Ask question

Ask question

All categories

BlackZzzverrR [31]

3 years ago

6

the perimeter of a rectangle is 48 inches. the ration of the width the length is 3:5, as shown. find the width and the length of

the rectangle

1 answer:

aleksandrvk [35]3 years ago

7 0

Answer:

Width= 18inches Length= 30inches

Step-by-step explanation:

3+5= 8

48/8=6

3*6=18

5*6=30

You might be interested in

1/5 of a box of erasers and youneed to share with 3 people including yourself what fraction of the box would each person get

CaHeK987 [17]

1 1. 1
— x. — = —
4. 5. 20

1/20 is the answer

8 0

3 years ago

What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

telo118 [61]

Answer:

$f(x)=-\frac{1}{8}(x-3)^2+3$

Step-by-step explanation:

We want to find the equation of the parabola with a focus of $(3,1)$ and directrix $y=5$ .

Considering the directrix, the quadratic graph must open downwards.

The equation of this parabola is given by the formula,

$(x-h)^2=4p(y-k)$ , where $(h,k)$ is the vertex of the parabola.

The axis of this parabola meets the directrix at $(3,5)$ .

Since the vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix,

$h=\frac{3+3}{2}=3$ and $k=\frac{5+1}{2}=3$ .

The equation of the parabola now becomes,

$(x-3)^2=4p(y-3)$ .

Also $|p|$ is the distance between the vertex and the directrix.

$|p|=2$

This implies that $p=-2\:or\:2$ .

Since the parabola turns downwards,

$p=-2$ .

Our equation now becomes,

$(x-3)^2=4(-2)(y-3)$ .

$(x-3)^2=-8(y-3)$ .

We make y the subject to get,

$y=-\frac{1}{8}(x-3)^2+3)$ .

This is the same as

$f(x)=-\frac{1}{8}(x-3)^2+3)$ .

4 0

2 years ago

The curve given by x=sin(t),y=sin(t+sin(t)) has two tangent lines at the point (x,y)=(0,0). List both of them in order of increa

SOVA2 [1]

Answer:

y = 0

y =2x

Step-by-step explanation:

Given parametric equations:

x (t) = sin (t)

y (t) = sin (t + sin (t))

The slope of the curve at any given point is given by dy / dx we will use chain rule to find dy / dx

(dy / dx) * (dx / dt) = (dy / dt)

(dy / dx) = (dy / dt) / (dx / dt)

Evaluate dx / dt and dy / dt

dx / dt = cos (t)

dy / dt = cos (t + sin (t)) * (1+cos (t))

Hence,

dy / dx = (1+cos(t))*cos(t + sin (t))) / cos (t)

@Given point (x,y) = 0 we evaluate t

0 = sin (t)

t = 0 , pi

Input two values of t and compute dy / dx

@ t = 0

dy / dx = (1 + cos (0))*cos (0 + sin (0))) / cos (0)

dy / dx = (1+1)*(1) / (1) = 2 @ t = 0

@t = pi

dy / dx = ( 1 + cos (pi))* cos (pi + sin (pi)) / cos (pi)

dy / dx = (1-1) * (-1) / (-1) = 0 @ t = pi

The corresponding gradients are 0 and 2 in increasing order and their respective equations are:

y = 2x

y = 0

5 0

2 years ago

You are dealt one card from a 52-card deck. Find the probability that you are not dealt a black picture card.

elena55 [62]

Answer: 1 in 51

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

On a vacation in Puerto Rico rose jumped off a cliff into a river in El Yunque go forest reserve her height as a function of tim

gayaneshka [121]

Answer: t = 6 s

Step-by-step explanation:

When Rose hit the water, the height of the jump is 0, so: h(t) = 0.

Resolving it, we have:

-16t² + 16t + 480 = 0

To simplify the second degree equation, divided it by 16:

-t² + t + 30 = 0

Now, solve the equation using Bhaskara:

Δ = 1² - 4. (-1) . 30

Δ = 1 + 120

Δ = 121

t = $\frac{-1+\sqrt{121} }{-2}$

t₁ = $\frac{-1 + 11}{-2}$ = - 5

t₂ = $\frac{-11-11}{-2}$ = 6

Since time can be negative, it took t = 6s for Rose to hit the water.

6 0

3 years ago