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3 years ago

6

Howard's pawn shop bought an antique clock at the wholesale price of $725. Howard marked up the price of the clock

1 answer:

kkurt [141]3 years ago

5 0

Answer:

942.50

Step-by-step explanation:

725×30% or 0.3 = 217.5

217.5+725=942.5

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Which statement is a counterexample to the statement "If x is a prime number, then x is an odd number?"

valentinak56 [21]

Answer:

2

Step-by-step explanation:

2 is a prime number (it can pnly be divided by itself and by one), but it is an even number.

So it's a counterexample of the statement "If x is a prime number, then x is an odd number?"

5 0

3 years ago

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

What is the value of f(7)

kkurt [141]

F(7) means f(x) when x = 7. The x is replaced with 7.

So we'll replace every x with 7 to go from x = 7 to 3-x = 3-7 = -4

Put another way
f(x) = 3-x
f(7) = 3-7
f(7) = -4

Answer: -4

8 0

3 years ago

Read 2 more answers

Harry has 8 more marbles than hermione. together they have 40 marbles. how many does each have?

aksik [14]

Answer:

Harry has 24; Hermione has 16

3 0

3 years ago

Read 2 more answers

The slope of the graph of the equation y=2x-2 s 2 What is y-intercept

DaniilM [7]

Answer:

Y=2x-2

2x is the slope

-2 is the y intercept

Step-by-step explanation:

3 0

3 years ago