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4 years ago

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Strike441 [17]4 years ago

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24 sponge fingers and 420 jelly

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In ΔXYZ, ∠X=82° and ∠Y=84°. ∠XWZ=90° and XY=97. Find the length of XW to the nearest integer.

ivanzaharov [21]

Check the picture below to the left, let's use those sides with the law of sines

$\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(14^o)}{97}=\cfrac{sin(84^o)}{XZ}\implies XZ = \cfrac{97\cdot sin(84^o)}{sin(14^o)}\implies XZ \approx 398.76 \\\\\\ \stackrel{\textit{now using SOH CAH TOA}}{cos(82^o) = \cfrac{XW}{XZ}}\implies XZcos(82^o)=XW \\\\\\ 398.76cos(82^o)\approx XW\implies 55.497\approx XW\implies \stackrel{\textit{rounded up}}{55=XW}$

7 0

3 years ago

The water height of a pool is determined by 5g2 + 3g − 2, the rate that the pool is filled, and 6g2 − 4g − 3, the rate that wate

lyudmila [28]

Answer:

$h_g=-g^2+7g+1\\\\h_1=7\\\\h_2=11\\\\h_3=13\\\\h_4=13$

Step-by-step explanation:

Given the rate of filling is $5g^2+3g-2$ and the rate of emptying the pool is $6g^2-4g-3$ . The height of the pool at any time is:

$h_t=R_{in}-R_{out}, h_t- \ height \ at\ time\ t\\\\h_t=(5g^2+3g-2)-(6g^2-4g-3)\\\\h_t=-g^2+7g+1$

#Substitute the value of g in the height equation to find the height of the pool:

#g=1

$h_t=-g^2+7g+1, \ g=1\\\\h_t=-(1)^2+7(1)+1\\\\=7$

#g=2

$h_t=-g^2+7g+1, \ g=1\\\\h_t=-(2)^2+7(2)+1\\\\=11$

#g=3

$h_t=-g^2+7g+1, \ g=1\\\\h_t=-(3)^2+7(3)+1\\\\=13$

#g=4

$h_t=-g^2+7g+1, \ g=1\\\\h_t=-(4)^2+7(4)+1\\\\=13$

6 0

4 years ago

What is 7.4×10 the 2 power +2.73×10 to the 5th power ?

murzikaleks [220]

$(7.4 * 10^{2}) + (2.73 * 10^{5})$

$74 + 273000$

$273074$

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4 years ago

2. The new Avengers movie just came out. Tickets

liq [111]

Answer:

$85.46

Step-by-step explanation:

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3 years ago

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What the ratio to 7 to 1 written in 3 different ways

Sholpan [36]

Answer: 14:2, 35:5, 21:3

Step-by-step explanation:

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3 years ago

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