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3 years ago

Please help. 20 points. Show all work. Thank you.

Mathematics

1 answer:

Bogdan [553]3 years ago

5 0

The lateral area of a cone is the surface area (aka area of the sides of the object) minus the area of the base of the cone.

The equation for the lateral area of a cone is: $lateral \: area = \pi rl$
where r = radius and l = slant height.

Since you know that the lateral area = $500 \pi \: cm^{2}$ and the radius, r = 50 cm, you can plug those values into the equation for the lateral area and solve for l, the slant height:
$lateral \: area = \pi rl\\
500 \pi = \pi (50)(l)\\
500 = 50l\\
l = 10$

The slant height of the cone is A) 10cm.

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Please could you find the answers to the questions in the attachment.

Fudgin [204]

( $\frac{x1+x2}{2} , \frac{y1+y2}{2}$ )we need 3 equations
1. midpoint equation which is ( $\frac{x1+x2}{2} , \frac{y1+y2}{2}$ ) when you have 2 points

2. distance formula which is D= $\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$

3. area of trapezoid formula whhic is (b1+b2) times 1/2 times height

so

x is midpoint of B and C
B=11,10
c=19,6
x1=11
y1=10
x2=19
y2=6
midpoint=( $\frac{11+19}{2} , \frac{10+6}{2}$ )
midpoint=( $\frac{30}{2} , \frac{16}{2}$ )
midpoint= (15,8)

point x=(15,8)

y is midpoint of A and D
A=5,8
D=21,0
x1=5
y1=8
x2=21
y2=0
midpoint=( $\frac{5+21}{2} , \frac{8+0}{2}$ )
midpoint=( $\frac{26}{2} , \frac{8}{2}$ )
midpoint=(13,4)

Y=(13,4)

legnths of BC and XY
B=(11,10)
C=(19,6)
x1=11
y1=10
x2=19
y2=6
D= $\sqrt{(19-11)^{2}+(6-10)^{2}}$
D= $\sqrt{(8)^{2}+(-4)^{2}}$
D= $\sqrt{64+16}$
D= $\sqrt{80}$
D= $4 \sqrt{5}$
BC= $4 \sqrt{5}$

X=15,8
Y=(13,4)
x1=15
y1=8
x2=13
y2=4
D= $\sqrt{(13-15)^{2}+(4-8)^{2}}$
D= $\sqrt{(-2)^{2}+(-4)^{2}}$
D= $\sqrt{4+16}$
D= $\sqrt{20}$
D= $2 \sqrt{5}$
XY= $2 \sqrt{5}$

the thingummy is a trapezoid
we need to find AD and BC and XY
we already know that BC= $4 \sqrt{5}$ and XY= $2 \sqrt{5}$

AD distance
A=5,8
D=21,0
x1=5
y1=8
x2=21
y2=0
D= $\sqrt{(21-5)^{2}+(0-8)^{2}}$
D= $\sqrt{(16)^{2}+(-8)^{2}}$
D= $\sqrt{256+64}$
D= $\sqrt{320}$
D= $4 \sqrt{2}$
AD= $4 \sqrt{2}$

so we have
AD= $4 \sqrt{2}$
BC= $4 \sqrt{5}$
XY= $2 \sqrt{5}$

AD and BC are base1 and base 2
XY=height
so
(b1+b2) times 1/2 times height
( $4 \sqrt{2}+4 \sqrt{5}$ ) times 1/2 times $2 \sqrt{5}$ =
( $4 \sqrt{2}+4 \sqrt{5}$ ) times \sqrt{5} [/tex] =
$4 \sqrt{10}+4*5$ = $4 \sqrt{10}+20$ =80 $\sqrt{10}$ =252.982

X=(15,8)
Y=(13,4)
BC= $4 \sqrt{5}$
XY= $2 \sqrt{5}$
Area=80 $\sqrt{10}$ square unit or 252.982 square units

7 0

3 years ago

Vertex A in quadrilateral ABCD lies at (-3, 2). If you rotate ABCD 180° clockwise about the origin, what will be the coordinates

natali 33 [55]

The rule for a rotation by 180° about the origin is (x,y) -->(−x,−y)

So A(-3, 2) to A'(3, -2)

Answer:

A'(3, -2)

4 0

3 years ago

Mr. Con makes punch by mixing 10.6 L of apple juice 0.6 L of oranges and 8 L of Ginger ale. He pours the mixture equally into 6

sattari [20]

Answer:

3.2

Step-by-step explanation:

For this we need to get the entire volume of the mixture. We get it by summing each quantities:

Vol = 10.6 + 0.6 + 8 = 19.2 L

So, we have 19.2 L for 6 bowls.

For getting the punch of each bowl we just need to divide this volume between the 6 bowls:

19.2 / 6 = 3.2 L

So, each bowl has 3.2 L

3 0

3 years ago

Please help a brother out I will give you brainliest -x-y=1 y=-x+4

Vera_Pavlovna [14]

Answer:

x=3 y=1

Step-by-step explanation:

-x-y=1

y=-x+4

x=-y-1

x=-y+4

x=-1+4

x=3

y=-3+4

y=1

7 0

3 years ago

A greengrocer sells a melon at a profit of 37.5% on the price he pays for it. what is the ratio the cost price to the selling pr

strojnjashka [21]

$\frac{100}{137.5} = \frac{1}{1.375}$ I simply divided by 100 and moved the decimal two places to the left.

4 0

3 years ago