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2 years ago

9

Select the correct answer.

1 answer:

Nat2105 [25]2 years ago

6 0

Answer:

Step-by-step explanation:

Both distances are in the scientific notation:

Earth - Sun = 9.3 * 10^7 miles

Saturn - Sun = 8.87 * 10^8 miles

8.87 * 10^8 - 9.3 * 10^7 =

= 88.7 *10^7 - 9.3 * 10^7 =

= 79.4 * 10^7 = 7.94 * 10 ^8 = 794,000,000 miles

Answer: Saturn is 7.94 * 10^8 miles farther from Sun than Earth is.

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3. An artist is creating a sculpture from clay. He starts with clay in the shape of a sphere with a radius of 3 inches.

Colt1911 [192]

Answer:

Step-by-step explanation:

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2 years ago

Find the derivative of f(x)= e^(4x) + e^-(4x)

ololo11 [35]

Answer:

$f'(x)=4e^{4x} -4e^{-4x}$

Step-by-step explanation:

To find this derivative, we will need to use the chain rule.

As there is a variable in the exponent we can use this formula:

$f'(x)=u'e^u$

In this case, $u=4x$ and $u=-4x$

This means that $u'=4$ and $u'=-4$ respectively

This gives us $f'(x)=4e^{4x} -4e^{-4x}$

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2 years ago

Read 2 more answers

Use synthetic division to find (5x<br> + 31x + 32) = (x + 5).

LiRa [457]

We move all terms to the left:
+31x+32)-((+5)=0
So your answer is 0

5 0

3 years ago

Find the area of the given triangle to the nearest square unit. Angle a= 30 degrees, b=10, angle B=45 degrees

storchak [24]

Answer:

$A=34\ units^2$

Step-by-step explanation:

Suppose we have a general triangle like the one shown in the figure.

We know the angle A, the angle B and the length b.

$A = 30\°\\\\B = 45\°\\\\b = 10$

By definition I know that the sum of the internal angles of a triangle is always equal to 180 °.

So

$A + B + C = 180\\\\30 + 45 + C = 180$

We solve the equation and thus we find the angle C.

$C = 180 - 30-45\\\\C = 105$

We already know the three triangle angles.

Now we use the sine theorem to calculate the sides c and a.

The sine theorem says that:

$\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$

Then

$\frac{sin(30)}{a}=\frac{sin(45)}{10}$

$\frac{sin(30)}{\frac{sin(45)}{10}}=a$

$a=7.071$

Also

$\frac{sin(105)}{c}=\frac{sin(45)}{10}$

$\frac{sin(105)}{\frac{sin(45)}{10}}=c$

$c=13.660$

Finally, we use the Heron formula to calculate the triangle area

$A=\sqrt{s(s-a)(s-b)(s-c)}$

Where s is:

$s=\frac{a+b+c}{2}$

Therefore

$s=\frac{7.071+10+13.660}{2}$

$s=15.37$

$A=\sqrt{15.37(15.37-7.071)(15.37-10)(15.37-13.66)}$

$A=34\ units^2$

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2 years ago

Janna jumped 156 inches in the long jump competition at the high school track meeting . how many feet did janna jump?

Fiesta28 [93]

Janna jumped 13 feet. Hope it help!

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3 years ago