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trapecia [35]
3 years ago
14

Solve for x to the nearest 10th. 410 = 1080(0.915)^x

Mathematics
1 answer:
Hunter-Best [27]3 years ago
4 0

Answer:

410/1080=(0.915)^x

0.379=(0.915)^x

ln0. 379/ln0.915=x

X=10.903

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If x = a sin α, cos β, y = b sin α.sin β and z = c cos α then (x²/a²) + (y²/b²) + (z²/c²) = ?​
Oduvanchick [21]

\large\underline{\sf{Solution-}}

<u>Given:</u>

\rm \longmapsto x = a \sin \alpha  \cos \beta

\rm \longmapsto y = b \sin \alpha  \sin \beta

\rm \longmapsto z = c\cos \alpha

Therefore:

\rm \longmapsto \dfrac{x}{a}  = \sin \alpha  \cos \beta

\rm \longmapsto \dfrac{y}{b}  = \sin \alpha  \sin \beta

\rm \longmapsto \dfrac{z}{c} = \cos \alpha

Now:

\rm =  \dfrac{ {x}^{2} }{ {a}^{2}} +  \dfrac{ {y}^{2} }{ {b}^{2} } +  \dfrac{ {z}^{2} }{ {c}^{2} }

\rm =  { \sin}^{2} \alpha  \cos^{2}  \beta   +  { \sin}^{2} \alpha  \sin^{2} \beta  +  { \cos}^{2} \alpha

\rm =  { \sin}^{2} \alpha  (\cos^{2}  \beta   +  \sin^{2} \beta  )+  { \cos}^{2} \alpha

\rm =  { \sin}^{2} \alpha \cdot1+  { \cos}^{2} \alpha

\rm =  { \sin}^{2} \alpha + { \cos}^{2} \alpha

\rm = 1

<u>Therefore:</u>

\rm \longmapsto\dfrac{ {x}^{2} }{ {a}^{2}} +  \dfrac{ {y}^{2} }{ {b}^{2} } +  \dfrac{ {z}^{2} }{ {c}^{2} }  = 1

5 0
3 years ago
There are 4 pitchers.
Westkost [7]

Answer:

7.2 litters of milk

Step-by-step explanation:

4 times 1.8

4 0
3 years ago
Read 2 more answers
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mars1129 [50]

Answer:

Al will need 91 feet of tile to go into his kitchen.

Step-by-step explanation:

A=L x W

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7 0
3 years ago
at the dog show, there are 4 times as many boxer as spaniels. if there are a total of 30 dogs, how many dogs are spaniel?
Lyrx [107]
Firstly, given this information there could be 25 labradors and poodles and only 4 boxers and 1 spaniel. However, assuming that there are only boxers and spaniels at the dog show the first thing to do is to divide 30 by 5 = 6 so the answer is, There are 6 spaniels.
5 0
3 years ago
Solve for the roots in the equation below. x4 + 3x2 - 4 = 0
fgiga [73]
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(x²  )(x²  )
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Notice that the x²-4 is a difference of two squares, so can be further factorised into (x+2)(x-2)
This leaves you with a final factorisation of:
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Now we handle each bracket individually to obtain our four solutions for x:
x+2=0
x=-2
x-2=0
x=2
x²+1=0
x²=1
x=<span>±1</span>

8 0
3 years ago
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