Answer:
The answer to your question is:
x = 13
x + 10 = 23
5x - 42 = 23
Step-by-step explanation:
Data
angle 1 = x + 10
angle 2 = 5x - 42
They are vertical angles so, they measure the same.
x + 10 = 5x -42
x - 5x = -42 - 10
- 4x = -52
x = -52/-4
x = 13
angle 1 = x + 10 = 13 + 10 = 23
angle 2 = 5x - 42 = 5(13) -42 = 65 -42 = 23
I think you forgot to add a photo
Answer:
These opposite angles are called Vertical Angles.
1st problem:
Use the Pythagorean theorem:
a^2+b^2=c^2
49+361=c^2
c^2=410
c=20.24
The answer is 20m
2nd problem:
First calculate the height using the Pythagorean theorem:
a^2+b^2=c^2
20^2+b^2=625 (i got 20 {radius} by half-ing the base edge length)
400+b^2=625
b^2=225
b=15
Next, solve for the volume:
V=a^2*h/3
V=40^2*15/3
V=1600*5
V=8000
The answer is the second choice or B.
Answer:
a = 
. Surface Area = 
. and area of the Dish = +pi
= +50.27=51.6
Step-by-step explanation:
(1) Constant. y(x) = a
that is the curve that we need to rotate around the y axis to get the parabola with diameter of 8 feet and 2 meter depth that statement is translated in mathematics as x = -4 to 4 and y = 0 to 2.
y max = 2, x max = 4 setting up a equation with a unknown gives
2=a4 and a = .
so we have now.
y(x) = 
(Done with solving for a Constant).
(2) Surface Area.
Setting Up surface integral.
(i) range in x = 0 to 4.
(ii) range in y = 0 to 2.
integral is.
Integral(0-2)[{integral[(0-4)
]}]dy
Evaluating this integral gives. .
and area is surface area + area of the circle with 8ft diameter.
= +pi = +50.27=51.6...
Note the Difference between area and aurface area.!
