How many hours must you run if you want to run 27 km at a rate of 9 km/h? (Apex)

Mathematics

1 answer:

Nuetrik [128]4 years ago

7 0

Answer:

Step-by-step explanation:

27 km

9 km every hour

so 27/9=3

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A car radiator needs a 80% antifreeze solution. The radiator now holds 15 liters of a 70% solutions. How many liters of this sho

slavikrds [6]

So... the radiator has 15 liters of 70% antifreeze.. but needs an 80% antifreeze

well, so, you need to drain some and put some with higher percentage, seems to be, you will end up at the same 15 liters, possible the radiator's capacity, of 80% antifreeze

so, the same amount going out, of 70% is the same amount going in, of 100% antifreeze

now.. let's use the decimal format for the percents, or 70% is 70/100 or 0.7 and so on
$\bf \begin{array}{lccclll}
&amount&concentration&
\begin{array}{llll}
concentration\\
amount
\end{array}\\
&-----&-------&-------\\
\textit{70\% sol'n, out}&x&0.7&0.7x\\
\textit{100\% sol'n, in}&x&1.00&x\\
\textit{current 70\% sol'n}&15&0.7&10.5\\
-----&-----&-------&-------\\
mixture&15&0.8&12
\end{array}$

so.. let's subtract, from the current solution, 0.7x and add 1x or x, our antifreeze concentration amount, should be 12 though

10.5 - 0.7x + x = 12

solve for "x"

3 0

4 years ago

Read 2 more answers

Given that 1 x2 dx 0 = 1 3 , use this fact and the properties of integrals to evaluate 1 (4 − 6x2) dx. 0

Debora [2.8K]

So, the definite integral $\int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74$

Given that

$\int\limits^1_0 {x^{2} } \, dx = 13$

We find

$\int\limits^1_0 {(4 - 6x^{2} )} \, dx$

<h3>Definite integrals </h3>

Definite integrals are integral values that are obtained by integrating a function between two values.

So, $Integral \int\limits^1_0 {(4 - 6x^{2} )} \, dx$

So, $\int\limits^1_0 {(4 - 6x^{2} )} \, dx = \int\limits^1_0 {4} \, dx - \int\limits^1_0 {6x^{2} } \, dx \\= 4[x]^{1}_{0} - \int\limits^1_0 {6x^{2} } \, dx \\= 4[x]^{1}_{0} - 6\int\limits^1_0 {x^{2} } \, dx \\= 4[1 - 0] - 6\int\limits^1_0 {x^{2} } \, dx\\= 4[1] - 6\int\limits^1_0 {x^{2} } \, dx\\= 4 - 6\int\limits^1_0 {x^{2} } \, dx$