Answer:
The answer to your question is x = 37.74
Step-by-step explanation:
Data
Right triangle
hypotenuse = c = 45
angle = 33°
adjacent side = x
Process
To solve this problem use trigonometric functions. The trigonometric function that relates the adjacent side and the hypotenuse is cosine.
cos Ф = Adjacent side / Hypotenuse
-Solve for Adjacent side
Adjacent side = hypotenuse x cosФ
-Substitution
Adjacent side = 45 x cos 33
-Simplification
Adjacent side = 45 x 0.839
-Result
Adjacent side = x = 37.74
Answer:
136 Degrees
Step-by-step explanation
Set up as (3x+11) + (5x-9) = 90
then solve for x using algebra.
you can do this because angle NSO and RSQ are eqaul once you know x you will be able to solve all the other angles and subtract from 360 (the total angle) to find NSR.
Steps:
3x+11+5x-9 = 90
8x+2=90
<u>x= 11</u>
Solve 3(11)+11 = 44
add known angles:
44+90+90 = 224
360-224 = 136 degrees
We use concepts like <u>complimentary angles</u> and<u> vertical angle theroem</u>.
Answer:
You need to invest at a continuous compound interest rate of 6.701355026%
Step-by-step explanation:
The formula to use is the compound interest formula:A=P(1+r/100)^t
where A=Total amount at the end of the investment period
P=Principal amount
R=Rate of interest
T=Investment tenor/time
Now,
350,000=50000(1+r/100)^30 is what needs to be simplified to 6.701355026%
Answer:
Acute angle between the two planes: approximately 
.
Step-by-step explanation:
Find the normal vector of each plane:
- The normal vector of the plane
is 
. - The normal vector of the plane
is 
.
As the name suggests, there is a 
angle between a plane and its normal vector. The following four angles will correspond to the vertices of a quadrilateral:
- The angle between the first plane and its normal vector.
- The angle between the normal vector of each plane.
- The angle between the second plane and its normal vector.
- The smallest angle between these two planes.
The sum of these four angles should be 
. Two of these four angles were known to be . Once the third angle (the angle between the two normal vectors) is found, subtractions would give the measure of the other angle (the smallest angle between these two planes.)
Make use of the dot product to find the angle between these two normal vectors. Let 
denote the angle between these two vectors.
.
Before continuing, notice that the smallest angle between the two planes would be 
.
Consider the identity: 
.
In other words, 
, the cosine of the smallest angle between the two planes (which the question is asking for) will be the opposite of 
, the cosine of the angle between the two normal vectors.
Therefore, the cosine of the smallest angle between the two planes will be 
.
Apply the inverse cosine function to find the size of that angle:
.
Answer:
hello : (D.) 6x + 3
Step-by-step explanation:
(4x+3) + 2x = 4x + 3 +2x = ( 4x+2x)+3 = 6x+3
