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natima [27]
2 years ago
12

The ratio of red cars to blue cars in a parking lot was 7 : 2.If there were 35 red cars, how many blue cars were there?

Mathematics
1 answer:
Rufina [12.5K]2 years ago
3 0
Let there are x blue cars.
7/2 = 35/x
7x=70
x=10
so there are 10 blue cars.
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MATH HELP PLZ!!!
RoseWind [281]

Answer:

a)    tan (157.5) = \frac{1-cos 315}{sin315}

b)

            sin (165) =\sqrt{ \frac{1-cos (330) }{2}}

c)

      sin^{2} (157.5) = \frac{1-cos (315) }{2}

d)

  cos 330° = 1- 2 sin² (165°)

       

         

Step-by-step explanation:

<u><em>Step(i):-</em></u>

By using trigonometry formulas

a)

cos2∝  = 2 cos² ∝-1

cos∝ = 2 cos² ∝/2 -1

1+ cos∝ =  2 cos² ∝/2

cos^{2} (\frac{\alpha }{2}) = \frac{1+cos\alpha }{2}

b)

cos2∝  = 1- 2 sin² ∝

cos∝  = 1- 2 sin² ∝/2

sin^{2} (\frac{\alpha }{2}) = \frac{1-cos\alpha }{2}

<u><em>Step(i):-</em></u>

Given

              tan\alpha = \frac{sin\alpha }{cos\alpha }

          we know that trigonometry formulas

        sin\alpha = 2sin(\frac{\alpha }{2} )cos(\frac{\alpha }{2} )

         1- cos∝ =  2 sin² ∝/2

      Given

         tan(\frac{\alpha }{2} ) = \frac{sin(\frac{\alpha }{2} )}{cos(\frac{\alpha }{2}) }

put ∝ = 315

      tan(\frac{315}{2} ) = \frac{sin(\frac{315 }{2} )}{cos(\frac{315 }{2}) }

     multiply with ' 2 sin (∝/2) both numerator and denominator

        tan (\frac{315}{2} )= \frac{2sin^{2}(\frac{315)}{2}  }{2sin(\frac{315}{2} cos(\frac{315}{2}) }

Apply formulas

 sin\alpha = 2sin(\frac{\alpha }{2} )cos(\frac{\alpha }{2} )

  1- cos∝ =  2 sin² ∝/2

now we get

 tan (157.5) = \frac{1-cos 315}{sin315}

       

b)

          sin^{2} (\frac{\alpha }{2}) = \frac{1-cos\alpha }{2}

               put ∝ = 330° above formula

             sin^{2} (\frac{330 }{2}) = \frac{1-cos (330) }{2}

            sin^{2} (165) = \frac{1-cos (330) }{2}

            sin (165) =\sqrt{ \frac{1-cos (330) }{2}}

c )

         sin^{2} (\frac{\alpha }{2}) = \frac{1-cos\alpha }{2}

               put ∝ = 315° above formula

             sin^{2} (\frac{315 }{2}) = \frac{1-cos (315) }{2}

            sin^{2} (157.5) = \frac{1-cos (315) }{2}

           

d)

     cos∝  = 1- 2 sin² ∝/2

   put      ∝ = 330°

       cos 330 = 1 - 2sin^{2} (\frac{330}{2} )

      cos 330° = 1- 2 sin² (165°)

3 0
3 years ago
A boat sails on a bearing of 038°anf then 5km on a bearing of 067°.
I am Lyosha [343]

This question is not complete

Complete Question

A boat sails 4km on a bearing of 038 degree and then 5km on a bearing of 067 degree.(a)how far is the boat from its starting point.(b) calculate the bearing of the boat from its starting point

Answer:

a)8.717km

b) 54.146°

Step-by-step explanation:

(a)how far is the boat from its starting point.

We solve this question using resultant vectors

= (Rcos θ, Rsinθ + Rcos θ, Rsinθ)

Where

Rcos θ = x

Rsinθ = y

= (4cos38,4sin38) + (5cos67,5sin67)

= (3.152, 2.4626) + (1.9536, 4.6025)

= (5.1056, 7.065)

x = 5.1056

y = 7.065

Distance = √x² + y²

= √(5.1056²+ 7.065²)

= √75.98137636

= √8.7167296826

Approximately = 8.717 km

Therefore, the boat is 8.717km its starting point.

(b)calculate the bearing of the boat from its starting point.

The bearing of the boat is calculated using

tan θ = y/x

tan θ = 7.065/5.1056

θ = arc tan (7.065/5.1056)

= 54.145828196°

θ ≈ 54.146°

7 0
2 years ago
Use the definition of continuity to determine whether f is continuous at a. f(x) = 5x+5 a = -5 Question
Andrej [43]

ANSWER

lim_{x \to  - 5}(f(x))  = f( - 5)

EXPLANATION

If f(x) is continuous at

x = a

Then,

lim_{x \to a}(f(x))  = f(a)

The given function is

f(x) = 5x + 5

f( - 5) =  5( - 5) + 5

f( - 5) =  - 25 + 5 =  - 20

lim_{x \to  - 5}(f(x))  = 5( - 5) + 5

lim_{x \to  - 5}(f(x))  =  - 20

Since,

lim_{x \to  - 5}(f(x))  = f( - 5)

The function is continuous at

x =  - 5

4 0
3 years ago
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Suppose that g(x)=f(x+8)+4 which statement best compares the graph of g(x) with the graph of f(x)
olga nikolaevna [1]


The graph of G(x) is the graph of F(x) shifted 4 units down. B. The graph of G(x) is the graph of F(x) shifted 4 units to the left C. The graph of G(x)...



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3 years ago
Simplify<br> 50(x^2+7x+6)
worty [1.4K]

Distribute 50 to every term inside the parentheses.

50\cdotx^2+50\cdot7x+50\cdot6

Simplify with multiplication.

\huge\boxed{50^2+350x+300}

You can't simplify further by adding, so leave the answer as-is.

4 0
1 year ago
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