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nikdorinn [45]
3 years ago
8

Susan works as a tutor for $10 and hour, and as a waitress for $11 an hour. This month, she worked a combined total of 90 hours

at her two jobs. Let T be the number of hours Susan worked this month. Write an expression for the combined total dollar amount she earned this month. <, >, greater than or equal to, less than or equal to?
Mathematics
1 answer:
uysha [10]3 years ago
3 0

Answer:

\$(990-t)

Step-by-step explanation:

The correct question is

Susan works as a tutor for $10 and hour, and as a waitress for $11 an hour. This month, she worked a combined total of 90 hours at her two jobs. Let t be the number of hours Susan worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month

Let

t -----> the number of hours that Susan work as a tutor

y ----> the number of hours that Susan work as a waitress

z ---> the combined total dollar amount she earned this month

we know that

t+y=90

y=90-t-----> equation A

we know that

The combined total dollar amount she earned this month is equal to the number of hours that Susan work as a tutor multiplied by $10 plus the number of hours that Susan work as a waitress multiplied by $11

z=10t+11y ----> equation B

substitute equation A in equation B

z=10t+11(90-t)

z=10t+990-11t

z=990-t

therefore

The expression for the combined total dollar amount is $(990-t)

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The answer:

according to the image the coordinates of pre image are:

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3 years ago
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Consider the parabola r​(t)equalsleft angle at squared plus 1 comma t right angle​, for minusinfinityless thantless thaninfinity
kodGreya [7K]

Given:-   r(t)=< at^2+1,t>  ; -\infty < t< \infty , where a is any positive real number.

Consider the helix parabolic equation :  

                                              r(t)=< at^2+1,t>

now, take the derivatives we get;

                                            r{}'(t)=

As, we know that two vectors are orthogonal if their dot product is zero.

Here,  r(t) and r{}'(t)  are orthogonal i.e,   r\cdot r{}'=0

Therefore, we have ,

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                                              =2a^2t^3+2at+t

2a^2t^3+2at+t=0

take t common in above equation we get,

t\cdot \left (2a^2t^2+2a+1\right )=0

⇒t=0 or 2a^2t^2+2a+1=0

To find the solution for t;

take 2a^2t^2+2a+1=0

The numberD = b^2 -4ac determined from the coefficients of the equation ax^2 + bx + c = 0.

The determinant D=0-4(2a^2)(2a+1)=-8a^2\cdot(2a+1)

Since, for any positive value of a determinant is negative.

Therefore, there is no solution.

The only solution, we have t=0.

Hence, we have only one points on the parabola  r(t)=< at^2+1,t> i.e <1,0>




                                               




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