A circle has a circumference of 907.46 units. What is the diameter of the circle?

The ratio of the same side interior angles of two parallel lines is 1:14. Find the measures of all eight angles formed by the pa

prisoha [69]

Answer:

At the intersection of the first parallel line with the transversal, a = 12°, c = 168°, d = 12°, e = 168°. Counting counterclockwise from a.

At the first intersection of the second parallel line with the transversal, b = 168°, f = 12°, g = 168°, h = 12°. Counting clockwise from b.

Step-by-step explanation:

Let a be the first interior angle. Since they are in 1:14, the second same side interior angle is b = 14a.

We know that the sum of interior angles equals 180°.

So, a + b = 180°

a + 14a = 180°

15a = 180°

a = 180/15

a = 12°

At alternate angle to the other interior angle, b adjacent to a is c = b = 14a = 14 × 12 = 168°

The angle vertically opposite to a is d = a = 12°

The angle vertically opposite to a is b = e = 168°

At the intersection of the second parallel line and the transversal, the angle alternate to a is f = a = 12°

the angle vertically opposite to angle b is g = b = 168°

the angle vertically opposite to f is h = 12°

4 0

2 years ago

Which of the following rational functions is graphed below?

AlekseyPX

Answer:

The rational function that is graphed is B

6 0

2 years ago

Read 2 more answers

The equation h(t) = -16t² + 80t + 64 represented the height, in feet, of a potato t seconds after it has been launched.

Lyrx [107]

Answer:

Part A) The potato hit the ground at t=5.70 seconds (see the explanation)

Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

we have

$h(t)=-16t^2+80t+64$

where

h(t) is the height of a potato in feet

t is the time in seconds

Part A) Write an equation that can be solved to find when the potato hits the ground. Then solve the equation

we know that

When the potato hit the ground, the value of h(t) must be equal to zero

so

For h(t)=0

$-16t^2+80t+64=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^2+80t+64=0$

so

$a=-16\\b=80\\c=64$

substitute in the formula

$t=\frac{-80\pm\sqrt{80^{2}-4(-16)(64)}} {2(-16)}$

$t=\frac{-80\pm\sqrt{10,496}} {-32}$

$t=\frac{-80+\sqrt{10,496}} {-32}=-0.70$

$t=\frac{-80-\sqrt{10,496}} {-32}=5.70$

therefore

The potato hit the ground at t=5.70 seconds

Part B) Write an equation that can be solved to find when the potato is 40 feet off the ground. Then solve the equation

For h(t)=40 ft

substitute in the quadratic equation

$-16t^2+80t+64=40$

$-16t^2+80t+24=0$

Solve the quadratic equation

we have

$a=-16\\b=80\\c=24$

substitute in the formula

$t=\frac{-80\pm\sqrt{80^{2}-4(-16)(24)}} {2(-16)}$

$t=\frac{-80\pm\sqrt{7,936}} {-32}$

$t=\frac{-80+\sqrt{7,936}} {-32}=-0.28$

$t=\frac{-80-\sqrt{7,936}} {-32}=5.28$

therefore

The potato is 40 feet off the ground at the time t=5.28 seconds

3 0

2 years ago

A small ball is released from rest from a point that is 40m above horizontal ground. The ball bounces on the ground and rebounds

Marina CMI [18]

Answer:

(a) 5.714s

(b) 0.625m

Step-by-step explanation:

Acceleration due to gravity=a=±9.8m/s/s (+ when falling, - when going upwards)

(a)

STAGE A: between start and first bounce

Initial speed=u=0m/s, Distance=s=40m, and Final velocity=v

v²=u²+2as

v²=0²+2(10)(40)

v²=794

v=28m/s (As the ball hits the ground)

v=u+at

28=0+9.8t $_{a}$

t $_{a}$ =28/9.8=2.85714285714s

STAGE B: from the first bounce until it starts to fall

u=half the speed it hit the ground with=(28/2)=14m/s, and v=0m/s(when it starts to fall)

v=u+at

0=14-9.8t $_{b}$

t $_{b}$ =14/9.8=1.42857142857s

STAGE C: between when it starts to fall after bounce 1, and bounce 2

We can assume that the time it takes to go from the ground to max height after bounce 1 is equal to the time it takes to fall from that same height to the ground. Therefore, t $_{c}$ =1.42857142857s

The time from when the ball was released to when it hit the ground for the second time = t

t = t $_{a}$ + t $_{b}$ + t $_{c}$

t=2.85714285714+1.42857142857+1.42857142857

t=5.71428571428s≈5.714s

<u />

(b)

Before bounce 1, u=28m/s (see stage a)

After bounce 1, u= 28/2= 14m/s

After bounce 2, u= 14/2 = 7m/s

After bounce 3, u= 7/2 =3.5m/s

u=3.5m/s and v=0m/s(when it starts to fall)

v²=u²+2as

0²=3.5²+2(-9.8)s

19.6s=12.25

s=<u>0.625m (max height after third bounce)</u>

8 0

1 year ago

This figure is made up of a triangle and a semicircle.

salantis [7]

We know that

[the area of semicircle]=pi*r²/2
for r=3.5 units
[the area of semicircle]=pi*3.5²/2---> 19.24 units²

[the area of the triangle]=b*h/2
b=7 units
h=3 units
[the area of the triangle]=7*3/2-----> 10.5 units²

the area of the figure=19.24+10.50----> 29.74 units²----> 29.7 units ²

the answer is
29.7 units ²

5 0

2 years ago