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3 years ago

GivenGiven 15 cot A = 8, find sin A and sec A.

Mathematics

1 answer:

Leviafan [203]3 years ago

8 0

Answer:

$sin A = \frac{15}{17}, \ sec A = \frac{17}8$

Step-by-step explanation:

$15cot A = 8\\\\cotA = \frac{8}{15}\\\\1 + cot^2A = cosec^2 A\\\\1 + (\frac{8}{15})^2 = cosec^2 A\\\\1 + \frac{64}{225} = cosec^2A\\\\\frac{225+64}{225} = cosec^2 A\\\\cosec^2 A = \frac{289}{225}\\\\cosec A = \frac{17}{15}\\\\That \ is, \ \frac{1}{sin A} = \frac{17}{15}\\\\sin A = \frac{15}{17}$

$cot A = \frac{8}{15}\\\\\frac{cos A}{sinA} = \frac{8}{15}\\\\cos A = \frac{8}{15} \times sin A = \frac{8}{15} \times \frac{15}{17} = \frac{8}{17}\\\\\frac{1}{cosA} = \frac{17}{8}\\\\sec A = \frac{17}{8}$

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Seven decreased by four times a number what is the answer

Lesechka [4]

Answer:

7-4g

Step-by-step explanation:

let the number =g

four times the number = 4×g = 4g

seven decreased br four times the number= 7- 4g

therefore, the answer = 7-4g

7 0

2 years ago

Manufacture wants to enlarger it's floor area 1.5 times that of the current facility. The current facility is 260 ft by 140 ft.

Lady bird [3.3K]

Answer:

New dimensions of the floor is approximately 301.25 ft by 181.25 ft

Step-by-step explanation:

The question is incomplete. The complete question should be:

Manufacture wants to enlarger it's floor area 1.5 times that of the current facility. The current facility is 260 ft by 140 ft. The manufacture wants to increase each dimension the same amount. Write the dimensions of the new floor.

Given:

Length of floor = 260 ft

Width of floor = 140 ft

The floor area is increased 1.5 times.

To find the new dimensions of the floor.

Solution:

Original area of the floor = $length\times width= 260\times 140=36400\ ft^2$

New area = $1.5\times Original\ Area = 1.5\times 36,400=54,600\ ft^2$

Let the length and width be increased by $x$ ft.

Thus, new length = $(260+x)\ ft$

New width = $(140+x)\ ft$

Area of the new floor can be given as:

⇒ $new\ length\times new\ width$

⇒ $(260+x)(140+x)$

Multiplying using distribution.

⇒ $x^2+260x+140x+36400$

⇒ $x^2+400x+36400$

Thus we can equate this with new area to get the equation to find $x$

$x^2+400x+36400=54600$

subtracting both sides by 54600.

$x^2+400x+36400-54600=54600-54600$

$x^2+400x+18200=0$

Using quadratic formula:

For a quadratic equation $ax^2+bx+c=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

For the equation $x^2+400x-18200=0$

$x=\frac{-400\pm\sqrt{(400)^2-4(1)(-18200)}}{2(1)}$

$x=\frac{-400\pm\sqrt{232800)}}{2}$

$x=\frac{-400\pm482.49}{2}$

$x=\frac{-400+482.49}{2} \ and\ x= \frac{-400-482.49}{2}$

∴ $x\approx 41.25 \ and\ x\approx-441.25$

Since length is being increased, so we take $x\approx41.25$

New dimensions are:

New length $\approx 260\ ft + 41.25\ ft =301.25\ ft$

New width $\approx 140\ ft + 41.25\ ft =181.25\ ft$

3 0

3 years ago

FREE COINS!<br> say thank u after ........

andrew11 [14]

Answer:

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Step-by-step explanation:

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2 years ago

Read 2 more answers

A straight line with the equation y=ax-3 goes through the point (2,11). Work out the value of a

Rzqust [24]

The value a is 7.

<h3>What is Straight Line?</h3>

A line is simply an object in geometry that is characterized under zero width object that extends on both sides. A straight line is just a line with no curves.

Here, the given equation of line

y = ax -3

line passing through point (2, 11), then

11 = a X 2 - 3

11 + 3 = 2a

2a = 14

a = 7

Thus, the value a is 7.

Learn more about Straight line from:

brainly.com/question/20492082

#SPJ1

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2 years ago

Which ordered pair is the best estimate for the solution of the system of equations?

Rasek [7]

Answer:

<u>The ordered pair of the solution is (0.022, -0.55). None of the alternatives given we can consider as the best estimate because there isn't at least one positive value for x, when it's actually positive. Picking (0, -2) as the best estimate is also far from the best estimate.</u>

Step-by-step explanation:

Let's solve the system of equations:

y = −25x

−2y = 5x+1

***********************

Substituting y in the 2nd equation:

-2 (-25x) = 5x + 1

50x = 5x + 1

45x = 1

x = 1/45

x = 0.022

**********************

Solving for y in the 1st equation:

y = -25 (0.022)

y = - 0.55

6 0

3 years ago

GivenGiven 15 cot A = 8, find sin A and sec A.​

GivenGiven 15 cot A = 8, find sin A and sec A.