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3 years ago

Solve the remaining sides of the triangle: C=95(degrees), a=1/2, and b=1/3

Mathematics

2 answers:

o-na [289]3 years ago

8 0

There is only 1 remaining side

We have 2 sides and an included angle, we use the Law of Cosines to solve the third side:

c^2 = a^2 + b^2 -2ab *cos(C)

c^2 = .5^2 + .333333333...^2 - 2 * .5 * .3333333... * cos (95)

c^2 = .25 + .1111111111111111... -2*.5*.3333333333...* -0.087156

c^2 = 0.3611111111 + 0.029052

c^2 = 0.3901631111

c = 0.6246303796

snow_tiger [21]3 years ago

6 0

There is only 1 remaining side

We have 2 sides and an included angle, we use the Law of Cosines to solve the third side:

c^2 = a^2 + b^2 -2ab *cos(C)

c^2 = .5^2 + .333333333...^2 - 2 * .5 * .3333333... * cos (95)

c^2 = .25 + .1111111111111111... -2*.5*.3333333333...* -0.087156

c^2 = 0.3611111111 + 0.029052

c^2 = 0.3901631111

c = 0.6246303796

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A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric

larisa86 [58]

Answer:

525 x 1,050

A = 551,250 m²

Step-by-step explanation:

Let 'L' be the length parallel to the river and 'S' be the length of each of the other two sides.

The length of the three sides is given by:

$2S+L=2,100\\ L=2100-2S$

The area of the rectangular plot is given by:

$A=S*L\\A=S(2100-2S)\\A=2100 S -2S^2$

The value of 'S' for which the area's derivate is zero, yields the maximum total area:

$\frac{dA(S)}{dS}=\frac{d(2100 S -2S^2)}{dS}\\0= 2100 - 4S\\S=525$

Solving for 'L':

$L=2100-(2*525)\\L=1,050$

The largest area enclosed is given by dimension of 525 m x 1,050 and is:

$A = 525*1,025\\A=551,250\ m^2$

5 0

3 years ago

Tim,Griff and Kay baked chocolate for Kay s birthday party.Tim baked 3 times as many as Kay.Griff baked half as many as Tim.Alto

lianna [129]

Answer: 48

------------------------------------------------------------------------------
Define the number of cakes they baked in term of x
------------------------------------------------------------------------------
Let the number of cakes Kay baked be x

Kay = x
Tim = 3x   ← Tim baked 3 times as many as Kay
Griff = 1.5x   ← Griff baked 1/2 as many as Tim

------------------------------------------------------------------------------
Construct the equation and solve for x
------------------------------------------------------------------------------
The total number of cakes baked was 88.

x + 3x + 1.5x = 88   ← Combine like terms
5.5 x = 88 ← Divide by 5.5
÷5.5   ÷5.5
x = 16

------------------------------------------------------------------------------
Find the number of cakes each baked
------------------------------------------------------------------------------
Kay = x = 16
TIm = 3x = 16 x 3 = 48
Griff = 1.5x = 1.5(16) = 24

------------------------------------------------------------------------------
Answer: Tim baked 48 cakes.
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