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3 years ago

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analyze the solution to the system to determine whether there is a catapult arm length that Aiden and Natalie can both use to la

unch their tennis balls the same distance. Explain your reasoning

1 answer:

kow [346]3 years ago

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Please insert another pic

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Which represents the solution to the absolute value equation?<br> 312x + 4 - 1 = 11

Nataly_w [17]

Answer:

the last one

Step-by-step explanation:

absolute value signs means that it can be positive or negative if this helps please put brainliest

4 0

3 years ago

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Pleasee help mee<br><br>12sin(x)-5cos(x)=6,5

abruzzese [7]

We turn -5,12 into polar coordinates. It's a Pythagorean Triple so

r = 13 Ф=arctan(-12/5) + 180° ( in the second quadrant )

so -5 = 13 cos Ф, 12 = 13 sin Ф

12 sin x - 5 cos x = 6.5

13 sinФ sin x + 13 cos Ф cos x = 6.5

13 cos(x - Ф) = 6.5

cos(x - Ф) = 1/2

cos(x - Ф) = cos 60°

x - Ф = ± 60° + 360° k integer k

x = Ф ± 60° + 360° k

x = 180° + arctan(-12/5) ± 60° + 360° k

That's the exact answer;

x ≈ 180° - 67.38° ± 60° + 360° k

x ≈ 122.62° ± 60° + 360° k

x ≈ { 62.62°, 182.62°} + 360° k, integer k

3 0

3 years ago

In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree

Degger [83]

The formula for arc length is s=r*angle theta where s is the arc length, r is the radius, and angle theta is central angle formed by the arc in radians.

In this case, the angle would be s/r or 4.2/4 which is 1.05 radians. We have to convert this into degrees and so you would multiply 1.05 by (180/pi) which results in approximately 60 degrees. Remember, if you want to convert radians into degrees, the conversion factor is 180/pi and for degrees into radians, it is pi/180.

4 0

3 years ago

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A person invest $1200 in an account that earns 2% interest compound quarterly. Find when the value of the investment reaches $15

Basile [38]

Answer:

After 11 years the value of the investment reaches $1500.00

.

Step-by-step explanation:

The formula used for finding time (when the value reaches certain amount) is:

$A= P(1+\frac{r}{n})^{nt}$

where A= Future VAlue

P= Principal Value

r= rate of interest (in decimal)

n= no of times investment is compounded

t= time

Putting the values given and finding Time t,

A= $1500

P= $1200

r= 2% or 0.02

n= 4 (compound quarterly)

$A= P(1+\frac{r}{n})^{nt}$

$1500= 1200(1+\frac{0.02}{4})^{4t}$

Dividing both sides by 1200 and solving 0.02/4 = 0.005

$1.25= (1+0.005)^{4t}$

$1.25= (1.005)^{4t}$

Since t is in power we take the logarithm ln on both sides.

The rule of logarithm says that the exponent can be multiplied with the base when taking log

$\ln1.25=ln( 1.005)^{4t}\\\ln1.25=4t * ln( 1.005)\\0.22 = 4t * 0.005\\Solving\,\,\\\frac{0.22}{4*0.005} = t\\=> t= 11\, years$

8 0

3 years ago

A total of 426 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student t

VashaNatasha [74]

I hope this helps you

8 0

3 years ago