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3 years ago

Can someone please help me with these

Mathematics

1 answer:

OLga [1]3 years ago

7 0

Answer:

1. 1072.6

2. 753.6

3. 194.2

4. 59.5

5. 4848.3

6. 1818.3

Step-by-step explanation:

We have to use the trigonometric functions sin, cos, and tan. Remember the mnemonic SOH-CAH-TOA when solving these problems. (sinθ=opposite/hypotenuse, cosθ=adjacent/hypotenuse, tanθ=opposite/adjacent)

1. tan(40)=900/x

x=900/tan(40)

x=1072.6

2. tan(37)=x/1000

1000tan(37)=x

753.6=x

3. sin(18)=60/x

x=60/sin(18)

x=194.2

4. sin(48)=x/80

80sin(48)=x

59.5=x

5. tan(22)=x/12000

12000tan(22)=x

4848.3=x

6. tan(33)=x/2800

2800tan(33)=x

1818.3=x

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3 years ago

7. If U= {2, 4, 6, 8, 10, 12, 14, 16} and A = {6, 10, 14}, what is A'?

Tresset [83]

The compliment of set A that is A' is equal to {2, 4, 8, 12, 16}.

We are given the universal set as:

U = {2, 4, 6, 8, 10, 12, 14, 16}

We are also given that set A is:

A = {6, 10, 14}

We need to find A'

For this, we will subtract set A from the universal set, U.

So, we get that:

A' = U - A

A' = {2, 4, 6, 8, 10, 12, 14, 16} - {6, 10, 14}

Solving the expression, we get that:

A' = {2, 4, 8, 12, 16}

Therefore, we get that, the compliment of set A that is A' is equal to {2, 4, 8, 12, 16}.

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10 months ago

Make y the subject to the following questions

skelet666 [1.2K]

In this question it basically wants you to leave Y alone in a side of the equation.

In this case,
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$y=\frac{w}{A}$

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Y=cw

For y/a=2c
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2 years ago

Suppose that Prolog facts are used to define the pred- icates mother(M, Y) and father(F, X), which represent that M is the mothe

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Answer and Explanation:

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Prolog expressions are containing truth-functional symbols, which have the same intervention as in predicate calculus.

For example:

English Predicate calculus prolog

and ^ ,

or v ;

By using information, given in the question,

We can make prolog:

Grandfather(X, Y) :-mother(M,Y), father(X,M); father (F, Y), father(X,F)

Prolog (:- ) means define,

Prolog (,) represents a conjunction

And

Prolog (;) represent a disjunction

7 0

3 years ago

A rancher wishes to build a fence to enclose a 2250 square yard rectangular field. Along one side the fence is to be made of hea

Bess [88]

Answer:

The least cost of fencing for the rancher is $1200

Step-by-step explanation:

Let x be the width and y the length of the rectangular field.

Let C the total cost of the rectangular field.

The side made of heavy duty material of length of x costs 16 dollars a yard. The three sides not made of heavy duty material cost $4 per yard, their side lengths are x, y, y. Thus

$C=4x+4y+4y+16x\\C=20x+8y$

We know that the total area of rectangular field should be 2250 square yards,

$x\cdot y=2250$

We can say that $y=\frac{2250}{x}$

Substituting into the total cost of the rectangular field, we get

$C=20x+8(\frac{2250}{x})\\\\C=20x+\frac{18000}{x}$

We have to figure out where the function is increasing and decreasing. Differentiating,

$\frac{d}{dx}C=\frac{d}{dx}\left(20x+\frac{18000}{x}\right)\\\\C'=20-\frac{18000}{x^2}$

Next, we find the critical points of the derivative

$20-\frac{18000}{x^2}=0\\\\20x^2-\frac{18000}{x^2}x^2=0\cdot \:x^2\\\\20x^2-18000=0\\\\20x^2-18000+18000=0+18000\\\\20x^2=18000\\\\\frac{20x^2}{20}=\frac{18000}{20}\\\\x^2=900\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{900},\:x=-\sqrt{900}\\\\x=30,\:x=-30$

Because the length is always positive the only point we take is $x=30$ . We thus test the intervals $(0, 30)$ and $(30, \infty)$

$C'(20)=20-\frac{18000}{20^2} = -25 < 0\\\\C'(40)= 20-\frac{18000}{20^2} = 8.75 >0$

we see that total cost function is decreasing on $(0, 30)$ and increasing on $(30, \infty)$ . Therefore, the minimum is attained at $x=30$ , so the minimal cost is

$C(30)=20(30)+\frac{18000}{30}\\C(30)=1200$

The least cost of fencing for the rancher is $1200

Here’s the diagram:

3 0

2 years ago