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3 years ago

When you divide a decimal by a decimal why do you multiply the dividend and the divisor by a power of 10

Mathematics

1 answer:

Xelga [282]3 years ago

7 0

To make both sides of the equations equal and balanced.

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Using a common denominator to order fractions, please help fast...

marshall27 [118]

3/10=15/50 and then 8/25=16/50

So, 3/10<8/25

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2 years ago

2 Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.

vaieri [72.5K]

Answer:

Dimension of box:-

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

$500=x^2y$

Therefore, $y=\dfrac{500}{x^2}$

It is open box. The surface area of box, S .

$S=x^2+4xy$

Put $y=\dfrac{500}{x^2}$

$S(x)=x^2+\dfrac{2000}{x}$

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

$S'(x)=2x-\dfrac{2000}{x^2}$

For critical point, S'(x)=0

$2x-\dfrac{2000}{x^2}=0$

$x^3=1000$

$x=10$

Put x = 10 into $y=\dfrac{500}{x^2}$

y = 5

Double derivative of S(x)

$S''(x)=2+\dfrac{4000}{x^3}$ at x = 10

$S''(10) > 0$

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²

7 0

3 years ago

Given f(x)=-3x+4 , what is f(2) ?

user100 [1]

F(X) means plug in te number within the parenthesis for the given function. It's simply an equation expressed through different notation. In this case it asks you to plug in two, so you do:
-3(2)+4 = f(2)
That means that f(2)=-2.

3 0

2 years ago

Someone please help me with this one quick

astraxan [27]

The length of AC is 16 km.

Solution:

Given data:

AB = c = 14 km, ∠A = 30° and ∠B = 89°

AC = b = ?

Let us first find angle C:

Sum of all angles in a triangle = 180°

m∠A+ m∠B + m∠C = 180°

30° + 89° + m∠C = 180°

119° + m∠C = 180°

Subtract 119° from both sides, we get

m∠C = 61°

To find the length of AC:

Using sine formula:

$$\frac{b}{\sin B } =\frac{c}{\sin C}$

Substitute the given values in the formula.

$$\frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ }$

Multiply by sin 89° on both sides.

$$\sin 89^\circ \times \frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ } \times \sin 89^\circ$

$$b=\frac{14}{0.8746 } \times0.9998$

$b=16$

The length of AC is 16 km.

4 0

2 years ago

Math help pls? Picture attached.

stich3 [128]

I think it's A, but I'm not sure

8 0

3 years ago