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trapecia [35]
3 years ago
10

what is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5x 10 and passes through the point (

15, –5)?
Mathematics
1 answer:
bazaltina [42]3 years ago
6 0
Perpendiculare means the slopes multiply to -1

y=3/5x+10
slope is 3/5
3/5 times what is -1
-5/3 is answer

slope of perpenduclar is-5/3 find y int
y=-5/3+b
point given is (15,-5)
x=15
y=-5

-5=-5/3(15)+b
-5=-25+b
add 25 to both sides
20=b

the yintercept is y=20 or the oint (0,20)
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For the function given below, find a formula for the Riemann sum obtained by dividing the interval [0,5] into n equal subinterva
sergij07 [2.7K]

Given

we are given a function

f(x)=x^2+5

over the interval [0,5].

Required

we need to find formula for Riemann sum and calculate area under the curve over [0,5].

Explanation

If we divide interval [a,b] into n equal intervals, then each subinterval has width

\Delta x=\frac{b-a}{n}

and the endpoints are given by

a+k.\Delta x,\text{ for }0\leq k\leq n

For k=0 and k=n, we get

\begin{gathered} x_0=a+0(\frac{b-a}{n})=a \\ x_n=a+n(\frac{b-a}{n})=b \end{gathered}

Each rectangle has width and height as

\Delta x\text{ and }f(x_k)\text{ respectively.}

we sum the areas of all rectangles then take the limit n tends to infinity to get area under the curve:

Area=\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\Delta x.f(x_k)

Here

f(x)=x^2+5\text{ over the interval \lbrack0,5\rbrack}\Delta x=\frac{5-0}{n}=\frac{5}{n}x_k=0+k.\Delta x=\frac{5k}{n}f(x_k)=f(\frac{5k}{n})=(\frac{5k}{n})^2+5=\frac{25k^2}{n^2}+5

Now Area=

\begin{gathered} \lim_{n\to\infty}\sum_{k\mathop{=}1}^n\Delta x.f(x_k)=\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\frac{5}{n}(\frac{25k^2}{n^2}+5) \\ =\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\frac{125k^2}{n^3}+\frac{25}{n} \\ =\lim_{n\to\infty}(\frac{125}{n^3}\sum_{k\mathop{=}1}^nk^2+\frac{25}{n}\sum_{k\mathop{=}1}^n1) \\ =\lim_{n\to\infty}(\frac{125}{n^3}.\frac{1}{6}n(n+1)(2n+1)+\frac{25}{n}n) \\ =\lim_{n\to\infty}(\frac{125(n+1)(2n+1)}{6n^2}+25) \\ =\lim_{n\to\infty}(\frac{125}{6}(1+\frac{1}{n})(2+\frac{1}{n})+25) \\ =\frac{125}{6}\times2+25=66.6 \end{gathered}

So the required area is 66.6 sq units.

3 0
1 year ago
Question 2 (1 point) (11.01 MC) Nina has a piece of fabric measuring 5 yards. How many 1-inch strips can be cut from the fabric?
maw [93]

Answer:

180 strips

Step-by-step explanation:

Note that:

1 yard = 36 inches

5 yards = x

Cross Multiply

x = 5 × 36 inches

x = 180 inches

Hence:

1 piece of fabric = 180 inches

How many 1-inch strips can be cut from the fabric?

180 inches = 1 piece of fabric

1 inch = x

x = 180 strips

8 0
3 years ago
In mrs. prosser's class there are 32 students. If 3 out of every 8 prefer to ride their bicycles to school, how many students in
Molodets [167]
First divide 32 by 8

32/8

=4

Then multiply the 4 by 3 to find out how many students in the class like to ride their bicycles to school

4x3

12 students is your answer
8 0
3 years ago
7 x 3/4
Mkey [24]

7 3/4

Step 1: Multiply 7 and 4.

            7 x 4=28

Step 2:Add 3 to their product.

         28+3=31

Step 3:The number so obtained is the numerator and the denominator remains the same.

Answer: 31/4

I think that is what you are looking for!

Hope that helps!!!

7 0
3 years ago
Select the scatter plot with the strongest association.
borishaifa [10]
I would say probably the top left im not posititive sorry if u get it wrong

7 0
3 years ago
Read 2 more answers
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