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3 years ago

2 questions! area of plane and composite figures

Mathematics

1 answer:

VikaD [51]3 years ago

4 0

Find the base and height of each side, subtract the triangle from the trapezoid then find the area of the parrellogram and add the subracted one and the obtuse square

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A student is given that point P(a, b) lies on the terminal ray of angle Theta, which is between StartFraction 3 pi Over 2 EndFra

Harman [31]

Answer:

A.

The student made an error in step 3 because a is positive in Quadrant IV; therefore,

$cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}$

Step-by-step explanation:

Given

$P\ (a,b)$

$r = \± \sqrt{(a)^2 + (b)^2}$

$cos\theta = \frac{-a}{\sqrt{a^2 + b^2}} = -\frac{\sqrt{a^2 + b^2}}{a^2 + b^2}$

Required

Where and which error did the student make

Given that the angle is in the 4th quadrant;

The value of r is positive, a is positive but b is negative;

Hence;

$r = \sqrt{(a)^2 + (b)^2}$

Since a belongs to the x axis and b belongs to the y axis;

$cos\theta$ is calculated as thus

$cos\theta = \frac{a}{r}$

Substitute $r = \sqrt{(a)^2 + (b)^2}$

$cos\theta = \frac{a}{\sqrt{(a)^2 + (b)^2}}$

$cos\theta = \frac{a}{\sqrt{a^2 + b^2}}$

Rationalize the denominator

$cos\theta = \frac{a}{\sqrt{a^2 + b^2}} * \frac{\sqrt{a^2 + b^2}}{\sqrt{a^2 + b^2}}$

$cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}$

So, from the list of given options;

The student's mistake is that a is positive in quadrant iv and his error is in step 3

3 0

3 years ago

What is the value of the function at x=−3? A) y = 0 B) y=−3 C) y = 4 D) y = 3

Alexus [3.1K]

Answer:

y=4

Step-by-step explanation:

From the graph we can see that-

when, x=-3 , y=4

That is , the graph passes through (-3 , 4)

So,

for x=-3 ,

we get y=4

So, the answer is y=4

5 0

3 years ago

In a 30°-60°-90° triangle, what is the length of the longer leg when the length of the hypotenuse is 18 inches?

max2010maxim [7]

Answer:

9sqrt(3) in.

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is:

short leg : long leg : hypotenuse

1 : sqrt(3) : 2

If the short leg measures 1, then the hypotenuse measures 2.

The length of the hypotenuse is twice the length of the short leg.

The length of the long leg is sqrt(3) times the length of the short leg.

If the hypotenuse measures 18 in., then the short leg measures 9 in.

Then the long leg measures 9sqrt(3) in.

8 0

3 years ago

HELP NEEDED! Evaluate: 8 + -12 - -12/2

svp [43]

Answer:

Step-by-step explanation:

because if 8+-12= about-4 so if you have a negative number plus a positive it equals a negative number then you have -4 minus -12 equals a positive is 8 because if its negative and negative it equals a positive number then you have 8/2 and it equals 4 because that slash is a divided sign all together it is 8+-12-(-12)/2=2

3 0

3 years ago

Read 2 more answers

Use quadrilateral ABCD to find the value of X. The figure is not drawn to scale. Use the following dimensions: mABC=4x, mBCD=3x,

Dmitrij [34]

Answer: x=30

Step-by-step explanation:

The sum of the angles must be 360.

4x+3x+3x+2x = 12x

12x = 360

x =360/12 = 30

5 0

3 years ago

Read 2 more answers