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nordsb [41]
3 years ago
13

What is the prime factorization of 96? 8 · 12 2 · 2 · 2 · 2 · 3 25 · 3 25 · 32

Mathematics
1 answer:
olganol [36]3 years ago
8 0
96
/ \
8 • 12
/ \ / \
4 • 2 • 4 • 3
/ \ / \
2 2 2 2
96 is 2•2•2•2•2•3 or 2^5•3
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Christopher can eat 8 bags of skittles in 5 minutes. What is his rate per minute? Round your answer to the nearest hundredth. At
Dennis_Churaev [7]
<span>8/5 = 1.6 bag per minute

8 bags of skittles in 5 minutes
?                              10 minutes

8 x 10 / 5 
= 80 /5
= 16

answer
</span>1.6 bag per minute
<span>and
16 bags in 10 minutes</span>
7 0
3 years ago
A 140 kg camera is suspended by two wires over a 40 metre wide football field to get shots of the action from above. At one poin
Katen [24]

Answer:

Please red the answer below

Step-by-step explanation:

In order to determine the length of each cable you use the Newton second law for each component of the forces involved in the situation.

For the x component you have:

T_1cos\theta_1-T_2cos\theta_2=0           (1)

T1: tension of the first cable = 1500N

T2: tension of the second cable = 800N

θ1: angle between the horizontal and the first cable

θ2: angle between the horizontal and the first cable

For the y component you have:

T_1sin\theta_1+T_2sin\theta_2-W=0               (2)

W: weight of the camera = Mg = (140kg)(9.8m/s^2) = 1372N

You can squared both equations (1) and (2) and the sum the two equations:

T_1^2cos^2\theta_1=T_2^2cos^2\theta_2\\\\T_1^2sin^2\theta_1=T_2^2sin^2\theta_2-2WT_2sin\theta_2+W^2

Then, you sum the equations:

T_1^2(cos^2\theta_1+sin^2\theta_1)=T_2^2(sin^2\theta_2+cos^2\theta_2)-2Wsin\theta_2+W^2        (3)

Next, you use the following identity:

sin^2\theta+cos^2\theta=1

and you obtain in the equation (3):

T_1^2=T_2^2-2WT_2sin\theta_2+W^2\\\\sin\theta_2=\frac{T_2^2-T_1^2+W^2}{2WT_2}=\frac{(800N)^2-(1500)^2+(1372N)^2}{2(800N)(1372N)}=0.066\\\\\theta_2=sin^{-1}0.066=27.23\°

With this values you can calculate the value of the another angle, by using the equation (1):

\theta_1=cos^{-1}(\frac{T_2cos(27.23\°)}{T_1})=cos^{-1}(\frac{(800N)(cos27.23\°)}{1500N})\\\\\theta_1=61.69\°

Now, you can calculate the length of each cable by using the information about the width of the football field. You use the following trigonometric relation:

l_1cos\theta_1=40-d\\\\l_2cos\theta_2=d\\\\

d: distance to the right side of the field

By using the cosine law you can fins a system of equation and then you can calculate the values of l1 and l2.

3 0
2 years ago
4x - Зу = -3<br> 4x + y = 17<br> Explain how as well
Jobisdone [24]

Step-by-step explanation:

I will solve your system by substitution.

(You can also solve this system by elimination.)

4x+y=17;4x−3y=−3

Step: Solve4x+y=17for y:

4x+y+−4x=17+−4x(Add -4x to both sides)

y=−4x+17

Step: Substitute−4x+17foryin4x−3y=−3:

4x−3y=−3

4x−3(−4x+17)=−3

16x−51=−3(Simplify both sides of the equation)

16x−51+51=−3+51(Add 51 to both sides)

16x=48

16/x = 48/16

(Divide both sides by 16)

x=3

Step: Substitute 3 for x in y=−4x+17:

y=−4x+17

y=(−4)(3)+17

y=5(Simplify both sides of the equation)

Answer:

x=3 and y=5

6 0
2 years ago
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Alla [95]
2 multiply by 4 is 8 , 8 multiply 3 is 24
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I think its 384 because if you multiply the two numbers underneath then you get 384 which is how they got all the other numbers

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