Answer:
To the nearest tenth of a degree
∠E= 47.9°
Step-by-step explanation:
ΔDEF , let's recognize that it's a right angle triangle because of the presence of ∠F=90°.
Other important measurements are
DE = 82 feet, and EF = 55 feet.
We are to find ∠E
Let's find the missing side first
Side DF
DF² = DE² - EF²
DF²= 82²_55²
DF²=6724-3025
DF²= 3699
DF= 60.82 feet
Let's use the sine formula to look for the angle.
DF/sin ∠E= DE/sin 90
Sin 90= 1
DE= 82
DF= 60.82
Sin ∠E= DF/DE
Sin ∠E= 60.82/82
Sin ∠E= 0.7417
∠E= sin^-1 (0.7417)
∠E= 47.8764
To the nearest tenth of a degree
= 47.9°
Answer:
Step-by-step explanation:
I believe you wanted to type that the volume of a cylinder is 40 cubic feet, and try to find what the volume of the same base and height would be in comparison.
Recall that the volume of a cylinder of base B and height H is given by the formula:
Recall as well that the volume of a cone of base B and height H is given by the formula: 
Therefore, if the cone has the same base (B) as the cylinder, and equal height (H), then we can say that the volume of the cone is "one third" of the volume of the cylinder, which in Math terms is written as:
Therefore, in our case, given that the volume of the cylinder is 40 
, the volume of the cone would be:
Answer:
2
Step-by-step explanation:
The mode is the number that appear most often
The number with the most dots is 2
The mode is 2
Answer:
x = 8
Step-by-step explanation:
2x + 11 = 4x - 5
2x - 4x = -5 - 11
-2x = -16
-2x/-2 = -16/-2
x = 8
The diagonals are:
diagonal₁=2x+3y
diagonal₂=(x+8)+(2y+5)
We have to solve the following system of equations:
2x=3y
(x+8)=(2y+5)
We solve this system by substitution method:
2x=3y ⇒x=3y/2
(3y/2 +8)=2y+5
3y+16=4y+10
-y=-6
y=6
x=3y/2=3*6/2=9
we obtain the measure of the diagonals:
diagonal₁=2x+3y=2*9+3*6=18+18=36
diagonal₂=(x+8)+(2y+5)=(9+8)+(2*6+5)=17+17=34
Answer: The longest diagonal is 36 units.
