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3 years ago

Pls help i will mark brainleist

Mathematics

1 answer:

lara [203]3 years ago

6 0

Answer:

ok so term 9 coefficent 5 term factor 1 quotient division sign sum add sign product x signf

Step-by-step explanation:

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How do you determine the area under a curve in calculus using integrals or the limit definition of integrals?

RSB [31]

Answer:

Please check the explanation.

Step-by-step explanation:

Let us consider

$y = f(x)$

To find the area under the curve $y = f(x)$ between $x = a$ and $x = b$ , all we need is to integrate $y = f(x)$ between the limits of $a$ and $b$ .

For example, the area between the curve y = x² - 4 and the x-axis on an interval [2, -2] can be calculated as:

$A=\int _a^b|f\left(x\right)|dx$

= $\int _{-2}^2\left|x^2-4\right|dx$

$\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx$

$=\int _{-2}^2x^2dx-\int _{-2}^24dx$

solving

$\int _{-2}^2x^2dx$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1$

$=\left[\frac{x^{2+1}}{2+1}\right]^2_{-2}$

$=\left[\frac{x^3}{3}\right]^2_{-2}$

computing the boundaries

$=\frac{16}{3}$

Thus,

$\int _{-2}^2x^2dx=\frac{16}{3}$

similarly solving

$\int _{-2}^24dx$

$\mathrm{Integral\:of\:a\:constant}:\quad \int adx=ax$

$=\left[4x\right]^2_{-2}$

computing the boundaries

$=16$

Thus,

$\int _{-2}^24dx=16$

Therefore, the expression becomes

$A=\int _a^b|f\left(x\right)|dx=\int _{-2}^2x^2dx-\int _{-2}^24dx$

$=\frac{16}{3}-16$

$=-\frac{32}{3}$

$=-10.67$ square units

Thus, the area under a curve is -10.67 square units

The area is negative because it is below the x-axis. Please check the attached figure.

6 0

3 years ago

A produce store sold 45 red apples. If the ratio of red apples to green apples sold was 5 : 2, what is the combined amount of re

lisabon 2012 [21]

The ratio of Red Apples to Green Apples is 5:2. The proportion of red apple is 5/7.

The store sold 45 red apples.

So the combined amount of red and green apples sold = No of red apples sold divided by the proportion of red apples = 45/ (5/7) = 63

The combined amount of red and green apples sold is 63 apples.

6 0

4 years ago

How do you make a word problem for a two step inequality equation

8_murik_8 [283]

First :<span>Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
second:</span>
<span> Simplify using the inverse of addition or subtraction. Simplify further by using the inverse of multiplication or division.
then find what you want to use!
</span>

8 0

4 years ago

Read 2 more answers

A circle is inscribed inside a square as shown. If graphed on the coordinate plane, the coordinates of the center of the circle

avanturin [10]

Length of side of the square = 2r
where r=radius of inscribed circle

Given an inscribed circle
Centre of circle , O(2,5)
Point on circle, P(-2,2)
Radius of circle
=distance OP
=sqrt((2-(-2))^2+(5-2)^2)
=sqrt(4^2+3^2)
=5

Therefore area of square
=(2r)^2
=(2*5)^2
=10^2
=100

8 0

4 years ago

Read 2 more answers

Jim used his debit card to withdraw $35 from the ATM. Then, he wrote a check for $8.00. Which equation represents the total amou

alexgriva [62]

X - (35 + 8) = y
x = original amount in bank
y = new amount in bank

7 0

3 years ago