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MAXImum [283]
3 years ago
9

List two ways a rectangle and a square are alike

Mathematics
2 answers:
madreJ [45]3 years ago
6 0
Rectangles<span> and squares are </span>alike<span> in that both have </span>two<span> pairs of parallel sides and four right angles.</span>
Setler [38]3 years ago
4 0
Rectangle is congruent and has four right angles and parallel sides eight square has all congruent sides parallel and four right angles
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Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 9t + 9 cot(t/2), [π/4, 7π/4]
agasfer [191]

Answer:

the absolute maximum value is 89.96 and

the absolute minimum value is 23.173

Step-by-step explanation:

Here we have cotangent given by the following relation;

cot \theta =\frac{1 }{tan \theta} so that the expression becomes

f(t) = 9t +9/tan(t/2)

Therefore, to look for the point of local extremum, we differentiate, the expression as follows;

f'(t) = \frac{\mathrm{d} \left (9t +9/tan(t/2)  \right )}{\mathrm{d} t} = \frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9  \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2}

Equating to 0 and solving gives

\frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9  \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2} = 0

t=\frac{4\pi n_1 +\pi }{2} ; t = \frac{4\pi n_2 -\pi }{2}

Where n_i is an integer hence when n₁ = 0 and n₂ = 1 we have t = π/4 and t = 3π/2 respectively

Or we have by chain rule

f'(t) = 9 -(9/2)csc²(t/2)

Equating to zero gives

9 -(9/2)csc²(t/2) = 0

csc²(t/2)  = 2

csc(t/2) = ±√2

The solutions are, in quadrant 1, t/2 = π/4 such that t = π/2 or

in quadrant 2 we have t/2 = π - π/4 so that t = 3π/2

We then evaluate between the given closed interval to find the absolute maximum and absolute minimum as follows;

f(x) for x = π/4, π/2, 3π/2, 7π/2

f(π/4) = 9·π/4 +9/tan(π/8) = 28.7965

f(π/2) = 9·π/2 +9/tan(π/4) = 23.137

f(3π/2) = 9·3π/2 +9/tan(3·π/4) = 33.412

f(7π/2) = 9·7π/2 +9/tan(7π/4) = 89.96

Therefore the absolute maximum value = 89.96 and

the absolute minimum value = 23.173.

7 0
3 years ago
What is the answer to what X is?
solmaris [256]

Answer:

x=3

Step-by-step explanation:

By the exterior angle theorem,

(45x)\degree=(57+x)\degree+(26x)\degree

Group like terms and solve for x.

45x-26x-x=57

19x=57

Divide both sides by 19;

x=3

3 0
3 years ago
Read 2 more answers
A spinner is divided into blue green and red part.George spin the spinner 300 times. It lands 91 times on blue 107 times on gree
Fed [463]
Estimated probability=number of outcomes in question/divided by total number of trials

ep=102/300

ep=51/150  (34%)
3 0
3 years ago
If I want to buy a pair of sunglasses and the original price is $120, how much will I pay if they are 50% off? What if they were
gogolik [260]

Answer:

$60, $90

Step-by-step explanation:

Amount paid when 50% off

=$ 120 - 50/100 * 120 = $ 120 - $60 = $60

Amount paid when 25% off

=$ 120 - 25/100 * 120 = $ 120 - $30 = $90

4 0
3 years ago
PLEASE ANSWER ME ASAP!!**NO LINKS!!**THANK YOU SOOO MUCH IF YOU HELP ME!! =D
Morgarella [4.7K]

Answer:

The best deal is the middle one.

Step-by-step explanation:

35.95 with a 20% discount.

You can do this the straight forward way. Take 20% 35.95

20/100 * 35.95 = 7.19

Now subtract this from 35.95

35.95 - 7.19 = 28.76

15/100 * 29.75 = 4.46

29.75 - 4.46 = 25.28

 

25% * 38.49 = 9.62

38.49 - 9.62 = 28.86

6 0
2 years ago
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