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3 years ago

The sum of 4 squared and a number t

Mathematics

2 answers:

drek231 [11]3 years ago

7 0

Answer:

16+t

4^2+t would give you this answer

BartSMP [9]3 years ago

3 0

Answer:

4^2 + t

Step-by-step explanation:

<u>Step 1: Change words into an expression</u>

Sum of 4 squared and number t

4^2 + t

Answer: 4^2 + t

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At Westside middle school there are 42 classrooms with a 28 desks in each. About how many desks are there?

Marianna [84]

42*28=1176.
There are 1176 desks

5 0

3 years ago

If Roger were 32 years older, he would be three times as old as he is now. How old is<br> Roger?

stellarik [79]

Answer:

Step-by-step explanation:

Set up the equation ->

x+32=3x

(you can get this easily by writing the equation down as you read the problem)

--> revisiting x+32=3x

-x on both sides to isolate the number and put the like terms together

We are left with 32=2x

Divide 2 on both sides, and you will get x (his current age) --> x=16

Roger is currently 16 years old.

6 0

2 years ago

Read 2 more answers

What is the approximate volume of a cylinder with a height of 2 ft and a radius of 6 ft?

patriot [66]

We know, Volume of a Cylinder = πr²h
Here, r= 6 & h = 2

Substitute their values into the expression:
V = 3.14 * (6)² * 2
V = 3.14 * 36 * 2
V = 3.14 * 72
V = 226.08

In short, Your Answer would be 226.08 Ft³

Hope this helps!

5 0

3 years ago

On an alien planet with no atmosphere, acceleration due to gravity is given by g = 12m/s^2. A cannonball is launched from the or

almond37 [142]

Answer:

a) $\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$ , b) $\theta = \frac{\pi}{4}$ , c) $y_{max} = 84.375\,m$ , $t = 3.75\,s$ .

Step-by-step explanation:

a) The function in terms of time and the inital angle measured from the horizontal is:

$\vec r (t) = [(v_{o}\cdot \cos \theta)\cdot t]\cdot i + \left[(v_{o}\cdot \sin \theta)\cdot t -\frac{1}{2}\cdot g \cdot t^{2} \right]\cdot j$

The particular expression for the cannonball is:

$\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$

b) The components of the position of the cannonball before hitting the ground is:

$x = (90\cdot \cos \theta)\cdot t$

$0 = 90\cdot \sin \theta - 6\cdot t$

After a quick substitution and some algebraic and trigonometric handling, the following expression is found:

$0 = 90\cdot \sin \theta - 6\cdot \left(\frac{x}{90\cdot \cos \theta} \right)$

$0 = 8100\cdot \sin \theta \cdot \cos \theta - 6\cdot x$

$0 = 4050\cdot \sin 2\theta - 6\cdot x$

$6\cdot x = 4050\cdot \sin 2\theta$

$x = 675\cdot \sin 2\theta$

The angle for a maximum horizontal distance is determined by deriving the function, equalizing the resulting formula to zero and finding the angle:

$\frac{dx}{d\theta} = 1350\cdot \cos 2\theta$

$1350\cdot \cos 2\theta = 0$

$\cos 2\theta = 0$

$2\theta = \frac{\pi}{2}$

$\theta = \frac{\pi}{4}$

Now, it is required to demonstrate that critical point leads to a maximum. The second derivative is:

$\frac{d^{2}x}{d\theta^{2}} = -2700\cdot \sin 2\theta$

$\frac{d^{2}x}{d\theta^{2}} = -2700$

Which demonstrates the existence of the maximum associated with the critical point found before.

c) The equation for the vertical component of position is:

$y = 45\cdot t - 6\cdot t^{2}$

The maximum height can be found by deriving the previous expression, which is equalized to zero and critical values are found afterwards:

$\frac{dy}{dt} = 45 - 12\cdot t$

$45-12\cdot t = 0$

$t = \frac{45}{12}$

$t = 3.75\,s$

Now, the second derivative is used to check if such solution leads to a maximum:

$\frac{d^{2}y}{dt^{2}} = -12$

Which demonstrates the assumption.

The maximum height reached by the cannonball is:

$y_{max} = 45\cdot (3.75\,s)-6\cdot (3.75\,s)^{2}$

$y_{max} = 84.375\,m$

7 0

3 years ago

Find the 11th term of the geometric sequence 6, -18, 54

Nataly [62]

I don’t feel like doing it but I we’ll tell you how to do it you multiply it by 3 so 6 x 3 equals 18 just in negative do 18 x 3 equal 54 so every other on is a negative it’s Simone

4 0

3 years ago