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ASHA 777 [7]
3 years ago
11

Antoine has $18.20 to spend on some oranges and a pumpkin. Oranges cost

Mathematics
1 answer:
Oksana_A [137]3 years ago
7 0

Answer:

10 pounds

Step-by-step explanation:

You forgot the inequality sing, but since Antoine can't spend more than $18.20, I am positive that the sign is \leq (Antony can spend $18.20 or less than $18.20).

Therefore, our inequality is: 1.30x+5.20\leq 18.20

where x is the pounds of oranges

Let's solve step-by-step to find how many pounds of oranges he can buy

Step 1. Subtract 5.20 fro both sides of the inequality

1.30x+5.20-5.20\leq 18.20-5.20

1.30x\leq 13

Step 2. Divide both sides of the inequality by 1.30

\frac{1.30x}{1.30} \leq \frac{13}{1.30}

x\leq 10

We can conclude that Antony can buy 10 pounds of oranges.

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Find the angle between u=(8, -2) and v=(9,3) Round to the nearest tenth of a degree.
Kryger [21]

Answer:

the angle between u=(8, -2) and v=(9,3) is 32.5°

Step-by-step explanation:

u=(8,-2)=(u1,u2)→u1=8, u2=-2

v=(9,3)=(v1,v2)→v1=9, v2=3

We can find the angle between two vectors using the formula of dot product:

u . v =║u║║v║cos α   (1)

And the dot product is:

u . v = u1 v1 + u2 v2

u . v = (8)(9)+(-2)(3)

u . v = 72-6

u . v = 66


║u║=√(u1²+u2²)

║u║=√((8)²+(-2)²)

║u║=√(64+4)

║u║=√(68)

║u║=√((4)(17))

║u║=√(4)√(17)

║u║=2√(17)


║v║=√(v1²+v2²)

║v║=√((9)²+(3)²)

║v║=√(81+9)

║v║=√(90)

║v║=√((9)(10))

║v║=√(9)√(10)

║v║=3√(10)


Replacing the known values in the formula of dot product (1):

u . v =║u║║v║cos α

66 = 2√(17) 3√(10) cos α

Multiplying:

66 = 6√((17)(10)) cos α

66 = 6√(170) cos α

Solving first for cos α: Dividing both sides of the equation by 6√(170):

\frac{66}{6\sqrt{170} }=\frac{6\sqrt{170}cos \alpha}{6\sqrt{170} }

\frac{66}{6\sqrt{170}}=cos\alpha

Simplifying: Dividing the numerator and denominator on the left side of the equation by 6:

(66/6)/(6√170/6)=cosα→11/√170=cosα→cosα=11/√170

cosα=11/13.03840481→cosα=0.84366149

\alpha=cos^{-1}0.84366149\\\alpha=32.47119205^{\°}\\ \alpha=32.5^{\°}

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