Answer:
the original volume is lesser than the new volume by 242.47 in³
Step-by-step explanation:
Volume of a cone is;
V = ⅓πr²h
Where;
r is radius
h is height
For the original chamber;
r = 5.7/2 = 2.85 inches
h = 12 inches
Volume of this original chamber is;
V_orig = ⅓ × π × 2.85² × 12
V_orig = 102.02 in³
In the new design, the chamber is scaled by a factor of 1.5.
Thus;
r_new = 2.85 × 1.5 = 4.275 inches
h_new = 12 × 1.5 = 18 inches
V_new = ⅓ × π × 4.275² × 18
V_new = 344.49 inch³
V_new - V_orig = 344.49 - 102.02 =
Thus, the original volume is lesser than the new volume by 242.47 in³
Answer:
47.10
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
... Cos = Adjacent/Hypotenuse
The value y is the length of the hypotenuse, and the given length 35 is the side adjacent to the given angle. Thus, the cosine relationship will be helpful.
Filling in the given values, we have ...
... cos(42°) = 35/y
Multiplying by y/cos(42°), we can find y to be ...
... y = 35/cos(42°) ≈ 35/0.7431
... y ≈ 47.10
Y will be approximately 47.10 in length
Step-by-step explanation:
we will use this form that we memorized in our schools ............. SOH CAH TOA
CAH means , Cos ∅= Adjacent/Hypotenuse
Given values
∅ =42°
hypotenuse= y
adjacent side length = 35
now putting in our values into
Cos ∅= Adjacent/Hypotenuse
OR
cos(42°) = 35/y
by multiplying y on both sides we get
y= 35/cos( 42°)
cos(42°)= 0.743
so y= 35/0.743
y = 47.10632
OR
y ≈ 47.10
Answer:
y = 8x + 14
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 
x + 6 ← is in slope- intercept form
with slope m = -
Given a line with slope m then the slope of a line perpendicular to it is
= - 
= - 
= 8 , then
y = 8x + c ← is the partial equation
To find c substitute (- 3, - 10 ) into the partial equation
- 10 = - 24 + c ⇒ c = - 10 + 24 = 14
y = 8x + 14 ← equation of perpendicular line
Answer:
its ASA
Step-by-step explanation:
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