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Hoochie [10]
3 years ago
11

Please help me asap​

Mathematics
1 answer:
puteri [66]3 years ago
3 0

1. 3.875

2. .35

3. 9 3/4

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Convert the polar coordinates (-3, -60°) to Cartesian coordinates.
notsponge [240]

Answer:

(1.5,-2.6)

Step-by-step explanation:

Given the polar coordinates (-3,60°).

Let our Cartesian coordinates be (x,y)

#We know that when converting the rectangular coordinates (x,y) to polar (r,θ), then:

r=\sqrt{x^2+y^2}\\\\\therefore r^2=x^2+y^2\\\\\theta=tan^{-1}(y/x)\\\therefore tan \theta=y/x

#Using the illustration above, we can express our polar coordinates as:

-3=\sqrt{x^2+y^2}\\\\-60\textdegree=tan^{-1}(y/x}

#Solve simultaneously to solve for x and y:

(-3)^2=x^2+y^2\ \ \ \ \ \ \ \ \ \ i\\\\tan(-0\texdegree)=y/x\ \ \ \ \ \ \ \ ...ii\\\\y=x\ tan(-60\textdegree)\ \ \ \ \ \ \ ...iii\\\\\#substitute\  y \ in\  i\\\\(-3)^2=x^2+(x \ tan (-60\textdegree))^2\\\\9=x^2+3x^2\\\\x=\sqrt{9/4}=1.5\\\\y=1.5\ tan(-60\textdegree)=-2.5981\approx-2.6

Hence, the Cartesian coordinates are (1.5,-2.6)

6 0
3 years ago
X - (-20) = 5 _________________
tamaranim1 [39]

X - (-20) = 5

When you subtract a negative, change it to addition:

X + 20 = 5

Subtract 20 from both sides:

X = -15

8 0
3 years ago
Read 2 more answers
Solve the quadratic equation below for the exact values of x:<br> 4x^2-5=75
grandymaker [24]

Step-by-step explanation:

4 {x}^{2}  - 5 = 75 \\ 4 {x}^{2}  = 75 + 5 \\ 4 {x}^{2}  = 80 \\  {x}^{2}  =  \frac{80}{4}  \\  {x}^{2}  = 20 \\ x = \pm \sqrt{20}  \\ x = \pm 2 \sqrt{5}

6 0
3 years ago
Sharon wants to buy a shirt that costs $60. The sales tax is 5%. How much is the sales tax? What is her total cost for the shirt
Ivahew [28]

Answer:

$3 sales tax

$63 total cost

Step-by-step explanation:

5% of 60 is 3, so that'd be 60 + 3 which is 63, or $63

hope this helps!!!

stay safe!!!

4 0
3 years ago
Read 2 more answers
In how many ways can the letters of the word "WINNER' be arranged?
andre [41]
Because there are 6 letters in WINNER, you can use factorials to find out how many ways the letters can be arranged.

Factorials are represented with the ! symbol. Use the factorial of 6 to solve the problem:

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

There are 720 different ways the letters can be arranged.
6 0
3 years ago
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