Answer is Provided in the image attached.
The speed of the ball is
ds/dt = 32t
At t =1/2 s
ds/dt = 16 ft/s
The distance from the ground
50 - 16(1/2)^2 = 46 ft
The triangles formed are similar
50/46 = (30 + x)/x
x = 345 ft
50 / (50 - s) = (30 + x)/x
Taking the derivative and substituing
ds/dt = 16
and
Solve for dx/dt
The initial value equals the y-intercept. The equation is in the slope-intercept formula where b is the y-intercept. The answer would be -7. [Note: If it's + in front of the b value, it's a positive value (b). If - is in front of it, it's a negative value (-b).]
If RS is congruent to MN then the value of x in all the parts are 6,4, and 10.
Given RS is congruent to MN.
We are required to find the value of x if RS is congruent to MN.
Congruent lines are those lines whose lengths are equal to each other.
1) RS=x+10, MN=2x+4.
Because the congruent lines have equal lengths so , RS=MN.
x+10=2x+4
x-2x=4-10
-x=-6
x=6
2) RS=3x-2, MN=x+6
Because the length of lines are equal,so RS=MN.
3x-2=x+6
3x-x=6+2
2x=8
x=4
3) RS=5x-10, MN=2x+20
The lengths are equal so RS=MN.
5x-10=2x+20
5x-2x=20+10
3x=30
x=10
Hence if RS is congruent to MN then the value of x in all the parts are 6,4, and 10.
Learn more about congruent lines at brainly.com/question/28220245
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Using the magic of algebra!:
The time each train goes in 1 hour will be represented as a / b.
b is 30 more than a, so if we add 30 to a it should equal b.
a + 30 = b
In three hours, the trains are 330 miles apart.
Esentially, we're adding up the distance each train goes from the starting point to find the distance between them.
3b + 3a = 330
Now we have a system of equations to solve.
a + 30 = b
3b + 3a = 330
We want to get the variables on seperate sides of the equation for easy solving.
a + 30 = b
3b = 330 - 3a
Then get the value of the one variable the same so we can use the transitive property.
a + 30 = b
b = 110 - a
a + 30 = 110 - a
2a + 30 = 110
2a = 80
a = 40 mph
(And thus b = 70 mph)
