![\Huge\bf{\underline{\red \dag { Aиѕωєя }}} \red \dag](https://tex.z-dn.net/?f=%5CHuge%5Cbf%7B%5Cunderline%7B%5Cred%20%5Cdag%20%7B%20A%D0%B8%D1%95%CF%89%D1%94%D1%8F%20%7D%7D%7D%20%5Cred%20%5Cdag)
4 Packs of water and 7 Packs of candy bars.
So, we wanna know the smallest number that both 35 and 20 will go into.
Find the Least Common Multiple (LCM), but to find the LCM we need to find the prime factorization of each of the following number :-
![\sf {35 = 5(7)}](https://tex.z-dn.net/?f=%20%5Csf%20%7B35%20%3D%205%287%29%7D)
![\sf \red {20 = 5(4)}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cred%20%7B20%20%3D%205%284%29%7D)
![\sf {4 = 2(2)}](https://tex.z-dn.net/?f=%20%5Csf%20%7B4%20%3D%202%282%29%7D)
![\sf \red {20 = 5(2)(2)](https://tex.z-dn.net/?f=%20%5Csf%20%5Cred%20%7B20%20%3D%205%282%29%282%29)
~Now multiply all the numbers by 5 :-
![\sf \pink{5(7)(2)(2) = 35(2)(2) = 70(2) = 140}](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Cpink%7B5%287%29%282%29%282%29%20%3D%2035%282%29%282%29%20%3D%2070%282%29%20%3D%20140%7D)
This means she needs 140 bottles of water and 140 candybars.
Water is sold in packs of 35, this means that she needs :
![\sf \orange{ \frac{140}{35} = 4\: packs \: of \: water}](https://tex.z-dn.net/?f=%20%5Csf%20%5Corange%7B%20%5Cfrac%7B140%7D%7B35%7D%20%20%3D%204%5C%3A%20packs%20%5C%3A%20of%20%5C%3A%20water%7D)
Candy bars are sold in packs of 20, this means she needs :
![\sf \green{ \frac{140}{20} = 7 \: packs \: of \: candy \: bars}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cgreen%7B%20%5Cfrac%7B140%7D%7B20%7D%20%20%3D%207%20%5C%3A%20packs%20%5C%3A%20of%20%5C%3A%20candy%20%5C%3A%20bars%7D)
<u>___________________</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u>
∠1 and ∠8 are alternate exterior angles and ∠3 and ∠6 are alternate interior angles
step-by-step explanation:
When the transversal crosses line m and n, alternate angles are the pair of angles formed on the outside of each of the lines and opposite side of the transversal (∠1 and ∠8). However,alternate interior angles will form opposite of the transversal but inside the lines.(∠3 and ∠6 ).
Learn More
brainly.com/question/12441758
Keywords : Transversal, angles
#LearnwithBrainly
Answer:
![x =\dfrac{45 \sqrt{6}}{ 2}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B45%20%5Csqrt%7B6%7D%7D%7B%202%7D)
Step-by-step explanation:
From the given information:
The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.
Now, let V(x) be the time needed for the runner to reach the buoy;
∴ We can say that,
![\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}](https://tex.z-dn.net/?f=%5Cmathtt%7BV%28x%29%20%3D%20%5Cdfrac%7B70-x%7D%7B7%7D%2B%5Cdfrac%7B%5Csqrt%7B54%5E2%2Bx%5E2%7D%7D%7B5%7D%7D)
In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.
i.e
The differential of V(x) = V'(x) =0
=![\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%5Cbegin%20%7Bbmatrix%7D%20%5Cdfrac%7B70-x%7D%7B7%7D%20%2B%20%5Cdfrac%7B%5Csqrt%7B54%5E2%2Bx%5E2%7D%7D%7B5%7D%20%5Cend%20%7Bbmatrix%7D%3D%200)
![-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0](https://tex.z-dn.net/?f=-%5Cdfrac%7B1%7D%7B7%7D%2B%20%5Cdfrac%7B1%7D%7B5%7D%5Ctimes%20%5Cdfrac%7Bx%7D%7B%5Csqrt%7B54%5E2%2Bx%5E2%7D%7D%3D0)
![\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B5%7D%5Ctimes%20%5Cdfrac%7Bx%7D%7B%5Csqrt%7B54%5E2%2Bx%5E2%7D%7D%3D%20%5Cdfrac%7B1%7D%7B7%7D)
![\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}](https://tex.z-dn.net/?f=%5Cdfrac%7B5x%7D%7B%5Csqrt%7B54%5E2%2Bx%5E2%7D%7D%3D%20%5Cdfrac%7B1%7D%7B7%7D)
![\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B%5Csqrt%7B54%5E2%2Bx%5E2%7D%7D%3D%20%5Cdfrac%7B1%7D%7B%5Cdfrac%7B7%7D%7B5%7D%7D)
![\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B%5Csqrt%7B54%5E2%2Bx%5E2%7D%7D%3D%20%5Cdfrac%7B5%7D%7B7%7D)
squaring both sides; we get
![\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%7D%7B54%5E2%2Bx%5E2%7D%3D%20%5Cdfrac%7B5%5E2%7D%7B7%5E2%7D)
![\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%7D%7B54%5E2%2Bx%5E2%7D%3D%20%5Cdfrac%7B25%7D%7B49%7D)
By cross multiplying; we get
![49x^2 = 25(54^2+x^2)](https://tex.z-dn.net/?f=49x%5E2%20%3D%2025%2854%5E2%2Bx%5E2%29)
![49x^2 = 25 \times 54^2+ 25x^2](https://tex.z-dn.net/?f=49x%5E2%20%3D%2025%20%5Ctimes%2054%5E2%2B%2025x%5E2)
![49x^2-25x^2 = 25 \times 54^2](https://tex.z-dn.net/?f=49x%5E2-25x%5E2%20%3D%2025%20%5Ctimes%2054%5E2)
![24x^2 = 25 \times 54^2](https://tex.z-dn.net/?f=24x%5E2%20%3D%2025%20%5Ctimes%2054%5E2)
![x^2 = \dfrac{25 \times 54^2}{24}](https://tex.z-dn.net/?f=x%5E2%20%3D%20%5Cdfrac%7B25%20%5Ctimes%2054%5E2%7D%7B24%7D)
![x =\sqrt{ \dfrac{25 \times 54^2}{24}}](https://tex.z-dn.net/?f=x%20%3D%5Csqrt%7B%20%5Cdfrac%7B25%20%5Ctimes%2054%5E2%7D%7B24%7D%7D)
![x =\dfrac{5 \times 54}{\sqrt{24}}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B5%20%5Ctimes%2054%7D%7B%5Csqrt%7B24%7D%7D)
![x =\dfrac{270}{\sqrt{4 \times 6}}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B270%7D%7B%5Csqrt%7B4%20%5Ctimes%206%7D%7D)
![x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B45%20%5Ctimes%206%7D%7B%202%20%5Csqrt%7B%206%7D%7D)
![x =\dfrac{45 \sqrt{6}}{ 2}](https://tex.z-dn.net/?f=x%20%3D%5Cdfrac%7B45%20%5Csqrt%7B6%7D%7D%7B%202%7D)
Answer:
Step-by-step explanation: ok