, the number of ways of selecting 1 woman for female president out of 8 will be:

= 8C1

= 8

Since Pete can not be a treasurer, then the treasurer will then be selected from the remaining 10(11 - 1). The number of ways of selecting 1 treasurer out of 10 will be:

= 10C1

= 10

Thirdly, since none can hold more then one office, in this case, the selection will be done by selecting 1 person out of 7 women and 10 men. Therefore, the number of ways of selecting 1 person out of 17 will be:

= 17C1

= 17

Therefore, the total number of ways will then be:

= 8 × 10 × 17

= 1360

Answer: 18.75 lb.ft

Step-by-step explanation:

Given

Force required to stretch spring 8 in. is 18 lb

it can be written

[tex]\Rightarrow F=kx\\\Rightarrow 18=k(8)\\\\\Rightarrow k=\dfrac{18}{8}=\dfrac{9}{2}\ lb/in.[/tex]

Work done in stretching from its natural length to 10 in.

[tex]\Rightarrow W=\dfrac{1}{2}kx^2\\\\\Rightarrow W=0.5\times \dfrac{9}{2}\times (10)^2\\\\\Rightarrow W=225\ lb.in.\ or\\\Rightarrow W=18.75\ lb.ft[/tex]

Answers:

a = 2

b = 3

=======================================================

Explanation:

Plug in x = 0 and y = 2 to find that

y = a*b^x

2 = a*b^0

2 = a*1

2 = a

a = 2

Then plug in x = 3 and y = 54 to determine the value of b

y = a*b^x

y = 2*b^x

54 = 2*b^3

2b^3 = 54

b^3 = 54/2

b^3 = 27

b = (27)^(1/3)

b = 3

So we have y = a*b^x update to y = 2*3^x

Answer:

y = 2x - 5

Step-by-step explanation:

[tex]y+3=2(x-1)\\y+3=2x-2\\y+3-3=2x-2-3\\y=2x-5[/tex]

Answer:

x = 20

y = 10

Answered by Gauthmat

9514 1404 393

Answer:

  (2x -11)(x -1)

Step-by-step explanation:

The middle term can be rewritten as a sum using the coefficients of the first and last terms. Then the expression can be factored by pairs of terms.

  2x^2 -13x +11 = 2x^2 -2x -11x +11 = 2x(x -1) -11(x -1)

  = (2x -11)(x -1)

Answer:

6

Step-by-step explanation:

200. Move decimal twice to the left. 1% of 200 is 2. 2*3 is 6.

Answer:

18

Step-by-step explanation:

7-5=2

2x9=18

Answer:

Each kids weight in a chart

Step-by-step explanation:

I chose this because its the most organized way of doing that

Answer:

I think you mean this :

[tex] \sqrt{x - 5} = 6 \\ = > {( \sqrt{x - 5} })^{2} = {6}^{2} \\ = > x - 5 = 36 \\ = > x = 36 + 5 \\ = > x = 41[/tex]

Or,

Square root of x-5=6 is :

[tex] \sqrt{x - 5} \:=\:\sqrt{6} [/tex]

Answer:

(0.2, -1.2)

Step-by-step explanation:

When solving a system of equations by graphing, we first plot the two equations on a graph, then the point of intersection of the two graphs is the solution to the system of equations.

Therefore giving the equations y = - x - 1; and y = 14x - 4, we have to first plot the both linear equations using online geogebra graphing tool. The intersection of both linear graphs is the solution to the problem.

We can see that the point of intersection is A(0.2, -1.2)

Answer:

9 is. ................m.m..mk

Answer:

7 and 4

Step-by-step explanation:

when you multiply 7×4 the answer is 28 and when you add them the answer is 11.

I hope this helps

Answer:

4 and 7

Step-by-step explanation:

xy = 28 ..........1

x + y = 11........2

x = 11 - y.........3

substitute 3 in 1:

(11 - y)*y = 28

-y² + 11y - 28 = 0

y² - 11y + 28 = 0

( y - 7)( y - 4) = 0

y = 7 or y = 4

subs in 2:

x = 4 or x = 7

pairs: (4 ; 7) and (7 ; 4)

Answer:

To maximize the monthly rental profit, 90 units should be rented out.

The maximum monthly profit realizable is $38,200.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

In this question:

Quadratic equation with [tex]a = -12, b = 2160, c = -59000[/tex]

To maximize the monthly rental profit, how many units should be rented out?

This is the x-value of the vertex, so:

[tex]x_{v} = -\frac{b}{2a} = -\frac{2160}{2(-12)} = \frac{2160}{24} = 90[/tex]

To maximize the monthly rental profit, 90 units should be rented out.

