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Rufina [12.5K]
1 year ago
9

A gymnast dismounts the uneven parallel bars. Her height, h, depends on the time, t, that she is in the air h = −162 + 24t + 16.

How long will it take the gymnast to reach the ground?
Mathematics
1 answer:
dimulka [17.4K]1 year ago
5 0
That is when h=0
so assuming yo meant
h(t)=-16t²+24t+16
solve for t such that h(t)=0
because when height=0, the gymnast hits the ground

so
0=-16t²+24t+16
using math (imma complete the square
0=-16(t²-3/2t)+16
0=-16(t²-3/2t+9/16-9/16)+16
0=-16((t-3/4)²-9/16)+16
0=-16(t-3/4)²+9+16
0=-16(t-3/4)²+25
-25=-16(t-3/4)²
25/16=(t-3/4)²
sqrt both sides
+/-5/4=t-3/4
3/4+/-5/4=t
if we do plus (because minus would give us negative height)
8/4=t
2=t
it takes 2 seconds
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A rectangle that had the perimeter of 70 and the area of 250 has enlarged; its sides became twice as long. what is the new area
aliya0001 [1]
The perimeter of the original rectangle is:
 P = 2w + 2l = 70
 The area of the original rectangle is:
 A = w * l = 250
 Then, by modifying the length of its sides we have:
 Perimeter:
 P '= 2 (2w) +2 (2l)
 Rewriting:
 P '= 2 (2w + 2l)
 P '= 2P
 P '= 2 (70)
 P '= 140
 Area:
 A '= (2w) * (2l)
 Rewriting:
 A '= (2) * (2) (w) * (l)
 A '= 4 * w * l
 A '= 4 * A
 A '= 4 * 250
 A '= 1000
 Answer:
 
the new area and the new perimeter are:
 
P '= 140
 
A '= 1000
3 0
2 years ago
one angle of a linear pair is 10 more than two thirds the other angle. find the measure if both angles
BigorU [14]

Answer:

One Angle = 110°

Other Angle = 70°

Step-by-step explanation:

A linear pair means that two angles are in a straight line (or, a straight angle).

A straight line is 180 degrees.

THey are supplementary.

We can say one angle is "a" and another one is "b".

<em>One angle is 10 MORE THAN 2/3rds of the other, we can write:</em>

<em>a=\frac{2}{3}b+10</em>

<em />

<em>Also, since they are supplementary (add up to 180), we can write:</em>

<em>a + b = 180</em>

<em />

We can now substitute 1st equation in this one and find b:

a+b=180\\(\frac{2}{3}b+10)+b=180\\\frac{2}{3}b+b=180-10\\\frac{5}{3}b=170\\b=\frac{170}{\frac{5}{3}}\\b=170*\frac{3}{5}\\b=110

Since a + b = 180, we can write:

a + 110 = 180

so,

a = 180 - 110

a = 70

Thus,

One Angle = 110°

Other Angle = 70°

8 0
1 year ago
The ceiling of Katie’s living room is a square that is 10 ft long on each side. Katie knows the diagonal of the ceiling from cor
CaHeK987 [17]

Answer:

Answer: 14 feet. a. The Pythagorean theorem is a^2 + b^2 = c^2, where a and b are the sides of a right angle. By plugging in the sides of the wall, and solving for c, you can find the answer. 10^2 + 10^2 = c^2

| 100 + 100 = c^2 | 200 = c^2 | c = sqrt 200 | c = 14. The other way to solve this would be using the trig functions. You know that the angle between the hypotenuse and the wall side is 45 degrees, so you can use Sine to determine the hypotenuse. Sine is equal to opposite over hypotenuse. Sin (45) = 10/h | Sin (45) * h = 10 | h = 10/Sin (45) | h = 14. Both of the methods result in 14.

Read more on Brainly.com - brainly.com/question/16274528#readmore

Step-by-step explanation:

5 0
1 year ago
The APR of Vinny’s saving account is 3.5% but interest is compounded only once a year. what is the APY of Vinny’s savings accoun
SIZIF [17.4K]
                                                         HOI!!

ok 3.5 apr is equivelent to 2.5 so your answer would be A 

hope this helps!!!

:) :) :)


8 0
2 years ago
Read 2 more answers
A coin will be flipped repeatedly until the sequence TTH (tail/tail/head) comes up. Successive flips are independent, and the co
padilas [110]

Answer:

P = \frac{1}{3}

Step-by-step explanation:

The calculation of the value of p minimizes is shown below:-

We will assume the probability of coming heads be p

p(H) = p

p(T) = 1 - P

Now, H and T are only outcomes of flipping a coin

So,

P(TTH) = (1 - P) = (1 - P) (1 - P) P

= (1 + P^2 - 2 P) P

= P^3 - 2P^2 + P

In order to less N,TTH

we need to increase P(TTH)

The equation will be

\frac{d P(TTH)}{dP} = 0

3P^2 - 4P + 1 = 0

(3P - 1) (P - 1) = 0

P = 1 and 1 ÷ 3

For P(TTH) to be maximum

\frac{d^2 P(TTH)}{dP} < 0 for\ P\ critical\\\\\frac{d (3P^2 - 4P - 1)}{dP}

= 6P - 4

and

(6P - 4) is negative which is for

P = \frac{1}{3}

5 0
2 years ago
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