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konstantin123 [22]
2 years ago
13

Please help me answer this question

Mathematics
1 answer:
lbvjy [14]2 years ago
7 0

A. Let s be the smallest integer
B. We must add 2 to get the next greater integer
C. Second integer is s+2
D. s+(s+2)=118
2•s+2=118
2s+2-2=118-2
2s=116
2s/2=116/2
s=58
If the smallest even integer is 58 the consecutive integer is 58+2=60
Verify
58+60=118 ✔️
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A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = −16t2 + 48t where t equals the
zlopas [31]
1. The function h(t)=-16t^{2}+48t is a parabola of the form ax^{2}+bx. The the formula for the axis of symmetry of a parabola is x= \frac{-b}{2a}. We can infer from our function that a=-16 and b=48, so lets replace those values in our formula:
x= \frac{-b}{2a}
x= \frac{-48}{-2(16)}
x= \frac{-48}{-32}
x= \frac{3}{2}
x=1.5
We can conclude that to the left of the line of symmetry the ball is reaching its maximum height, and to the right of the line of symmetry the ball is falling.

2. Lets check how much time the ball takes to reach its maximum height and return to the ground. To do that we are going to set the height equal to zero:
0=-16t^{2}+48t
-16t(t-3)=0
t=0 or t-3=0
t=0 or t=3
From our previous point we know that the ball reaches its maximum time at t=1.5, which means that <span>it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.</span>

7 0
3 years ago
Read 2 more answers
Find a nonzero vector orthogonal to the plane through the points: ????=(0,0,1), ????=(−2,3,4), ????=(−2,2,0).
ser-zykov [4K]

Answer:

The nonzero vector orthogonal to the plane is <-9,-8,2>.

Step-by-step explanation:

Consider the given points are P=(0,0,1), Q=(−2,3,4), R=(−2,2,0).

\overrightarrow {PQ}==

\overrightarrow {PR}==

The nonzero vector orthogonal to the plane through the points P,Q, and R is

\overrightarrow n=\overrightarrow {PQ}\times \overrightarrow {PR}

\overrightarrow n=\det \begin{pmatrix}i&j&k\\ \:\:\:\:\:-2&3&3\\ \:\:\:\:\:-2&2&-1\end{pmatrix}

Expand along row 1.

\overrightarrow n=i\det \begin{pmatrix}3&3\\ 2&-1\end{pmatrix}-j\det \begin{pmatrix}-2&3\\ -2&-1\end{pmatrix}+k\det \begin{pmatrix}-2&3\\ -2&2\end{pmatrix}

\overrightarrow n=i(-9)-j(8)+k(2)

\overrightarrow n=-9i-8j+2k

\overrightarrow n=

Therefore, the nonzero vector orthogonal to the plane is <-9,-8,2>.

8 0
3 years ago
9. Convert 10,000 seconds into<br> hours
arlik [135]

Answer: 2.7777 hours

Step-by-step explanation: Here, we're asked to convert 10,000 seconds into hours.

Unfortunately, we don't have a conversion factor for seconds and hours. However, we know that 60 seconds = 1 minute and 60 minutes = 1 hour.

So we can convert 10,000 seconds into hours by using both of these conversion factors. Also, it's important to understand that when we go from a smaller unit, seconds, to a larger unit, hours, we divide.

So let's first convert 10,000 seconds into minutes by dividing 10,000 by the conversion factor, 60, to get 166.6666 minutes.

Next, we convert minutes to hours by dividing 166.6666 by the conversion factor, 60, to get 2.7777 hours.

So 10,000 seconds is approximately equal to 2.7777 hours.

8 0
2 years ago
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