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kupik [55]
3 years ago
14

A cell phone company has a monthly charge of 10 dollars for unlimited minutes and 15 cents for each text message. These charges

can be expressed as 10+.15t, where t represents the number of text messages sent.
Mathematics
1 answer:
professor190 [17]3 years ago
8 0

Answer:

I've seen your responses to the incomplete question. Now here is the answer:

The number of extra messages sent was 285.

&

The formula to get the total amount spent for the month on messages is;

$10 + $0.1t ;where t= the extra messages after the first 1000 sent for the month

Step-by-step explanation:

Let the cost of each additional message be "t"

Since the unit of total monthly cost was in dollars, let's convert the 10cents to dollars.

Since 100 cents = 1 dollars

Therefore 10 cents = 10/100 = $0.1

We can say that the total cost of the remaining text messages sent for the month was 0.1 x t = $0.1t

The cost of first 1000 messages is $10 dollars a month.

Therefore, total amount spent is $10 + 0.1t

Since we were given that he spent a total of $38.5 for that month,

We can say that $10 + $0.1t = $38.5

Subtract $10 from both sides;

$10 - $10 + $0.1t = $38.5 - $10

To give; $0.1t = $28.5

Dividing both sides 0.1, we get;

t = $28.5/$0.1 = 285

So the number of extra messages sent was 285.

The formula to get the total amount spent is;

$10 + $0.1t ;where t= the extra messages after the first 1000 sent for the month

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3 years ago
The perimeter of a rectangle is 68 ft and its width is 8/9 times its length. Find the dimensions of the rectangle.
Fantom [35]
Its 5.9 cus you have  the perimeter to 68 and the with 8.9 so its 5.9
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3 years ago
For f(x)=3x+1 and g(x)=(x^2)-6, find (g/f)(x).
iragen [17]

f(x)=3x+1;\ g(x)=x^2-6\\\\\left(\dfrac{g}{f}\right)(x)=\dfrac{g(x)}{f(x)}\\\\\boxed{\left(\dfrac{g}{f}\right)(x)=\dfrac{x^2-6}{3x+1}}

6 0
3 years ago
Read 2 more answers
the width, length, and height of a rectangular prism are each increased by $10\%$. what is the percent increase in the volume of
kondor19780726 [428]

The volume of the rectangular prism will increase by 33% if the width, length, and height are each increased by 10%.

Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

The formula for the volume of a rectangular prism is:

V = l x w x h

where

“l” is the base length

“w” is the base width

“h” is the height of the prism

If the width, length, and height are each increased by 10%, the equation will now become:

V_{2}= 1.10 l * 1.10 w*1.10h

V_{2}= 1.331* l*w*h            V = l*w*h

V_{2}= 1.331* V

Hence, if the width, length, and height are each increased by 10%, the volume of the rectangular prism will increase by 33%.

To learn more about the volume of a rectangular prism: brainly.com/question/24284033

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6 0
2 years ago
For the following parameterized​ curve, find the unit tangent vector T​(t) at the given value of t. r​(t) = < 8 t,10,3 sine 2
san4es73 [151]

Answer:

The tangent vector for t = 0 is:

\vec T (t) = \left \langle \frac{8}{10}, 0, \frac{6}{10}   \right\rangle

Step-by-step explanation:

The function to be used is \vec r(t) = \langle 8\cdot t, 10, 3\cdot \sin (2\cdot t)\rangle

The unit tangent vector is the gradient of \vec r (t) divided by its norm, that is:

\vec T (t) =  \frac{\vec \nabla r (t)}{\|\vec \nabla r (t)\|}

Where \vec \nabla is the gradient operator, whose definition is:

\vec \nabla f (x_{1}, x_{2},...,x_{n}) = \left\langle \frac{\partial f}{\partial x_{1}}, \frac{\partial f}{\partial x_{2}},...,\frac{\partial f}{\partial x_{n}} \right\rangle

The components of the gradient function of \vec r(t) are, respectively:

\frac{\partial r}{\partial x_{1}} = 8, \frac{\partial r}{\partial x_{2}} = 0 and \frac{\partial r}{\partial x_{3}} = 6 \cdot \cos (2\cdot t)

For t = 0:

\frac{\partial r}{\partial x_{1}} = 8, \frac{\partial r}{\partial x_{2}} = 0 and \frac{\partial r}{\partial x_{3}} = 6

The norm of the gradient function of \vec r (t) is:

\| \vec \nabla r(t) \| = \sqrt{8^{2}+0^{2}+ [6\cdot \cos (2\cdot t)]^{2}}

\| \vec \nabla r(t) \| = \sqrt{64 + 36\cdot \cos^{2} (2\cdot t)}

For t = 0:

\| \vec r(t) \| = 10

The tangent vector for t = 0 is:

\vec T (t) = \left \langle \frac{8}{10}, 0, \frac{6}{10}   \right\rangle

8 0
3 years ago
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