1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
liraira [26]
3 years ago
13

Which equation shows y-5=x converted to slope intercept form.

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
8 0

Answer:

C) y = x + 5

Step-by-step explanation

Add 5 to both sides

You might be interested in
More Calculus! (I'm so sorry)
Olenka [21]
Recall that converting from Cartesian to polar coordinates involves the identities

\begin{cases}y(r,\phi)=r\sin\phi\\x(r,\phi)=r\cos\phi\end{cases}

As a function in polar coordinates, r depends on \phi, so you can write r=r(\phi).

Differentiating the identities with respect to \phi gives

\begin{cases}\dfrac{\mathrm dy}{\mathrm d\phi}=\dfrac{\mathrm dr}{\mathrm d\phi}\sin\phi+r\cos\phi\\\\\dfrac{\mathrm dx}{\mathrm d\phi}=\dfrac{\mathrm dr}{\mathrm d\phi}\cos\phi-r\sin\phi\end{cases}

The slope of the tangent line to r(\phi) is given by

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\phi}}{\frac{\mathrm dx}{\mathrm d\phi}}=\dfrac{\frac{\mathrm dr}{\mathrm d\phi}\sin\phi+r\cos\phi}{\frac{\mathrm dr}{\mathrm d\phi}\cos\phi-r\sin\phi}

Given r(\phi)=3\cos\phi, you have \dfrac{\mathrm dr}{\mathrm d\phi}=-3\sin\phi. So the tangent line to r(\phi) has a slope of

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{-3\sin^2\phi+3\cos^2\phi}{-3\sin\phi\cos\phi-3\cos\phi\sin\phi}=\dfrac{3\cos2\phi}{-3\sin2\phi}=-\cot2\phi

When \phi=120^\circ=\dfrac{2\pi}3\text{ rad}, the tangent line has slope

\dfrac{\mathrm dy}{\mathrm dx}=-\cot\dfrac{4\pi}3=-\dfrac1{\sqrt3}

This line is tangent to the point (r,\phi)=\left(-\dfrac32,\dfrac{2\pi}3\right) which in Cartesian coordinates is equivalent to (x,y)=\left(\dfrac34,-\dfrac{3\sqrt3}4\right), so the equation of the tangent line is

y+\dfrac{3\sqrt3}4=-\dfrac1{\sqrt3}\left(x-\dfrac34\right)

In polar coordinates, this line has equation

r\sin\phi+\dfrac{3\sqrt3}4=-\dfrac1{\sqrt3}\left(r\cos\phi-\dfrac34\right)
\implies r=-\dfrac{3\sqrt3}{2\sqrt3\cos\phi+6\sin\phi}

The tangent line passes through the y-axis when x=0, so the y-intercept is \left(0,-\dfrac{\sqrt3}2\right).

The vector from this point to the point of tangency on r(\phi) is given by the difference of the vector from the origin to the y-intercept (which I'll denote \mathbf a) and the vector from the origin to the point of tangency (denoted by \mathbf b). In the attached graphic, this corresponds to the green arrow.

\mathbf b-\mathbf a=\left(\dfrac34,-\dfrac{3\sqrt3}4\right)-\left(0,-\dfrac{\sqrt3}2\right)=\left(\dfrac34,-\dfrac{\sqrt3}4\right)

The angle between this vector and the vector pointing to the point of tangency is what you're looking for. This is given by

\mathbf b\cdot(\mathbf b-\mathbf a)=\|\mathbf b\|\|\mathbf b-\mathbf a\|\cos\theta
\dfrac98=\dfrac{3\sqrt3}4\cos\theta
\implies\theta=\dfrac\pi6\text{ rad}=30^\circ

The second problem is just a matter of computing the second derivative of \phi with respect to t and plugging in t=2.

\phi(t)=2t^3-6t
\phi'(t)=6t^2-6
\phi''(t)=12t
\implies\phi''(2)=24

6 0
3 years ago
PLEEEEEEASE HELP A square rug covers 80 square feet of floor. What is the approximate length of one side of the rug? (Approximat
vaieri [72.5K]

Answer:

c

Step-by-step explanation:

i had the same q and got it right

8 0
2 years ago
What is the weight of a gallon of diesel?
Margarita [4]

Answer:

A gallon of diesel weighs 7 pounds.

Step-by-step explanation:

6 0
2 years ago
Y=3x+2-> parrell lines
Lelechka [254]
Using the slope-intercept form, the slope is 3 3 . To find an equation that is parallel<span>to </span>y=3x−2 y<span> = 3 ⁢ x - </span>2<span> , the slopes must be equal. Using the slope of the equation, find the </span>parallel line<span> using the point-slope formula. Find the value of b b using the formula for the equation of a </span>line<span>.</span>
6 0
3 years ago
Mid-Chapter Check
Nostrana [21]
An equation: 2x=3
an expression: 2x+5
4 0
3 years ago
Other questions:
  • Number 5 please thank you
    5·1 answer
  • What is 4 (3 times 5)
    13·2 answers
  • What is -4 divided by -0.2?
    13·1 answer
  • According to National Oceanic and Atmospheric Administration, the coastline of Alaska estimates 55 thousand kilometers. This is
    8·1 answer
  • Select the two values of x that are roots of this equation.<br> 2x - 3 = -5x2
    5·2 answers
  • ASAP HELPPPPPPPPB If I have a frequency of 3 Hz, how many waves passed a point in a given second?
    8·2 answers
  • Find the constant of proportionality (r) in the equation y = rx
    15·1 answer
  • Can anybody help me with this problem regarding Line Integrals (Calc 3)?
    7·1 answer
  • Please help beautifuls!
    14·1 answer
  • Evaluate the double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!