Less than a number is 18. What is the number (n)?

An explosion causes debris to rise vertically with an initial speed of 120 feet per second. The formula h equals negative 16 t s

Novay_Z [31]

Answer:

The debris will be at a height of 56 ft when time is <u>0.5 s and 7 s.</u>

Step-by-step explanation:

Given:

Initial speed of debris is, $s=120\ ft/s$

The height 'h' of the debris above the ground is given as:

$h(t)=-16t^2+120t$

As per question, $h(t)=56\ ft$ . Therefore,

$56=-16t^2+120t$

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

$-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0$

Using quadratic formula to solve for 't', we get:

$t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s$

Therefore, the debris will reach a height of 56 ft twice.

When time $t=0.5\ s$ during the upward journey, the debris is at height of 56 ft.

Again after reaching maximum height, the debris falls back and at $t=7\ s$ , the height is 56 ft.

5 0

3 years ago

This is just 2 real easy sentences. im just too lazy to do them its not actual math problems though don't worry.

Anika [276]

Hey!

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Answer - A job that uses geometry and symmetry is an Architect.

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Architect - geometry is structural and symmetry are shapes and figures that can be split and still look the same. Being an architect shows how geometric structures are transformed, then symmetry are design concepts throughout the plans of transformation.

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Hope This Helped! Good Luck!

7 0

3 years ago

Read 2 more answers

Rewrite the following equation in logarithmic form and exponential form

Slav-nsk [51]

Answer:The answer for the first one is log2(.25)=-2

The answer for the second one is 8^3=512

Step-by-step explanation:

7 0

3 years ago

What is eight thirds equivilent to

STatiana [176]

Eight thirds (also known as 8/3) is equivalent to two and two thirds (numerically written: 2 2/3). Explanation: to solve this, find out god many times 3 can fit into eight. Three can fit into eight 2 times (since 3*2 is 6), which leaves you with 2 left. Since this remainder of 2 can not be divided by 3, it is put into a fraction of 2/3. Therefore, the answer is 2 2/3.

3 0

4 years ago

Read 2 more answers

Adult tickets to the fall play cost $8 and student tickets cost $4. the drama class sold 20 more adult tickets than student tick

Ganezh [65]

Let a = Adult tickets, s = Student tickets; we are going to set up a system of equations.

8a + 4s = 880
a - s = 20

We are going to multiply the second equation by so that we can cancel out one of the variables and solve for the other. This gives you:

8a + 4s = 880
4a - 4s = 20

Notice the s-variables will cancel:

12a = 900
a = 75

Now we plug in the amount of adult tickets to solve for the student ones.

75 - s = 20
- s = - 55

Divide both sides by - 1
s = 55.

There were 55 student tickets sold and 75 adult tickets.

6 0

3 years ago