Q1: 1+2-3+4-5+6-…-99+100

18. During a clothing store's Bargain Days, the regular price for T-shirts is discounted to $8.25.

8090 [49]

Answer:

3.25

Step-by-step explanation:

7 0

2 years ago

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Simplify and then classify by degree and number of terms 2x+3x^2(4x-5)

Delicious77 [7]

Answer:

2x + 3x^2 (4x - 5)

2x + 12x^3 - 15x^2

12x^3 - 15x^2 + 2x

Degree - 3

Terms - 3 (Trinomial)

<h3>Lets explore more - </h3>

The degree of a polynomial is the highest power of its variable
Degree represents the no. of zeros of the polynomial

Linear  - Degree 1
Quadratic - Degree 2
Cubic - Degree 3
Biquadratic - Degree 4

Terms - Classification of polynomial On the basis of terms

monomial - polynomial which has only 1 term
Binomial - Polynomial which has 2 terms
Trinomial - Polynomial which has 3 terms

5 0

3 years ago

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1. Express <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%282x%2B3%29%20%7D" id="TexFormula1" title="\frac{1}{x(2x+3) }" a

katovenus [111]

1. Let a and b be coefficients such that

$\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}$

Combining the fractions on the right gives

$\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}$

$\implies 1 = (2a+b)x + 3a$

$\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23$

so that

$\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}$

2. a. The given ODE is separable as

$x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}$

Using the result of part (1), integrating both sides gives

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C$

Given that y = 1 when x = 1, we find

$\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)$

so the particular solution to the ODE is

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)$

We can solve this explicitly for y :

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)$

$\ln|y| = \dfrac13 \ln\left|\dfrac{5x}{2x+3}\right|$

$\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|$

$\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}$

2. b. When x = 9, we get

$y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}$

8 0

2 years ago

Help, WIll give 20 points

Kisachek [45]

Answer:

i dont know

Step-by-step explanation:

6 0

2 years ago

Find the radius of a circle having area 616cm square.

OLEGan [10]

Answer:

$\boxed{\sf Radius \ of \ circle = 14 \ cm}$

Given:

Area of circle = 616 cm²

To Find:

Radius of circle

Step-by-step explanation:

$\sf \implies Area \ of \ circle = \pi r^{2} \\ \\ \sf \implies 616 = \frac{22}{7} \times {r}^{2} \\ \\ \sf \implies 616 \times \frac{7}{22} = {r}^{2} \\ \\ \sf \implies 28 \times \cancel{22} \times \frac{7} { \cancel{22}} = {r}^{2} \\ \\ \sf \implies 28 \times 7 = {r}^{2} \\ \\ \sf \implies 196 = {r}^{2} \\ \\ \sf \implies {r}^{2} = 196 \\ \\ \sf \implies r = \sqrt{196} \\ \\ \sf \implies r = \sqrt{ {14}^{2} } \\ \\ \sf \implies r = 14 \: cm$

4 0

2 years ago