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3 years ago

Fill in the Blank: 10 quarts = pints

Mathematics

2 answers:

givi [52]3 years ago

8 0

Answer:

10 quarts = 20 pints.

Step-by-step explanation:

Hope my answer has helped you and if not I am sorry.

tresset_1 [31]3 years ago

4 0

10 quarts = 10 pints

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Trig proofs with Pythagorean Identities.

lorasvet [3.4K]

To prove:

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Solution:

$$LHS = \frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}$

Multiply first term by $\frac{1+cos x}{1+cos x}$ and second term by $\frac{1-cos x}{1-cos x}$ .

$$= \frac{1(1+\cos x)}{(1-\cos x)(1+\cos x)}-\frac{\cos x(1-\cos x)}{(1+\cos x)(1-\cos x)}$

Using the identity: $(a-b)(a+b)=(a^2-b^2)$

$$= \frac{1+\cos x}{(1^2-\cos^2 x)}-\frac{\cos x-\cos^2 x}{(1^2-\cos^2 x)}$

Denominators are same, you can subtract the fractions.

$$= \frac{1+\cos x-\cos x+\cos^2 x}{(1^2-\cos^2 x)}$

Using the identity: $1-\cos ^{2}(x)=\sin ^{2}(x)$

$$= \frac{1+\cos^2 x}{\sin^2x}$

Using the identity: $1=\cos ^{2}(x)+\sin ^{2}(x)$

$$=\frac{\cos ^{2}x+\cos ^{2}x+\sin ^{2}x}{\sin ^{2}x}$

$$=\frac{\sin ^{2}x+2 \cos ^{2}x}{\sin ^{2}x}$ ------------ (1)

$RHS=2 \cot ^{2} x+1$

Using the identity: $\cot (x)=\frac{\cos (x)}{\sin (x)}$

$$=1+2\left(\frac{\cos x}{\sin x}\right)^{2}$

$$=1+2\frac{\cos^{2} x}{\sin^{2} x}$

$$=\frac{\sin^2 x + 2\cos^{2} x}{\sin^2 x}$ ------------ (2)

Equation (1) = Equation (2)

LHS = RHS

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Hence proved.

5 0

4 years ago

the sign of the product of two integers with the same sign is positive what is the sign of the product of 3 integers with the sa

hammer [34]

The answer would be positive if all 3 signs were the same. Yes, the product of two integers with the same sign will be positive, but that goes for any number of integers as long as they still have the same sign.

6 0

3 years ago

80 points. Please answer!

klemol [59]

Answer:

a cube that is 1 yard long, 1 yard wide, and 1 yard high

Step-by-step explanation:

The dimensions for a unit cube are:

$1\times1\times1$

<u>Please note that the units for each side MUST be the same (or if they're different, then the lengths have to be equivalent). </u>

<u />

Looking at the answer choices, we can see that the last answer choice is a 1 yd by 1 yd by 1 yd cube, therefore it is a unit cube.

6 0

2 years ago

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Gala2k [10]

Answer:

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Step-by-step explanation: hope this helps

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2 years ago

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alukav5142 [94]

Answer:

Step-by-step explanation:

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3 years ago