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liq [111]
2 years ago
8

Evaluate 1/4 c + 3d when c = 6 and d = 7

Mathematics
2 answers:
Naddika [18.5K]2 years ago
8 0

           \rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}

       <em>Evaluate 1/4c+3d when c=6, and d=7.</em>

<em />

<em>         </em>\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}

       Replace c with 6, and d with 7:-

     \Large\text{$\displaystyle\frac{1}{4} (6)+3(7)$}

\bigstar On simplification,

   \Large\text{$\displaystyle\frac{1}{4} \times\frac{6}{1}+21$}

\bigstar On further simplification,

    \Large\text{$\displaystyle\frac{6}{4} +21$}

\bigstar On further simplification,

     \Large\text{$\displaystyle\frac{6}{4}+\frac{84}{4}$}

\bigstar Adding the numerators,

\Large\text{$\displaystyle\frac{90}{4}$}

\bigstar Finally, Reducing the fraction:-

\Large\text{$\displaystyle\frac{45}{2}$}

\Uparrow \mathbb{OUR\:SIMPLIFIED\:EXPRESSION}

<h3>Good luck with your studies.</h3>

         \rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{50}{1}

natulia [17]2 years ago
4 0

Answer:

SolutioN :

  • Just plug in the values of c & d in the given expression and calculate :

\longrightarrow \bf \:  \frac{1}{4}  \times 6 + 3 \times 7

\longrightarrow  \boxed{\bf{ \frac{45}{2} }}

  • Our final answer is 45/2 .

--------------HappY LearninG <3 -------

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Aleks04 [339]

The rate of change of temperature with time at a point in time is given by

the derivative of the function for the temperature of the soup.

The correct responses are;

  • a) H'(5) is approximately<u> -2.6 degrees Celsius per minute</u>.
  • b) Yes
  • c) The equation for the line tangent is<u> y = -3.6·t + 90.8</u>
  • The approximate value of C(5) is <u>72.8 °C</u>

  • d) The rate of change of the temperature of the soup at t = 3 minutes is <u>-3.6 degrees Celsius per minute</u>.

Reasons:

a) From the data in the table, we have;

The approximate value of H'(5) is given by the average value of the rate of

change of the temperature with time between points, t = 3, and t = 8

Therefore;

\displaystyle H'(5) = \mathbf{\frac{H(8) - H(3)}{8 - 3}}

Which gives;

\displaystyle H'(5) =  \frac{80 - 67}{8 - 3} = \mathbf{2.6}

Therefore, H'(5) = <u>-2.6°C per minute</u>

b) Given that the function is twice differentiable over the interval, 0 ≤ t ≤ 12, the function for the change in temperature is continuous in the interval 0 ≤ t ≤ 12

At t = 0, H(0) = 90 °C

At t = 12, H(12) = 58 °C

  • 58 °C < 60 < 90 °C

Therefore, there exist a temperature, of 60 °C between 90° C and 58 °C

c) The given derivative of <em>C</em> is, C'(t) = \mathbf{-3.6 \cdot e^{-0.05 \cdot t}}

At t = 3, we have;

The \ slope \ at \ t = 3 \ is \ C'(3) = -3.6 \cdot e^{-0.05 \times 3} \approx -3.1

Therefore, we have;

y - 80 ≈ -3.1 × (x - 3)

The equation for the tangent is; y = -3.6 × (x - 3) + 80

y = -3.6·x + 10.8 + 80 = -3.6·x + 90.8

  • The equation for the tangent is; <u>y = -3.6·x + 90.8</u>

The  value of C(5) is approximately, C(5) ≈ -3.6 × 5 + 90.8 = 72.8

  • <u>C(5) ≈ 72.8°</u>

<u />

d) Based on the the model above, the rate at which the temperature of the

soup is changing at t = 3 minutes is <u>-3.6 degrees per minute</u>.

Learn more about calculus and concepts here:

brainly.com/question/20336420

8 0
3 years ago
PLEASE HELP OR ELSE MOM WILL BE REALLY MAD!!!!! Two trains, one going from Boston to New York and the other going from New York
Rufina [12.5K]

Answer:

140 mile

Step-by-step explanation:

d_{1} +d_{2} =220\\2(2x-10+x)=220\\x=40\\d_{1}=2*(2*40-10)=140mile

While x is the speed of the second train.

6 0
3 years ago
Read 2 more answers
If f(x) = x + 1 and g(x) = 2x – 7, which expression is equivalent to [f o g](3)? (3 + 1)(2(3) –7) 2(3)2 – 6 2(3 + 1) – 7 (2(3) –
ValentinkaMS [17]

Answer:

Solution

-1

f

x=

1

-X+

2

Step-by-step explanation:

f(x=2x-7

Solving Steps

y=2x-7

Interchange the variables

x=2y-7

Swap the sides

2y-7=X

Move the constant to the right

2y=X+7

Divide both sides

1

y=

>+*.

7

2

Solution

-1

f

x=

1

-X+

2

5 0
2 years ago
Find the sides of a rectangle having area 125 square units if the sides are in the ratio 5:3.
tatiyna

For this case we have the following data:

Area of the rectangle, A = 125

Relationship of the sides 5: 3

By definition, the area of a rectangle is given by:

A = a * b

Where

  • a: is the longest side.
  • b: it is the side of least length.

If the sides have a 5: 3 ratio, it means:

\frac{a}{b}=\frac{5}{3}

a=\frac{5}{3}b

Substituting in the formula of the area, we have:

125 =a * b\\

125=\frac{5}{3}b*b

Clearing b:

3 * 125 = 5 * b ^ 2

\frac{375}{5}= b ^ 2

75 = b ^ 2

b =\sqrt{75}b = 8.7 units

Substituting and clearing:

125 = a * 8.7

a =\frac{125}{8.7}

a = 14.4units

So, the sides are:

a = 14.4units

b = 8.7units

Answer:

a = 14.4units

b = 8.7units


7 0
3 years ago
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=(x-1)(4x+2)-4x^2
myrzilka [38]
Linear.  The 4x^2 will cancel out
4 0
4 years ago
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