Answer:
(1, - 3 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ), thus
T(- 3, - 1 ) → T'(1, - 3 )
Answer:
INF for first while D for second
Step-by-step explanation:
Ok I think I read that integral with lower limit 1 and upper limit infinity
where the integrand is ln(x)*x^2
integrate(ln(x)*x^2)
=x^3/3 *ln(x)- integrate(x^3/3 *1/x)
Let's simplify
=x^3/3 *ln(x)-integrate(x^2/3)
=x^3/3*ln(x)-1/3*x^3/3
=x^3/3* ln(x)-x^3/9+C
Now apply the limits of integration where z goes to infinity
[z^3/3*ln(z)-z^3/9]-[1^3/3*ln(1)-1^3/9]
[z^3/3*ln(z)-z^3/9]- (1/9)
focuse on the part involving z... for now
z^3/9[ 3ln(z)-1]
Both parts are getting positive large for positive large values of z
So the integral diverges to infinity (INF)
By the integral test... the sum also diverges (D)
<h3>
Answer:</h3>
4 miles per hour
<h3>
Step-by-step explanation:</h3>
Unit rate is the rate of something per 1 unit. In other words, the unit rate is x units per 1 unit. In this situation, the unit rate is how many miles Hassan walks in 1 hour.
Proportion
First, to find the rate of anything we can set up a proportion. In the question, the rate is described as miles per hour, so the miles will be the numerator and the hours will be the denominator.
- This creates the proportion
So, the rate we are given is 12/3.
Unit Rate
To find the unit rate we need to make the denominator equal to 1. To do this, divide both the numerator and denominator by 3.
- 12/3 equals 4
- 3/3 equals 1
So, this means that the new proportion is 4/1. Next, we can add our units, which means that Hassan walks 4 miles per 1 hour.
Graph
Now we can resize the bar graph. The purple bar should be set to 4 because this represents the miles. Then, the green bar should be set to 1 because it represents the hours.
Let...
l=length
w=width
Because we know that the perimeter is 90, we can make this equation...
2l+2w=90
Because we know that the length is 5 feet less than 4 times the width, we can make this equation...
l=4w-5
We can solve this system through substitution...
2(4w-5)+2w=90
8w-10+2w=90
10w=100
w=10 ft
l=4(10)-5=35 ft
Answer:
6750
Step-by-step explanation:
simple interest = P×r%×t
P = $6000
r = 2.5%
t = 5 years
I = 6000 × 2.5/100 × 5
= 750
6000 + 750 = $6750
