Since this point is located in the fourth quadrant you have to rotate it 270 degrees counterclockwise which would end up being in third quadrant. which means the new point would be (-6,-9)

6 0

3 years ago

An adult takes 800 mg of ibuprofen. Each hour, the amount of ibuprofen in the person's

ss7ja [257]

Answer:

116.31468544 mg ibuprofen left

Step-by-step explanation:

Since there are 800 mg at the beginning and the system decreases by about 32% of the ibuprofen

After 1 hour

→ 800 - (800x32/100) = 800 - 256 = 544 mg ibuprofen left

After 2 hours

→ 544 - (544x32/100) = 544 - 174.08 = 369.92 mg ibuprofen left

After 3 hours

→ 369.92 - (369.92x32/100) = 369.92 - 118.3744 = 251.5456 mg ibuprofen left

After 4 hours

→ 251.5456 - (251.5456x32/100) = 251.5456 - 80.494592 = 171.051008 mg ibuprofen left

After 5 hours

→ 171.051008 - (171.051008x32/100) = 171.051008 - 54.73632256 = 116.31468544 mg ibuprofen left

3 0

2 years ago

Evaluate the integral. (remember to use absolute values where appropriate. Use c for the constant of integration.) 5 cot5(θ) sin

ozzi

$I=5\int \frac{cos^{4}\theta }{sin\theta }\times cos\theta d\theta \\\\I=5\int \left ( 1-sin^{2}\theta \right )^{2}\times \frac{cos\theta }{sin\theta }d\theta \\put\ \sin\theta =t\\\\dt=cos\theta d\theta \\\\I=5\int\frac{t^{4}+1-2t^{2}}{t}dt\ \ \ \ \ \ \ \ \ \ \because (a-b)^2=a^2+b^2-2ab\\\\I=5\left ( \int t^{3}dt + \int \frac{1}{t} -2\int t \right )dt$

by using the integration formula

we get,

$\\I=5\left ( \frac{t^{4}}{4} +logt -t^{2}\right )\\\\I=\frac{5}{4}t^{4}+5\log t-5t^{2}+c$

now put the value of t=\sin\theta in the above equation

we get,

$\int 5\cot^5\theta \sin^4\theta d\theta=\frac{5}{4}sin^{4}\theta+5\log \sin\theta - 5sin^{2} \theta+c$

hence proved

7 0

2 years ago

What are the two solutions of 2x^2 = -X^2 - 5x - 1?

Sidana [21]

Answer:

Step-by-step explanation:

Let's solve 2x^2 = -X^2 - 5x - 1. Consolidate all terms on the left side and write 0 on the right side:

3x^2 + 5x + 1 = 0. This is a quadratic equation. Let's solve it for x using the quadratic formula:

a = 3, b = 5, c = 1, and so the discriminant is b^2 - 4ac = 5^2 - 4(3)(1) = 13. Because the discriminant is positive, we know that there are two distinct, real roots; the graphs of y = 2x^2 and y = x^2 - 5x - 1 intersect in two places whose x-coordinates are the real roots mentioned above.

Answer A is not correct as stated, but would be correct if we were to replace "the y-coordinates" with "the x-coordinates."

Answer C would be correct if and only if we write y = x^2 - 5x - 1.

6 0

3 years ago