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LenaWriter [7]
3 years ago
11

Plsssss helppp im so lost on this

Mathematics
1 answer:
Alik [6]3 years ago
3 0

Answer:

2n-4>1n+3

Step-by-step explanation:

So basically 2 times a number go together because it means its multiplying and the greater sign is > and then 1 is multiplying with n so its 1n and then you just add 1

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Consider the region bounded by the curves y=|x^2+x-12|,x=-5,and x=5 and the x-axis
Tasya [4]
Ooh, fun

what I would do is to make it a piecewise function where the absolute value becomse 0

because if you graphed y=x^2+x-12, some part of the garph would be under the line
with y=|x^2+x-12|, that part under the line is flipped up

so we need to find that flipping point which is at y=0
solve x^2+x-12=0
(x-3)(x+4)=0
at x=-4 and x=3 are the flipping points

we have 2 functions, the regular and flipped one
the regular, we will call f(x), it is f(x)=x^2+x-12
the flipped one, we call g(x), it is g(x)=-(x^2+x-12) or -x^2-x+12
so we do the integeral of f(x) from x=5 to x=-4, plus the integral of g(x) from x=-4 to x=3, plus the integral of f(x) from x=3 to x=5


A.
\int\limits^{-5}_{-4} {x^2+x-12} \, dx + \int\limits^{-4}_3 {-x^2-x+12} \, dx + \int\limits^3_5 {x^2+x-12} \, dx

B.
sepearte the integrals
\int\limits^{-5}_{-4} {x^2+x-12} \, dx = [\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-5}_{-4}=(\frac{-125}{3}+\frac{25}{2}+60)-(\frac{64}{3}+8+48)=\frac{23}{6}

next one
\int\limits^{-4}_3 {-x^2-x+12} \, dx=-1[\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-4}_{3}=-1((-64/3)+8+48)-(9+(9/2)-36))=\frac{343}{6}

the last one you can do yourself, it is \frac{50}{3}
the sum is \frac{23}{6}+\frac{343}{6}+\frac{50}{3}=\frac{233}{3}


so the area under the curve is \frac{233}{3}
6 0
3 years ago
Expand the expression <br><br><br> -7(k - 3)
Illusion [34]
How can I help you?
−
7

(
k
−
3
)
-
7

(
k
-
3
)
Solve
4 0
3 years ago
A basketball player shoots a basketball that reaches a height above 15 feet before landing back on the ground exactly after 7 se
Papessa [141]

Answer:

I and IV

Step-by-step explanation:

Since the height of the basketball reaches above 15 feet, hence the maximum of the function should be greater than 15 feet. Also at 7 seconds, the ball is on the ground, hence f(7) = 0 feet

The maximum of a function is at x = -b/2a

i) f(x) = -(x-3)² + 16 = -(x² - 6x + 9) + 16 = -x² + 6x + 7

The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3

f(3) = -(3-3)² + 16 = 16 > 15

Also f(7) = - (7 - 3)² + 16 = 0

Hence this option is correct

ii) f(x) = -x² + 8x - 7

The maximum of a function is at x = -b/2a = -8 / 2(-1) = 4

f(4) = -4² + 8(4) - 7 = 9 < 15   not correct

Also f(7) = - 7² + 8(7) - 7 = 0

Hence this option is not correct since the maximum f(4) = 9 < 15  

iii)  f(x) = -(x-3)² + 14 = -(x² - 6x + 9) + 14 = -x² + 6x + 5

The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3

f(3) = -(3-3)² + 14 = 14 < 15

Also f(7) = - (7 - 3)² + 14 = -2

Hence this option is not correct since the maximum f(4) = 9 < 15 and f(7) ≠ 0

iv)f(x)  = -x² + 6x + 7

The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3

f(3) = -(3)² + 6(3) + 7 = 16 > 15

Also f(7) = - (7)² + 6(7) + 7 = 0

Hence this option is correct

3 0
3 years ago
Find the least number must be added to 4015 to make it a perfect square. also,find the square root of the perfect square so obta
Vladimir [108]

To solve this, I used guess and check.

I started by finding 60²=3600 and 70²=4900. 70² is too much, so I then did 65²=4,225.

After 65², I did 62²=3,844. I knew that was pretty close, so I did 64. 64²=4,096 and 63²=3,969. So, 64² was it.

4,096-4015=81

So, you would need to add 81 to 4015 in order to receive a perfect square, which is 64²(4,096).

7 0
3 years ago
The distance between Troy City and Ben City is 315 miles. How far apart<br> are they on the map?
Lemur [1.5K]
Maybe 1 yard and 15 minutes
8 0
3 years ago
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