Answer:
6.4 minutes, or 6 minutes and 24 seconds
Step-by-step explanation:
She is running 4 laps, so she is running 1600 meters total. If she runs 250 meters per minute, divide 1600 by 250 to determine how many minutes it will take...
1600/250 = 6.4
Which is 6 minutes + 0.4 minutes
*there are 60 seconds in a minute, so the 0.4 represents 40% of another minute. Multiply 60 by 0.4 to see how many seconds this is...
(0.4)60 = 24 seconds,
So she ran the laps in 6 minutes and 24 seconds
From the two right triangles, you can write the following equations using the Pythagorean theorem. Let's call that shared leg in the middle "y"
y^2 + b^2 = a^2
y^2 + c^2 = x^2
y^2 + b^2 = a^2
re-write this to get "y" alone for substitution.
y^2 = a^2 - b^2
substitute (a^2 - b^2) for y^2 in the other equation. y^2 + c^2 = x^2
a^2 - b^2 + c^2 = x^2
Now put in the values given for a,b,c to solve for x
(7.1)^2 - (5.6)^2 + (5.7)^2 = x^2
51.54 = x^2
square root
7.2 = x
Answer:
Equation is: y = 0.5x² + 0.5x - 3
Explanation:
general form of the parabola is:
y = ax² + bx + c
Now, we will need to solve for a, b and c.
To do this, we will simply get points from the graph, substitute in the general equation and solve for the missing coefficients.
First point that we will use is (0,-3).
y = y = ax² + bx + c
-3 = a(0)² + b(0) + c
c = -3
The equation now becomes:
y = ax² + bx - 3
The second point that we will use is (2,0):
y = ax² + bx - 3
0 = a(2)² + b(2) - 3
0 = 4a + 2b -3
4a + 2b = 3
This means that:
2b = 3 - 4a
b = 1.5 - 2a ...........> I
The third point that we will use is (-3,0):
y = ax² + bx - 3
0 = a(-3)² + b(-3) - 3
0 = 9a - 3b - 3
9a - 3b = 3 ...........> II
Substitute with I in II and solve for a as follows:
9a - 3b = 3
9a - 3(1.5 - 2a) = 3
9a - 4.5 + 6a = 3
15a = 7.5
a = 7.5 / 15
a = 0.5
Substitute with the value of a in equation I to get b as follows:
b = 1.5 - 2a
b = 1.5 - 2(0.5)
b = 0.5
Substitute with a and b in the equation as follows:
y = 0.5x² + 0.5x - 3
Hope this helps :)
Answer:
A) -9/2
B) 9/4
C) -9/2, same as A)
Step-by-step explanation:
We are given that 
. We use the properties of integrals to write the new integrals in terms of I.
A) 
. We have used that ∫cf dx=c∫f dx.
B) 
. Here we used that reversing the limits of integration changes the sign of the integral.
C) It's the same integral in A)
Answer:
B
Step-by-step explanation:
