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Len [333]
3 years ago
7

A grocer's shop sells carrots, onions and cucumbers.

Mathematics
1 answer:
kolezko [41]3 years ago
7 0

Answer: 3:4

Step-by-step explanation:

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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
List the angles of the triangle from SMALLEST to LARGEST .
soldier1979 [14.2K]
C. m k L hope it helps! not 100% sure
4 0
3 years ago
Read 2 more answers
A. Suppose you have just inherited a sum of money. Let’s say you choose to invest the money. How much did you inherit? Choose an
leva [86]

Amount =$48003.20

Step-by-step explanation:

Here apply the compound interest formula;

A=P(1+\frac{r}{n} )^{nt}

where;

P=Principal amount invested = $37500

r=rate of interest as a decimal, 2.5% =0.025

n=number of compounding per year=1

t=time period the amount in invested=10

In our case, the amount after investing will be;

A=37,500(1+0.025)^{10} \\\\A=37,500(1.025)^{10} \\\\A=48003.20

Interest earned after the period= $48003.20-$37500 =$10503.20

Learn More

Compound Interest formula application: brainly.com/question/7014337

Keywords: inherit, sum, money, interest

#LearnwithBrainly

3 0
3 years ago
Jess works in a store that sells toys.He earns 4% as his commissions for the sales that amounts above Nu 10,000.In one of the mo
Levart [38]

it's 400

hope this helps

7 0
3 years ago
At a middle school, 30% of the
Llana [10]

Answer:

I don't understand percentages

3 0
3 years ago
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