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3 years ago

Write an equation of the line that passes through (−3,7) and is perpendicular to the line y=−2x−5.

Mathematics

2 answers:

Murljashka [212]3 years ago

7 0

Answer:

Step-by-step explanation:

an equation is : Use the point-slope formula.

y - y_1 = m(x - x_1) ; m : the slope when : x_1 = -3 and y_1 = 7

- 2 ×m = - 1 because this line is perpendicular to the line y= -2x-5 when the slope is -2

so : m= 1/2

an equation is : y - 7 =(1/2)(x+3)

elena-14-01-66 [18.8K]3 years ago

4 0

Answer:

The desired equation is

y = (1/2)x + 17/2

Step-by-step explanation:

The slope of the perpendicular line is the negative reciprocal of -2: m = 1/2.

Start with y = mx + b.

Substituting 7 for y, 1/2 for m and -3 for x, we get:

7 = (1/2)(-3) + b. Then 7 = -3/2 + b, so that b = 17/2.

The desired equation is

y = (1/2)x + 17/2

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AP Calculus redo! I know the answer but can't figure out exactly how to get there. Thank you! I want to work through the steps.

Monica [59]

You're approximating

$\displaystyle\int_1^5 x^2\,\mathrm dx$

with a Riemann sum, which comes in the form

$\displaystyle\int_a^b f(x)\,\mathrm dx=\lim_{n\to\infty}\sum_{i=1}^nf(x_i)\Delta x_i$

where $x_i$ are sample points chosen according to some decided-upon rule, and $\Delta x_i$ is the distance between adjacent sample points in the interval.

The simplest way of approximating the definite integral is by partitioning the interval into equally-spaced subintervals, in which case $\Delta x=\dfrac{b-a}n$ , and since $[a,b]=[1,5]$ , we have

$\Delta x=\dfrac{5-1}n=\dfrac4n$

Using the right-endpoint method, we approximate the area under $f(x)$ with rectangles whose heights are determined by their right endpoints. These endpoints are chosen by successively adding the subinterval length to the starting point of the interval of integration.

So if we had $n=4$ subintervals, we'd split up the interval of integration as

$[1,5]=[1,2]\cup[2,3]\cup[3,4]\cup[4,5]$

Note that the right endpoints follow a precise pattern of

$2=1+\dfrac44$
$3=1+\dfrac84$
$4=1+\dfrac{12}4$
$5=1+\dfrac{16}4$

The height of each rectangle is then given by the values above getting squared (since $f(x)=x^2$ ). So continuing with the example of $n=4$ , the Riemann sum would be

$\displaystyle\sum_{i=1}^4\left(1+\dfrac{4i}4\right)^2\dfrac44$

For $n=5$ ,

$\displaystyle\sum_{i=1}^5\left(1+\dfrac{4i}5\right)^2\dfrac45$

and so on, so that the definite integral is given exactly by the infinite sum

$\displaystyle\lim_{n\to\infty}\sum_{i=1}^n\left(1+\dfrac{4i}n\right)^2\dfrac4n$

4 0

3 years ago

A new bank customer with $4 comma 500 wants to open a money market account. The bank is offering a simple interest rate of 1.5

Jet001 [13]

a) Simple interest earned by customer in 10 years is $ 675

b) Account balance after 10 years is $ 5175

Solution:

The simple interest is given by formula:

$Simple\ Interest = \frac{p \times n \times r}{100}$

Where,

"p" is the principal

"r" is the rate of interest

"n" is the number of years

a. How much interest will the customer earn in 10 years?

From given,

Principal = p = $ 4500

Simple interest rate = r =1.5 %

n = 10

Substituting the values in formula,

$Simple\ Interest = \frac{4500 \times 10 \times 1.5}{100}\\\\Simple\ Interest = 450 \times 1.5\\\\Simple\ Interest = 675$

Thus simple interest earned by customer in 10 years is $ 675

b. What will the account balance be after 10 years ?

Account balance = principal + simple interest

Account balance = 4500 + 675 = 5175

Thus account balance after 10 years is $ 5175

8 0

3 years ago

Show that the following rational number by expressing it as a ratio quotient of two integers 0.9

kipiarov [429]

A rational number can be expressed in the form a/b, where a and b are other integers. To satisfy this definition, 0.9 can be written as 9/10, 18/20, 90/100, etc.

7 0

4 years ago

Given this arithmetic sequence, find d 4,_,_,_,_,179

Margarita [4]

4 + (6-1)d = 179
4 + 5d = 179 
5d = 175 
d = 35

5 0

3 years ago

Read 2 more answers

there are 1720 women among the 3200 students at the local community college. Express this ratio in each of the following forms.

Karo-lina-s [1.5K]

53.75% are women
hope that helps.

5 0

3 years ago