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Greeley [361]
4 years ago
14

Which statements about the right triangle are correct

Mathematics
1 answer:
ozzi4 years ago
3 0

The statements 2, 4, and 5 are correct about the right-angled triangle.

Step-by-step explanation:

Step 1:

The formulae needed to solve the problem are;

sin\theta = \frac{oppositeside}{hypotenuse} , cos\theta = \frac{adjacent side}{hypotenuse}, tan\theta = \frac{opposite side}{adjacentside},

cosec\theta = \frac{hypotenuse}{oppositeside} , sec\theta = \frac{hypotenuse}{adjacent side}, cot\theta = \frac{adjacent side}{oppositeside}.

Step 2:

If the angle is B, the opposite side measures 5 units, the adjacent side measures 12 units, and the hypotenuse measures 13 units.

cos B = \frac{12}{13} , sec B = \frac{13}{12} .

Step 3:

If the angle is A, the opposite side measures 12 units, the adjacent side measures 5 units, and the hypotenuse measures 13 units.

cot A = \frac{5}{12} , cosecA = \frac{13}{12} , sinA =\frac{12}{13} , tan A = \frac{12}{5}.

Of the six given options, options cot A = \frac{5}{12}, sinA =\frac{12}{13} ,sec B = \frac{13}{12} are the right options.

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Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = t 9 − t2 , [−1, 3]
ahrayia [7]

The absolute minimum = -2√2.

The absolute maximum=  4.5

Consider f(t)=t√9-t on the interval (1,3].

Find the critical points: Find f'(t)=0.

f"(t) = 0

√9-t² d/dt t + t d/dt √9-t²=0

√9-t²  + t/2√9-t² (-2t)=0

9-t²-t²/√9-t²=0

9-2t²=0

9=2t²,   t²=9/2, t=±3/√2

since -3/√2∉  (1,3].

Therefore, the critical point in the interval  (1,3] is t= 3/√2.

Find the value of the function at t=1, 3/√2,3 to find the absolute maximum and minimum.

f(-1)=-1√9-1²

    = -√8 , =-2√2

f(3/√2)= 3/√2 √9-(3/√2)²

        = 3/√2 √9-9/2

      =3/√2 √9/2

     =9/2 = 4.5

f(3)= 3√9-3²

    = 3(0)

    =0

The absolute maximum is 4.5 and the absolute minimum is -2√2.

The absolute maximum point is the point at which the function reaches the maximum possible value. Similarly, the absolute minimum point is the point at which the function takes the smallest possible value.

A relative maximum or minimum occurs at an inflection point on the curve. The absolute minimum and maximum values ​​are the corresponding values ​​over the full range of the function. That is, the absolute minimum and maximum values ​​are bounded by the function's domain.

Learn more about Absolute minimum and maximum here:brainly.com/question/19921479

#SPJ4

6 0
2 years ago
Identify like terms of 8a b2 b3 4b2 4 5a
ipn [44]
Like terms are any terms that have the same variable value.

In the sequence 8a, b^2, b^3, 4b^2, 4, and 5a, the like terms are the ones that have the same variable to the same power.

8a and 5a are like terms, as well as b^2 and 4b^2, because both sets of terms have the same variable.
Hope that helped =)
7 0
4 years ago
Read 2 more answers
What kind of sequence is this? 143, 125, 107, 89, ...
podryga [215]

Hello from MrBillDoesMath!

Answer:   It is part of an arithmetic progression

Discussion:

143 - 125 = 18

125 - 107 = 18

107 - 89  = 18


The value 18 is subtracted from each term in the arithmetic sequence.

Regards, MrB

4 0
3 years ago
Five angles of a hexagon measure 119, 129, 104, 139, and 95. What is the measure of the sixth angle?
SIZIF [17.4K]

Answer:

134°

Step-by-step explanation:

The sum of interior angles of a regular polygon is: (n - 2)180

Hexagon has six sides, n is 6

Sum of it's angles is (6 - 2)180 = 720

sum of our hexagon:

119 + 129 + 104 + 139 + 95 + x = 720°

x is 134°

8 0
4 years ago
The cost of renting Party Palace is $ 120 plus $ 15 per person attending the party. If the total cost of renting Party Palace is
aalyn [17]

Answer:

24 individuals

Step-by-step explanation:

Since we are given the actual costs as well as the final total then we can calculate the total number of people that attended the party by doing the following. We first subtract the fixed cost of $120 by the total cost of the party, and then we divide the remainder by the cost per person, which would give us the number of people who attended (x) ...

($480 - $120) / $15 = x

$360 / $15 = x

24 = x

Finally, we can see that a total number of 24 individuals attended the party

5 0
3 years ago
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