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3 years ago

Simplify. Cos ^-1 (square root 3/2

Mathematics

1 answer:

bogdanovich [222]3 years ago

4 0

Hello,

As
$cos(30)=sin(60)=\dfrac{\sqrt{3} }{2}\\\\

cos^{-1}(\dfrac{ \sqrt{3} }{2})
$

=π/6+2kπ or -π/6+2kπ

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What is 7/8 as a percent fraction and decimal

irina [24]

7/8 as a percent - 87.5%

7/8 as a fraction - 7/8..? I don't get what you're talking about there

7/8 as a decimal - 0.875

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3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.

Anika [276]

Answer:

$\large\boxed{y=\dfrac{1}{2}x^2-2x+1}$

Step-by-step explanation:

The vertex form of an equation of a parabola:

$y=a(x-h)^2+k$

(h, k) - vertex

a - leading coefficient in equation y = ax² + bx + c

From the grap we can read coordinates of the vertex (2, -1) and y-intercept (0, 1).

Therefore h = 2, k = -1

Put the values of h, k and coordinates of the y-intercept to the equation of parabola:

$1=a(0-2)^2-1$ add 1 to both sides

$1+1=a(2)^2-1+1$

$2=4a$ divide both sides by 4

$\dfrac{2}{4}=\dfrac{4a}{4}\\\\\dfrac{1}{2}=a\to a=\dfrac{1}{2}$

Therefore we have the equation:

$y=\dfrac{1}{2}(x-2)^2-1$

Convert to the standard form:

$y=\dfrac{1}{2}(x-2)^2-1$ use (a - b)² = a² - 2ab + b²

$y=\dfrac{1}{2}(x^2-2(x)(2)+2^2)-1$

$y=\dfrac{1}{2}(x^2-4x+4)-1$ use the distributive property

$y=\dfrac{1}{2}x^2-\dfrac{1}{2}\cdot4x+\dfrac{1}{2}\cdot4-1$

$y=\dfrac{1}{2}x^2-2x+2-1$ combine like terms

$y=\dfrac{1}{2}x^2-2x+1$

5 0

3 years ago

An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a r

zimovet [89]

We know that solution of this system of inequalities will be shaded regions

so, we will select each option and check which one lies on shaded region

(A)

(10,-1)

$x=10,y=-1$

so, it does lie on shaded region

so, this point is the solution

(B)

(2,4)

$x=2,y=4$

so, it does lie on shaded region

so, this point is the solution

(C)

(0,-10)

$x=0,y=-10$

so, it does not lie on shaded region

so, this point is not the solution

(D)

(-2,0)

$x=-2,y=0$

so, it does not lie on shaded region

so, this point is not the solution

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3 years ago

Given that total revenue = price x quantity, what will happen to total revenue if price increases when demand is elastic?

Nitella [24]

Answer: the total revenue decreases

Step-by-step explanation:

In an elastic demand, an increase in price of of a product will lead to a large decrease in the quantity demanded resulting in a decrease in the total revenue acquired.

In the case above, given that the demand is elastic an increase in the price will lead to a decrease in the total revenue.

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3 years ago

The ratio of almond pieces to

AveGali [126]

Answer: There are 12 almonds and 16 cranberries.

Step-by-step explanation: This is a proportions problem.

If the ratio of almonds to cranberry is 3 to 4, that means for every 7 pieces, there are 3 almonds and 4 cranberries.
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Check: 12 + 16 = 28

4 0

3 years ago

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