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3 years ago

What is the total weight, in pounds, of 100 sharks that each weigh 5.015× 10 (to the 3rd power) pounds

Mathematics

1 answer:

kap26 [50]3 years ago

5 0

Answer:

12612837.8375

Step-by-step explanation:

first you have to multiply 5.015 x 10 and you get 50.15 the put that to the power of 3 and then multiply the total by 100.

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Find a unit vector that has the same direction as the given vector. 8i ? j + 4k

e-lub [12.9K]

Answer with Step-by-step explanation:

a.Let given vector

a=8i-j+4k

$\mid a\mid=\sqrt{(8)^2+(-1)^2+(4)^2}=9$

By using the formula

Magnitude of a vector= $\sqrt{x^2+y^2+z^2}$

Where x=Coefficient of i

y=Coefficient of j

z=Coefficient of k

Unit vector= $\hat{a}=\frac{a}{\mid a\mid}$

By using the formula

The unit vector= $\hat{a}=\frac{8i-j+4k}{9}=\frac{8}{9}i-\frac{1}{9}j+\frac{4}{9}k$

b.Let vector b=-2i+4j+2k

$\mid b\mid=\sqrt{(-2)^2+4^2+2^2}=2\sqrt 6$

$\hat{b}=\frac{-2i+4j+2k}{2\sqrt 6}$

Length of vector=6

Therefore, the vector in the direction of <-2,4,2> with length 6 is given by = $6\hat{b}=6\times \frac{-2i+4j+2k}{2\sqrt 6}$

The vector in the direction of <-2,4,2> with length 6 is given by = $-\sqrt 6(-i+2j+k)$

c. $\theta=\frac{\pi}{3}$

$\mid v\mid=8$

Let v= $v_x i+v_y j$

$v_x=\mid v\mid cos\theta$

$v_x=8cos\frac{\pi}{3}=8\times \frac{1}{2}=4$

$cos\frac{\pi}{3}=\frac{1}{2}$

$v_y=\mid v\mid sin\theta$

$v_y=8\times sin\frac{\pi}{3}=8\times \frac{\sqrt 3}{2}=4\sqrt 3$

$sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$

Therefore, the vector v in component form= $4i+4\sqrt 3j$

7 0

3 years ago

Apply the distributive property to create an equivalent expression.<br><br> (7−4n)⋅6= ?

AleksandrR [38]

Answer:

Step-by-step explanation:

The distributive property: <em>a(b - c) = ab - ac</em>

(7 - 4n) · 6 = (7)(6) - (4n)(6) = 42 - 24n

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3 years ago

10.01,10.1,10.001,1.101,10 least to <br> greatest

Leona [35]

Answer:

1.101 < 10 < 10.001 < 10.01 < 10.1

Step-by-step explanation:

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3 years ago

28. Last week, Lee earned some money babysitting. He

grigory [225]

Answer:

the answer should be 44 dollar correct me if im wrong

Step-by-step explanation:

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3 years ago

How do I show my work 826÷2

eduard

Hope this helps!! Good luck

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3 years ago