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2 years ago

14

Express 900cmcubic in dm cubic

2 answers:

Andrew [12]2 years ago

6 0

Answer:

0.9 dm³

Step-by-step explanation:

1 dm = 10cm

1 dm³ = 10cm×10cm×10cm = 1000 cm³

1000 cm³ .............. 1 dm³

900 cm³ ................x dm³

x = 900×1/1000 = 0.9 dm³

Y_Kistochka [10]2 years ago

6 0

Answer:

0.9 DM cubic

Step-by-step explanation:

1 cm cubic = 0.001 dm cubic

900 cm cubic = 0.001 × 900 dm cubic

=0.9 dm cubic

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Each big square is cut into 3 parts to represent multiplying by one-third. The number of small shaded squares in the circled par

sammy [17]

Answer:the answer is 5/9

Step-by-step explanation:

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3 years ago

Last year's computer models are discounted 20%. What was the original price to the nearest dollar of a computer that now costs $

Alisiya [41]

Answer:

<h3>$1850</h3>

Step-by-step explanation:

<h3>If the Original price was $ X , Then </h3>

$x - 0.20x \: = 1480$

$0.8x = 1480$

$x = 1480 \div 0.8$

<h3>So , X = 1850 dollars .</h3>

<h2>Hope this helps you !!! </h2>

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2 years ago

Find the exact value of the expression.<br> tan( sin−1 (2/3)− cos−1(1/7))

Sonja [21]

Answer:

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

Step-by-step explanation:

I'm going to use the following identity to help with the difference inside the tangent function there:

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

Let $a=\sin^{-1}(\frac{2}{3})$ .

With some restriction on $a$ this means:

$\sin(a)=\frac{2}{3}$

We need to find $\tan(a)$ .

$\sin^2(a)+\cos^2(a)=1$ is a Pythagorean Identity I will use to find the cosine value and then I will use that the tangent function is the ratio of sine to cosine.

$(\frac{2}{3})^2+\cos^2(a)=1$

$\frac{4}{9}+\cos^2(a)=1$

Subtract 4/9 on both sides:

$\cos^2(a)=\frac{5}{9}$

Take the square root of both sides:

$\cos(a)=\pm \sqrt{\frac{5}{9}}$

$\cos(a)=\pm \frac{\sqrt{5}}{3}$

The cosine value is positive because $a$ is a number between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ because that is the restriction on sine inverse.

So we have $\cos(a)=\frac{\sqrt{5}}{3}$ .

This means that $\tan(a)=\frac{\frac{2}{3}}{\frac{\sqrt{5}}{3}}$ .

Multiplying numerator and denominator by 3 gives us:

$\tan(a)=\frac{2}{\sqrt{5}}$

Rationalizing the denominator by multiplying top and bottom by square root of 5 gives us:

$\tan(a)=\frac{2\sqrt{5}}{5}$

Let's continue on to letting $b=\cos^{-1}(\frac{1}{7})$ .

Let's go ahead and say what the restrictions on $b$ are.

$b$ is a number in between 0 and $\pi$ .

So anyways $b=\cos^{-1}(\frac{1}{7})$ implies $\cos(b)=\frac{1}{7}$ .

Let's use the Pythagorean Identity again I mentioned from before to find the sine value of $b$ .

$\cos^2(b)+\sin^2(b)=1$

$(\frac{1}{7})^2+\sin^2(b)=1$

$\frac{1}{49}+\sin^2(b)=1$

Subtract 1/49 on both sides:

$\sin^2(b)=\frac{48}{49}$

Take the square root of both sides:

$\sin(b)=\pm \sqrt{\frac{48}{49}$

$\sin(b)=\pm \frac{\sqrt{48}}{7}$

$\sin(b)=\pm \frac{\sqrt{16}\sqrt{3}}{7}$

$\sin(b)=\pm \frac{4\sqrt{3}}{7}$

So since $b$ is a number between $0$ and $\pi$ , then sine of this value is positive.

This implies:

$\sin(b)=\frac{4\sqrt{3}}{7}$

So $\tan(b)=\frac{\sin(b)}{\cos(b)}=\frac{\frac{4\sqrt{3}}{7}}{\frac{1}{7}}$ .

Multiplying both top and bottom by 7 gives:

$\frac{4\sqrt{3}}{1}= 4\sqrt{3}$ .

Let's put everything back into the first mentioned identity.

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

$\tan(a-b)=\frac{\frac{2\sqrt{5}}{5}-4\sqrt{3}}{1+\frac{2\sqrt{5}}{5}\cdot 4\sqrt{3}}$

Let's clear the mini-fractions by multiply top and bottom by the least common multiple of the denominators of these mini-fractions. That is, we are multiplying top and bottom by 5:

$\tan(a-b)=\frac{2 \sqrt{5}-20\sqrt{3}}{5+2\sqrt{5}\cdot 4\sqrt{3}}$

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

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3 years ago

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posledela

Answer:

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Step-by-step explanation:

From the diagram, the side opposite the 60° angle is 28 feet.

We are looking for the approximate length of the cable.

The approximate length of the cable is the hypotenuse of the triangle shown.

Recall the sine ratio from SOH-CAH-TOA

Which means Sine of the angle is Opposite/Hypotenuse

Let the hypotenuse be h, then we have:

$\sin(60) = \frac{28}{h}$

$0.866 = \frac{28}{h}$

$h = \frac{28}{0.866}$

$h = 32.33$

The length of the cable is approximately 32 feet

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3 years ago

A rectangle has a width of 2xy3 and a length of 4x5y6. What is the area of the rectangle?

astraxan [27]

Answer:

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Step-by-step explanation:

(2xy3) x (4x5y6)

(2x) x (4x) = 6x²

(y) x (5y) =5y²

6x²5y²6 cm²

7 0

2 years ago