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3 years ago

In ∆ABC, ∠BAC= 80°, ∠ABC=60°, a = 7, b = x.

2 answers:

4 0

To solve the value of x we use the sine rule that states.
a/sinA = b/sinB = c/sinC
Where a, b, and c are the opposite sides of angle A, B. and C respectively.

x/sin60 = 7/sin80

x =(7sin60)/sin80

= 6.062/0.9848
=6.155696691

To 3 significant figures the answer is 6.16

prohojiy [21]3 years ago

4 0

Using the law of the sine we have two possibilities:
Way 1:
x / sine (60) = 7 / sine (80)
Rewriting we have:
x = (7 / sine (80)) * (sine (60))
x = 6.16
Way 2:
x / sine (80) = 7 / sine (60)
Rewriting we have:
x = (7 / sine (60)) * (sine (80))
x = 7.96
Answer:
x = 6.16
or
x = 7.96
Note: it depends on the location of a and b in the triangle.

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Find the area of the shaded region

VikaD [51]

Answer:

Area of the shades region = 244.6 ft²

Step-by-step explanation:

Area of the shaded region = Area of the rectangle ABCD- Area of the right angle triangle DEC

Area of the rectangle = Length × width

= 29.8 × 13

= 387.4 ft²

By applying Pythagoras theorem in the right triangle DEC,

(Hypotenuse)² = (leg 1)² + (leg 2)²

CD² = DE² + EC²

(29.8)² = DE² + (28)²

888.04 = DE² + 784

DE² = 888.04 - 784

DE = 10.2 ft

Area of ΔDEC = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(10.2)(28)$

= 142.8 ft²

Area of the shades region = 387.4 - 142.8

= 244.6 ft²

4 0

3 years ago

Please help WILL MARK BRAINLIEST I need the right answer

LUCKY_DIMON [66]

Answer: a

Step-by-step explanation:

6 0

3 years ago

Sphere A and Sphere B , are similar. The volumes of A and B, are 17 and 136 cubic centimetres, respectively. The diameter of B ,

xxMikexx [17]

Answer:

Step-by-step explanation:

Given: Sphere A and Sphere B are similar.

The volumes of A and B are 17 $cm^3$ and 136

The diameter of B is 6 cm.

To find: diameter of A

Solution:

Let R denotes radius of sphere A and r denotes radius of sphere B.

Radius of sphere A= R

Diameter of sphere B = 6 cm

So, radius of sphere B (r) = $\frac{6}{2}=3\,\,cm$

Volume of sphere is $\frac{4}{3}\pi(radius)^3$

Volume of sphere A = $\frac{4}{3}\pi(R)^3$

$\frac{\frac{4}{3}\pi R^3}{\frac{4}{3}\pi r^3}=\frac{17}{136}=\frac{1}{8}\\\frac{R^3}{r^3}=\frac{1}{8}\\\frac{R}{r}=\frac{1}{2}\\r=2R$

Put r = 3 cm

$3=2R\\R=\frac{3}{2}=1.5\,\,cm$

Diameter of sphere A = 2 × Diameter

= 2 × 1.5

=3 cm

6 0

3 years ago

A box making machine makes cardboard boxes at a rate of 40 boxes per minute. How many minutes does it take to make 360 boxes?

KATRIN_1 [288]

40/1=360/X
40x=360
Divide by 40
X=9 minutes

4 0

4 years ago

what is the equation of the line that is parallel to the given line and passes through the point (2, 3)?

Alik [6]

Given problems:

Line parallel that passes through (2,3);

Solution:

To solve this problem, we need to first understand what parallel lines are.

A parallel line is any two line that does not meet at any point.

In order to achieve this, both lines must have the same slope.

So, we find the slope of the given line and write in the form for a straight line.

Slope of line = $\frac{y_{2} - y_{1} }{x_{2} - x_{1} }$

let x₁, y₁ = (-2, -1)

x₂, y₂ = (2 , -3)

Now input the parameters and solve for the slope;

Slope of line = $\frac{-3-(-1)}{2- (-1)}$ = $\frac{-2}{3}$

Any line that would be parallel to this must have the same slope.

Equation of a straight line;

y = mx + c;

y and x are the coordinates;

m is the slope

c is the y-axis intercept;

From (2, 3);

y = 3 and x = 2; m = $\frac{-2}{3}$

3 = $\frac{-2}{3}$ x 2 + C

3 = $-\frac{4}{3}$ + C

C = $\frac{13}{3}$

So the equation of the line is;

y = $\frac{-2}{3} x$ + $\frac{13}{3}$

Multiply through by 3;

3y = -2x + 13

The equation of the line is 3y = -2x + 13

4 0

4 years ago