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3 years ago

I really need help with this

Mathematics

1 answer:

Sedbober [7]3 years ago

3 0

Answer:

A. ∠1 = 105°

B. ∠2 = 105°

C. ∠1 = 105°

Step-by-step explanation:

We are given the angle made by the 4th street with King's Avenue is 75° as shown in the figure below.

Ques A: It is given that, Car travelling west on the 4th street turns towards south on the King's Avenue.

So, the required angle is ∠1.

Since, The sum of angles formed on a straight line is 180°.

Then, ∠1 + 75° = 180° i.e. ∠1 = 180-75 = 105°

Thus, ∠1 = 105°

Ques B: It is given that, Car travelling southwest on King's Avenue and turns right on 3rd street.

So, the required angle is ∠2.

<em>We have, 'Corresponding anges of two parallel lines are equal' and 'The sum of angles formed on a straight line is 180°.</em>

Then, ∠2 + 75° = 180° i.e. ∠2 = 180-75 = 105°

Thus, ∠2 = 105°

Ques C: It is given that, Car travelling northeast on King's Avenue and turns right on 4th street.

So, the required angle is ∠1.

Since, The sum of angles formed on a straight line is 180°.

Then, ∠1 + 75° = 180° i.e. ∠1 = 180-75 = 105°

Thus, ∠1 = 105°

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3 years ago

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If x = 10, y = 5, and z = 11, what is the tangent ratio for g°?

loris [4]

Please, find attached the image with the complete question

Answer:

$\large\boxed{\large\boxed{tan(g\º )=2}}$

Explanation:

The triangle ACB is a right triangle with these features:

x represents the opposite side to the angle g

y represents the adjacent side to the angle g

The <em>tangent ratio </em>on an angle in a right triangle is equal to the length of the leg opposite to the angle divided by the length of the leg adjacent to the angle.

Hence:

$tangent(g\º )=x/y=10/5=2\leftarrow answer$

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3 years ago

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Which equation represents the line that passes through the points (2, 4) and (1, -3)?

zhannawk [14.2K]

Answer:

y = 7x - 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (1, - 3)

m = $\frac{-3-4}{1-2}$ = $\frac{-7}{-1}$ = 7, thus

y = 7x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 4), then

4 = 14 + c ⇒ c = 4 - 14 = - 10

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3 years ago

Evaluate Dx / ^ 9-8x - x2^

Solnce55 [7]

It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for $\sqrt x$ .

In that case, you want to find the antiderivative,

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}$

Complete the square in the denominator:

$9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2$

Now substitute $x+4=5\sin y$ , so that $\mathrm dx=5\cos y\,\mathrm dy$ . Then

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy$

which simplifies to

$\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy$

Now, recall that $\sqrt{x^2}=|x|$ . But we want the substitution we made to be reversible, so that

$x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)$

which implies that $-\dfrac\pi2\le y\le\dfrac\pi2$ . (This is the range of the inverse sine function.)

Under these conditions, we have $\cos y\ge0$ , which lets us reduce $\sqrt{\cos^2y}=|\cos y|=\cos y$ . Finally,

$\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C$

and back-substituting to get this in terms of $x$ yields

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C$

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