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3 years ago

Find the equation of the line through (5,7) that is perpendicular to y=2/3x-2

Mathematics

2 answers:

Rainbow [258]3 years ago

4 0

Answer:

y=-2/3x+10.3333333333333334

Step-by-step explanation:

to make it perpendicular 2/3 becomes -2/3

Ganezh [65]3 years ago

3 0

A line is perpendicular when M1xM2=-1
( when the first and second gradient together would equal -1)
Knowing this we can rearrange to get M2 (M2=-1/M1)
From this you can determine y intercept and that is it
(Answer is y=-1.5x+14.5)

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Solve for t.<br> -t = 9(t-10)<br> pls help

g100num [7]

Step-by-step explanation:

-t = 9(t-10)

-t = 9t - 90

90 = 9t + t

90 = 10t

90 ÷ 10 = t

9 = t

6 0

3 years ago

y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence

sukhopar [10]

Let

$\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots$

Differentiating twice gives

$\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots$

$\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n$

When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

$\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0$

$\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1) a_{n+2} - a_n\bigg) x^n = 0$

Then the coefficients in the power series solution are governed by the recurrence relation,

$\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}$

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

• If n is even, then n = 2k for some integer k ≥ 0. Then

$k=0 \implies n=0 \implies a_0 = a_0$

$k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}$

$k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}$

$k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}$

It should be easy enough to see that

$a_{n=2k} = \dfrac{a_0}{(2k)!}$

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

$k = 0 \implies n=1 \implies a_1 = a_1$

$k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}$

$k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}$

$k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}$

so that

$a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}$

So, the overall series solution is

$\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)$

$\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}$

4 0

3 years ago

If you were to take a cross section of a right circular cone parallel to its base, what shape would you get?

Leya [2.2K]

The cross section of a right circular cone parallel to its base is a circle.

<h3>What is a three dimensional shape?</h3>

A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are<em> cone, cylinder, prism and pyramid.</em>

A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are <em>circle, rectangle, square</em>.

A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top

The cross section of a right circular cone parallel to its base is a circle.

Find out more on three dimensional shape at: brainly.com/question/6636176

#SPJ1

3 0

2 years ago

An antique wooden chest has the shape of a rectangular prism. It has a width of 16 inches. Its length is 4 times its height. The

baherus [9]

The height is 4. (And the length is 64)

7 0

3 years ago

Read 2 more answers

*WILL GIVE 15 POINTS PLEASE HELP* You want to put 2500 in a simple interest account. It has 4% annual interest rate. How long mu

Arisa [49]

just fyi, if you spend x points on question, each user gets x/2 points (rounded up or down, I don't remember)

simple interest formula is

I=PRT

I=interest

P=principal

R=rate in decimal

T=time in years

assuming you mean that the principal is $2500 and not 2500 cents or 2500 of some other currency

interest=500

R=4%=0.04

I=PRT

500=(2500)(0.04)(T)

500=100T

divide both sides by 100

5=T

answer is 5 years

C is answer

6 0

3 years ago

Read 2 more answers