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3 years ago

13

Mario has $15. He spends $6.25 on admission to the ice skating rink. How much money does he

1 answer:

Ksenya-84 [330]3 years ago

4 0

Answer:

$8.75 is the answer hope this helps

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Three forces act on an object. Two of the forces are at an angle of 95◦ to each other and have magnitudes 35 N and 7 N. The thir

Cerrena [4.2K]

We want to find $\vec F_4$ such that the object needs is in equilibrium:

$\vec F_1+\vec F_2+\vec F_3+\vec F_4=\vec0$

We're told that $F_1=35\,\mathrm N$ , $F_2=7\,\mathrm N$ , and $F_3=9\,\mathrm N$ . We also know the angle between $\vec F_1$ and $\vec F_2$ is 95º, which means

$\vec F_1\cdot\vec F_2=F_1F_2\cos95^\circ=245\cos95^\circ$

$\vec F_3$ is perpendicular to both $\vec F_1$ and $\vec F_2$ , so $\vec F_1\cdot\vec F_3=\vec F_2\cdot\vec F_3=0$ .

If we take the dot product of $\vec F_1$ with the sum of all four vectors, we get

$\vec F_1\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0$

$\vec F_1\cdot\vec F_1+\vec F_1\cdot\vec F_2+\vec F_1\cdot\vec F_3+\vec F_1\cdot\vec F_4=0$

${F_1}^2+\vec F_1\cdot\vec F_2+0+\vec F_1\cdot\vec F_4=0$

$\implies\vec F_1\cdot\vec F_4=-\left({F_1}^2+\vec F_1\cdot\vec F_2\right)$

We can do the same thing with $\vec F_2$ and $\vec F_3$ :

$\vec F_2\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0$

$\implies\vec F_2\cdot\vec F_4=-\left(\vec F_1\cdot\vec F_2+{F_2}^2\right)$

$\vec F_3\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0$

$\implies\vec F_3\cdot\vec F_4=-{F_3}^2$

Finally, if we do this with $\vec F_4$ , we get

$\vec F_4\cdot(\vec F_1+\vec F_2+\vec F_3+\vec F_4)=0$

$\implies{F_4}^2=-\left(\vec F_1\cdot\vec F_4+\vec F_2\cdot\vec F_4+\vec F_3\cdot\vec F_4\right)$

$\implies{F_4}^2=-\left(-\left({F_1}^2+\vec F_1\cdot\vec F_2\right)-\left(\vec F_1\cdot\vec F_2+{F_2}^2\right)-{F_3}^2\right)$

$\implies F_4=\sqrt{{F_1}^2+{F_2}^2+{F_3}^2+2(\vec F_1\cdot\vec F_2)}$

$\implies\boxed{F_4\approx36.2\,\mathrm N}$

7 0

3 years ago

The staff of a school cafeteria makes 86 sandwiches for the students trip. if n represents the number of sandwiches that were ea

Nesterboy [21]

Answer:

c

Step-by-step explanation:

You had 86 then you eat n. You are subtracting.

6 0

3 years ago

There were94,172 People at a football game on Saturday on Monday 1000 fewer people were at the football game in word form how ma

8_murik_8 [283]

Answer:

93,172

Step-by-step explanation:

94,172-1,000

3 0

3 years ago

How is the structure of a hammer related to its function?

Stella [2.4K]

1.The curved claw in the back helps to pry a nail out if necessary
2.The flat surface is for striking the nail into various surfaces

3 0

3 years ago

Identify the like terms.

Olegator [25]

Answer:

the answer is D brootheerrrr

5 0

3 years ago