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3 years ago

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Mathematics

1 answer:

nlexa [21]3 years ago

4 0

Answer:

Step-by-step explanation:

● h(x) = 2-2x

The domain is {-3,-2,1,5}

● h(-3) = 2-2×(-3) = 2+6 = 8

● h(-2) = 2 -2×(-2) = 2+4 = 6

● h(1) = 2-2×1 = 2-2 = 0

● h(5) = 2-2×5 = 2-10 = -8

The range is {-8,0,6,8}

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Show that √(1-cos A/1+cos A) =cosec A - cot A

Gennadij [26K]

Hi there!

$\sqrt{\frac{1-cosA}{1+cosA}} =$

We can begin by multiplying by its conjugate:

$\sqrt{\frac{1-cosA}{1+cosA}} * \sqrt{\frac{1+cosA}{1+cosA}} = \\\\\sqrt{\frac{(1-cosA)(1 + cosA)}{(1+cosA)(1 + cosA)}} =$

Simplify using the identity:

$1 - cos^2A = sin^2A$

$\sqrt{\frac{(1-cos^2A)}{(1+cosA)^2}} =\\\\\sqrt{\frac{(sin^2A)}{(1+cosA)^2}} =$

Take the square root of the expression:

${\frac{sinA}{1+cosA} =$

Multiply again by the conjugate to get a SINGLE term in the denominator:

${\frac{sinA}{1+cosA} * {\frac{1-cosA}{1-cosA} =\\$

Simplify:

${\frac{sinA(1-cosA)}{1-cos^2A} =$

Use the above trig identity one more:

${\frac{sinA(1-cosA)}{sin^2A} =$

Cancel out sinA:

${\frac{(1-cosA)}{sinA} =$

Split the fraction into two:

${\frac{1}{sinA} - \frac{cosA}{sinA} =$

Recall:

$1/sinA = cscA\\\\cosA/sinA = cotA$

Simplify:

$\frac{1}{sinA} + \frac{cosA}{sinA} = \boxed{cscA - cotA}$

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2 years ago

Complete the square to rewrite y = x2 + 6x + 3 in vertex form. Then state whether the vertex is a maximum or a minimum and give

masha68 [24]

y = x² + 6x + 3

y = x² + 6x + 9 - 6

y = (x + 3)² - 6

since the coefficient of x² is positive, then min at (-3,-6). the answer is C.

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3 years ago

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lyudmila [28]

Answer:

Step-by-step explanation:

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3 years ago

If the FDIC has an insurance fund of $67. 8 billion and must use 7. 6% of it to cover several failed banks, approximately how mu

Black_prince [1.1K]

The remaining money will be $62. 65 billion

<h3>What will be the remaining fund in FDIC?</h3>

Given amount =$67. 8 billion

Amount used to cover several failed banks = 7.6% of the total amount

So the amount used to cover several failed banks= $\dfrac{67.8\times 7.6}{100}$

$Amount = 5.1528$

So the remaining amount = $67.8-5.15=62.65$

Thus the remaining money will be $62. 65 billion

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2 years ago

Which number is greater and by how much: A decreased by 50% and then increased by 50% of the result

cricket20 [7]

Answer:

the original number is greater

Step-by-step explanation:

1. let 1x be your starting number

2. therefore, 0.5 * 1x = 0.5x ( amount after you decreased it by 50%)

3. then increase: 0.5x * 1.5 = 0.75x (amount after you increased it by 50%)

4. 0.75x < 1x (this means that the original number is larger than the one you decreased and then increased)

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2 years ago