MATHEMATICS HIGH SCHOOL

What is the least positive integer with a square root greater than 4?

Answers

Answer 1

Answer:

The least positive integer will be 17.

Explanation

Lets assume, the integer is $x$

As the square root of this integer needs to greater than 4, that means....

$√(x) >4\n \n x>4^2\n \n x>16$

Thus, the integer should be greater than 16

So, the least positive integer with a square root greater than 4 will be 17.

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A right rectangular prism has base dimensions of 3 inches by 12 inches and a height of 5 inches. An oblique rectangular prism has base dimensions of 4 inches by 9 inches and a height of 5 inches. Are the volumes the same?

Answers

a rectangular right prism area=legnth times width times height or base area times height

base=3 b y12, area=3 times 12=36
height=5
36 times 5=180

an oblique rectangular prism volume is the same as the right rectangular prism formula so
4 times 9 times 5=180

180=180
the volumes are the same

In a group of 20 there are 7 boys what is the ratio of girls to boys?

Answers

Step-by-step explanation:

given,

total membersin grp =20

no.of boys =7

no.of girls=20-7=13

so,

the ratioof girlsto boys is =13:7

hope this answer helps youdear...take care and may u have a great day ahead!

76 is ,2% of what number ?

Answers

$p\%=(p)/(100)\n\n2\%=(2)/(100)=0.02\n\n76:0.02=3800\leftarrow solution$

A twons populations is 43,425. About 125 people move out of the town each month, 200 people on the average move into town. A nearby town has population of 45,000. it has no one moving in and an average of 150 people moving away every month. In about how many months will the population of the towns be equal? Write an equation that represents this situation and solve.

Answers

Answer:

After 7 months months the population of both the town will be equal.

Step-by-step explanation:

Let's assume, the population of both towns will be equal after x number of months.

Every month 125 people move out of the town and 200 people move into the town, where already 43,425 people are living. So, the population of the former town after x months is,

Every month 150 people move out of the town, where already 45,000 people are living. So, the population of the latter town after x months is,

when the population of both of the towns are same,then

7. (1 point) A fighter plane, which can shoot a laser beam straight ahead, travels along the path ~r(t) = 5 − t, 21 − t 2 , 3 − t 3 27 Show that there is precisely one time t at which the pilot can hit a target located at the origin.

Answers

Answer:

At t = 3, pilot can hit the target located at the origin.

Step-by-step explanation:

We have been given displacement vector:

r(t) = 5 - t, 21 - t², 3-t³/27

so, in this case r(t) and r'(t) should be in the parallel but opposite direction.

In order to get r'(t) we need to differentiate r(t).

r(t) = 5 - t, 21 - t², 3-t³/27

r'(t) = -1, -2t, -t²/9

Now perform the cross product among these two r(t) and r'(t).

r'(t) x r(t) = $\left[\begin{array}{ccc}i&j&k\n-1&-2t&(-t^(2) )/(9) \n5-t&21-t^(2) &3-(t^(3) )/(27) \end{array}\right]$

= i ((-6t + $(2t^(4) )/(27)$ )+ ( $(21t^(2) )/(9)$ - $(t^(2) )/(9)$ )) -j ((-3 + $(t^(3) )/(27)$ + $(5t^(2) )/(9)$ - $(t^(2) )/(9)$ )) + k ((-21 + $t^(2)$ + 10t -2 $t^(2)$ ))

= ( $(-t^(4) )/(27)$ + $(7t^(2) )/(3)$ - 6t )i + ( $(2t^(3) )/(27)$ - $(5t^(2) )/(9)$ +3) j + (-t² + 10t -21)k

In order to find the value of t, we need to put

$(-t^(4) )/(27)$ + $(7t^(2) )/(3)$ - 6t = 0

-t² + 10t -21 = 0

So, after solving for t, we will get

- ( t-3) (t-7) = 0

t = 3 or t = 7

In this case, only t = 3 satisfies the other two equations as well. t=7 is not satisfying. So take t =3 as the time. and for further assurance, we need to check are our vectors r(t) and r'(t) opposite at t = 3 or not. Let's check it out.

r(3) = 5-3, 21 - 3², 3 - 3³/27

r (3) = 2, 12, 2

r'(3) = -1, -2(3) , -3²/9

r'(3) = -1, -6 -1

Here, we can easily see that, r(3) = -2 r'(3) which is opposite and hence it is proved that, at exactly t = 3, pilot can hit a target located at the origin.

Alicia has 10 1/2 cups of flour in a container. She uses 7 3/4 cups to make banana bread

Answers

Answer:

9 6/8, 9 3/4. 9.75

Step-by-step explanation:

Next time finish the answer pls. Thankfully i was ble to answer it because i new what the question was.

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