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Ber [7]
3 years ago
13

GEOMETRY/INTRO TO TRIG QUESTION! Please show your work and explain.

Mathematics
2 answers:
postnew [5]3 years ago
4 0

Answer:

The answer to your question is AB = 6.9

Step-by-step explanation:

Data

∠A = 70°

∠C = 62°

BC = 7.3

AB = x

Process

1.- To solve this problem use the law of sines

                 AB / sin C = BC / sin A

Substitution

                 AB / sin 62 =  7.3 /  sin 70

Solve for AB

                AB = 7.3(sin 62) / sin 70

                AB = 7.3(0.883) / 0.940

                AB = 7.3 (0.939)

Result

                 AB = 6.8                

                     

Sloan [31]3 years ago
4 0

Answer:

Step-by-step explanation:

Since we are given 2 angles and 1 side, to determine AB, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle.

Therefore

AB/Sin62 = 7.3/Sin70

Cross multiplying, it becomes

AB × Sin 70 = 7.3 × Sin 62

AB × 0.9397 = 14 × 0.8829

0.9397AB = 12.3606

Dividing the left hand side and the right hand side of the equation by 0.9397, it becomes

0.9397AB/0.9397 = 12.3606/0.9397

AB = 13.2 to the nearest tenth

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kozerog [31]

Answer:

a) 74.0353 < u <  74.0367

b) 74.036 < u

Step-by-step explanation:

Given:

- Sample size n = 15

- Standard deviation s.d = 0.0001 in

- Sample mean x_bar = 74.036

Find:

A) Calculate the 99% two-sided confidence interval on the true mean piston diameter.

Solution:

- For 99% CI, We have a = 0.01 , and Z_a/2 = 2.58

------> (x_bar - Z_a/2*s.d / sqrt(n)) < u <  (x_bar + Z_a/2*s.d / sqrt(n))

------> (74.036 - 2.58*0.0001 / sqrt(15)) < u <  (74.036 + 2.58*0.0001 / sqrt(15))

------>                               74.0353 < u <  74.0367

Find:

B) Calculate the 95% one-sided lower confidence interval on the true mean piston diameter.

Solution:

- For 95% lower CI, We have a = 0.05 , and Z_a = 1.645

------> (x_bar - Z_a/2*s.d / sqrt(n)) < u

------> (74.036 - 1.645*0.0001 / sqrt(15)) < u

------>                               74.036 < u

5 0
3 years ago
An equilateral triangle with side length 7 cm is shown in the diagram, work out the area of the triangle.
ElenaW [278]
If a triangle has sides of 7 cm and it is an equilateral you can draw a line right down the middle to form two congruent triangles.

These smaller triangles have a hypotenuse of 7cm and a base of 3.5 cm (7/2)

To work out the height, use Pythagoras’ theorem.

a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the other two sides

7^2 - 3.5^2 = 36.75

Square root answer

= 6.06 cm

That’s the height of the triangle

Area of a triangle is base x height divided by 2

So 7 x 6.06 = 42.43…

/2

= 21.2 cm^2 to one d.p

Hope this helped!
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Irina18 [472]

Answer:

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Step-by-step explanation:

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7 0
2 years ago
Find the equation of the line with slope m=1/4 that contains the point (4,5).
sladkih [1.3K]

Answer: x - 4y = -16

Step-by-step explanation: Since we're given a point and a slope, we can write the equation of this line using the point-slope formula.

<h2>y  -  y₁  =  m(x  -  x₁)</h2><h2 />

The given point, (4, 5), represents (x₁, y₁).

So if we plug all our given information into the formula,

including our slope of 1/4, we get y - 5 = 1/4(x - 4).

To put our equation in standard form, first, distribute

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So we get y - 5 = 1/4x - 1.

Remember that standard form cannot have any fractions in it so our next step is to multiply both sides of the equation by 4 to get rid of the fraction.

That gives us 4y - 20 = x - 4.

Now moves the -20 to the right side by adding 20 to both sides.

So we get 4y = x + 16.

Now subtract x from both sides to get -x + 4y = 16.

Finally, our coefficient on our x term must be positive so we

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7 0
2 years ago
Given the polynomial 2x3 + 18x2 − 18x − 162, what is the value of the coefficient 'k' in the factored form?2x3 + 18x2 − 18x − 16
s344n2d4d5 [400]

Answer:

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Step-by-step explanation:

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f(x)=2x^3+18x^2-18x-162

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We factor the polynomial within the parenthesis by grouping.

f(x)=2(x^2(x+9)-9(x+9)

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We now compare to;

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It is now obvious that k=3

6 0
3 years ago
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