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2 years ago

What is the GCF of 36 and 68?

Mathematics

2 answers:

NeTakaya2 years ago

4 0

Answer:

The greatest common factor of 36 and 68 is 4

Step-by-step explanation:

36÷4=9

68÷4=17

andreev551 [17]2 years ago

3 0

Answer:

Step-by-step explanation:

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I am a 2 dimensional shape that had 5 obtuse angles

Montano1993 [528]

Answer:

A pentagon.

Step-by-step explanation:

A pentagon is a 5-sided polygon. Its interior angles each are equivalent to 108°.

108° ≥ 90°, so the angles are obtuse.

Therefore, a 2-D shape with 5 obtuse angles is a <u>pentagon</u>.

5 0

2 years ago

A cell phone cost $210 a battery charger costs $15 and batteries cost $5 .what is the sales tax and total price for purchasing t

Savatey [412]

The total price with sales tax is $ 246.1

<h3><u>Solution:</u></h3>

Cost of cellphone = $ 210

Cost of battery charger = $ 15

Cost of batteries = $ 5

So total cost can be calculated by adding cost of cellphone and Cost of battery charger and Cost of batteries

Total cost = 210 + 15 + 5 = $ 230

Given that sales tax is 7%

sales tax = 7% of total cost

sales tax = 7 % of 230

$\text {sales tax }=\frac{7}{100} \times 230=16.1$

Total cost including sales tax = 230 + 16.1 = $ 246.1

Thus the total price with sales tax is $ 246.1

3 0

2 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

2 years ago

Which function has the greater rate of change?

Gnoma [55]

Answer:

Function 1

Step-by-step explanation:

<u>Function 1:</u>

$y=\dfrac{5}{6}x+10$

The rate of change of the function 1 is:

$\dfrac{5}{6}\approx 0.83$

<u>Function 2:</u>

The rate of change of the function 2 is:

$\dfrac{15.75-14.25}{1-(1)}=\dfrac{1.5}{2}=0.75$

Hence, the greater rate of change has function 1.

3 0

2 years ago

What is the base (in inches) of a triangle with an area of 161 square inches and a height of 14 inches?

pantera1 [17]

$\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ h=14\\ A=161 \end{cases}\implies 161=\cfrac{1}{2}b(14) \\\\\\ 161=7b\implies \cfrac{161}{7}=b\implies 23=b$

7 0

1 year ago