The distance<u> between </u>Jays hair and the caffe shop is 2.5 km.
Since the mall is located 2.4 kilometers<u> north</u> of jays house and the caffe shop is located 0.7 kilometers <u>east </u>of the mall, both directions are perpendicular. So, the distance between Jays hair and the caffe shop forms the hypotenuse side of this right angled triangle.
So, using Pythagoras' theorem, we find the hypotenuse side of this triangle, L.
Pythagoras' theorem states that the sum of squares of the sides of a right angled triangle equal the square of the hypotenuse side.
So, L = √[(2.4 km)² + (0.7 km)²]
L = √[(5.76 km² + 0.49 km²]
L = √(6.25 km²)
L = 2.5 km
So, the distance<u> between </u>Jays hair and the caffe shop is 2.5 km.
Learn more about Pythagoras' theorem here:
brainly.com/question/8171420
So it tells us that g(3) = -5 and g'(x) = x^2 + 7.
So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))
now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16
Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84
So we have our linear approximation for the two.
If you wanted to, you could check your answer by finding g(x). Since you know g'(x), take the antiderivative and we will get
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35
So just to check our linear approximations use that to find g(2.99) and g(3.01)
g(2.99) = -5.1597
g(3.01) = -4.8397
So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer. Not a bad method if you ever need to use it.
Answer:
12,922
Step-by-step explanation:
estimate = 16,092 * 803/1,000 = 12,922
Answer:
The ratio is 12:20.
Step-by-step explanation:
3:5, if simplified.
