I buy a car for 24,000 dollars. My car depreciates 11% per year. How much will it cost after 5 years?

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 tests are used to determine the radius of convergence of a power series? A. Divergence TestB. Root Test C. Comparison Test

REY [17]

Answer:

The radius of convergence is half of the length of the interval of convergence. If the radius of convergence is R then the interval of convergence will include the open interval: (a − R, a + R). To find the radius of convergence, R, you use the Ratio Test.

7 0

3 years ago

A scientist has two solutions, which she has labeled Solution A and Solution Each contains salt. She knows that Solution A is 40

Alexxandr [17]

Answer:

Step-by-step explanation:

Let the number of ounces of

A = x

B = y

A scientist has two solutions, which she has labeled Solution A and Solution Each contains salt. She knows that Solution A is 40% salt and Solution B is 55% salt. She wants to obtain 90 ounces of a mixture that is 45% salt. How many ounces of each solution should she use?

Our system of equations is given as

x + y = 90.... Equation 1

x = 90 - y

40% × x + 55% × y = 45% × 90 ounces

0.4x + 0.55y = 40.5....Equation 2

We substitute 90 - y for x in Equation 2

6 0

3 years ago

A shipment of sugar fills 2 1/5 containers. If each container holds

chubhunter [2.5K]

8.25 tons or 8 1/4
just multiply the two numbers together

3 0

4 years ago

Is 11/20 greater than a half

jeyben [28]

Yes, as one half or 1/2 is also 10/20. 11/20 is greater than half by a 10% margin.

3 0

3 years ago

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