What is the maximum monthly profit realizable?

This is p(90). So

[tex]p(90) = -12(90)^2 + 2160(90) - 59000 = 38200[/tex]

The maximum monthly profit realizable is $38,200.

Answer:

(483.981 ; 504.019)

Step-by-step explanation:

Given :

σ = 100

Sample size, n = 661

xbar = 494

We use the Z distribution since we are working with the population standard deviation ;

C.I = xbar ± (Zcritical * σ/√n)

Zcritical at 99% = 2.576

C.I = 494 ± (2.576 * 100/√661)

C.I = 494 ± 10.019

Lower boundary = (494−10.019) = 483.981

Upper boundary = (494+10.019) = 504.019

C.I = (483.981 ; 504.019)

Answer:

$28000

Step-by-step explanation:

12×1000 + 12×1500 = 12000 + 18000 = $30000

the shortfall is the difference between $58000 and $30000

58000 - 30000 = $28000

36 different value meal packages are possible

Step-by-step explanation:

To answer this question, multiply all given numbers together.

4*3*3

12*3

36

Answer:

-1.25

Step-by-step explanation:

you first have to cross multiply

12(b-1)=4(7b+2)

12b-12=28b+8

group the like terms

12b-28b=8+12

-16b/-16=20/-16

b= -1.25

I hope it helps

Step-by-step explanation:

Answer is in the picture..

hope it helps

9514 1404 393

Answer:

  $8414

Step-by-step explanation:

The compound interest formula is useful for this.

  A = P(1 +r/n)^(nt)

where P is the principal invested at annual rate r compounded n times per year for t years. A is the ending balance.

  A = $5000(1 +0.035/2)^(2·15) = $5000·1.0175^30 ≈ $8414.00

Ivan will have $8414 in his account after 15 years.

Answer:

Since, mean of 200 items was 50 and number of items =200

So, mean =50

Also, we know mean = number of itemssum of items

∴50=200sum of items

Sum of items = 200×50=10000

Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88 respectively

Then  misread         instead         Correct item

             92                   192              192-92=100

              8                     88               88-8=80

∴ Correct sum of items =10000+180=10180

∴ Correct mean = number of items/sum of items

=10180/200 =50.9

Answer:

Hello,

203.6

Step-by-step explanation:

Sum of the item first= 50*200=10000

new sum is 10000+(192-92)+(88-8)=10180

New mean=10180/200=50.9

Answer:

+∞.

Step-by-step explanation:

That would be positive infinity.

The extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.

Extreme values of a polynomial are the peaks and valleys of the polynomial—the points where direction changes.

The following steps which are required to find the extreme value of polynomial are:

According to the given question.

We have a polynomial

[tex]f(x) = x^{2} -4[/tex]

Since, in the given polynomial the coefficient of [tex]x^{2}[/tex] is positive . Therefore, the extreme value of the given polynomial is infinity because the value will continue to grow as x increases.

Hence, the extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.

Find out more information about extreme value of a polynomial here:

https://brainly.com/question/16597253

#SPJ2

Quadratic Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a

2x^2 - 3x = 12

2x^2 - 3x - 12 = 0

a = 2

b = -3

c = -12

(--3 +/- sqrt( (-3)^2 - 4(2)(-12) )) / 2(2)

3 +/- sqrt( 9 + 96 ) / 4

3 +/- sqrt(105) / 4

Answers: [tex]\frac{3 + \sqrt{105} }{4}[/tex], [tex]\frac{3 - \sqrt{105} }{4}[/tex]

Hope this helps!

Answer:

The right solution is "68%".

Step-by-step explanation:

The empirical rule is:

[tex]X\sim N(8.43, 1.5)[/tex]

According to the question,

= [tex]P(6.93< \mu < 9.93)[/tex]

= [tex]P(\frac{6.93-8.43}{1.5} < \frac{\mu -8.43}{1.5} < \frac{9.93-8.43}{1.5} )[/tex]

= [tex]P(z(1)-P(z(-1))[/tex]

= [tex]68[/tex] (%)

Thus the above is the right solution.

Answer:

170.7

Step-by-step explanation:

We are aware that the base is a square, with side lengths 8cm, and we are given that the height is 8 cm. Since the volume of a square based pyramid is 1/3 x base area x height, we receive 1.3 x 64 x 8 which is 512/3 which is in turn 170.666 recurring. However, since this question asks you to round the the nearest tenth, you get 170.7

Answer:

A

Step-by-step explanation:

It just makes the most sense