Real answers only pls! no links either!

The perimeter of a rectangle is 96cm its shortest side has a length of 5cm state the length of the longest side

Rainbow [258]

Answer:

43cm

Step-by-step explanation:

96-10 (5 x2 sides)=86

86/2 sides=43 longest side

4 0

3 years ago

Let T be the plane-2x-2y+z =-13. Find the shortest distance d from the point Po=(-5,-5,-3) to T, and the point Q in T that is cl

GaryK [48]

Answer:

d=10u

Q(5/3,5/3,-19/3)

Step-by-step explanation:

The shortest distance between the plane and Po is also the distance between Po and Q. To find that distance and the point Q you need the perpendicular line x to the plane that intersects Po, this line will have the direction of the normal of the plane $n=(-2,-2,1)$ , then r will have the next parametric equations:

$x=-5-2\lambda\\y=-5-2\lambda\\z=-3+\lambda$

To find Q, the intersection between r and the plane T, substitute the parametric equations of r in T

$-2x-2y+z =-13\\-2(-5-2\lambda)-2(-5-2\lambda)+(-3+\lambda) =-13\\10+4\lambda+10+4\lambda-3+\lambda=-13\\9\lambda+17=-13\\9\lambda=-13-17\\\lambda=-30/9=-10/3$

Substitute the value of $\lambda$ in the parametric equations:

$x=-5-2(-10/3)=-5+20/3=5/3\\y=-5-2(-10/3)=5/3\\z=-3+(-10/3)=-19/3\\$

Those values are the coordinates of Q

Q(5/3,5/3,-19/3)

The distance from Po to the plane

$d=\left| {\to} \atop {PoQ}} \right|=\sqrt{(\frac{5}{3}-(-5))^2+(\frac{5}{3}-(-5))^2+(\frac{-19}{3}-(-3))^2} \\d=\sqrt{(\frac{5}{3}+5))^2+(\frac{5}{3}+5)^2+(\frac{-19}{3}+3)^2} \\d=\sqrt{(\frac{20}{3})^2+(\frac{20}{3})^2+(\frac{-10}{3})^2}\\d=\sqrt{\frac{400}{9}+\frac{400}{9}+\frac{100}{9}}\\d=\sqrt{\frac{900}{9}}=\sqrt{100}\\d=10u$

7 0

3 years ago

Renee has 1/4 yard of floral fabric. She cuts it into 5 equal pieces. How long is each new piece of fabric?

Zinaida [17]

Answer:

$\dfrac{1}{20}\ \text{yards}$

Step-by-step explanation:

Given that,

Renee has 1/4 yard of floral fabric.

She cuts it into 5 equal pieces.

We need to find the length of each new piece of fabric. It is equal to the total length divided by the total number of pieces. So,

$l=\dfrac{\dfrac{1}{4}}{5}\\\\=\dfrac{1}{4}\times \dfrac{1}{5}\\\\=\dfrac{1}{20}\ \text{yards}$

So, each new piece pf fabric is $\dfrac{1}{20}\ \text{yards}$ .

5 0

3 years ago

What is the volume of a cone that has a radius of 4 cm and a height of 9 cm?

vodka [1.7K]

For any sort of pyramid or cone, the volume is 1/3 of the volume of a prism with the same base and height. Since the volume of a prism/cylinder is $V=Bh$ , the volume of a pyramid/cone is $V=\frac{1}3Bh$ .

In this case, our base is a circle, which has a radius of 4 cm.
The area of a circle is $A=\pi r^2$ where r is the radius.
$A=\pi (4)^2=\pi (4\times4)=16\pi=B$

We now know that our base is 16π cm.
We also know that our height is 9 cm.
Let's plug these into our volume formula.

$V=\frac{1}3\times16\pi \times9$

Use 3.14 to approximate pi as the question states. 16 × 3.14 = 50.24.

$V\approx\frac{1}3\times50.24\times9$

We could punch all of that into our calculator to get the same answer, but since 1/3 of 9 is clearly 3, let's just go with that.

$V\approx3\times50.24$

$\boxed{V\approx150.72\ cm^3}$

8 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP!!!!!

attashe74 [19]

For this case what we must do is use the law of cosines.
We then have the following equation:
$c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos (x)
$
Where,
a, b: sides of the triangle
x: angle between sides a and b.
Substituting values we have:
$c^2 = 90^2 + 75^2 - 2*90*75*cos(85)
$
Clearing the value of c we have:
$c = \sqrt{ 90^2 + 75^2 - 2*90*75*cos(85)}$
Answer:
An expression that is equivalent to how many feet the oak trees are from each other is:
$c = \sqrt{ 90^2 + 75^2 - 2*90*75*cos(85)}$

7 0

3 years ago