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3 years ago

In any triangle ABC, which of the relations

Mathematics

1 answer:

MrRa [10]3 years ago

3 0

ab+bc>can is the correct answer

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When a bactericide is added to a nutrient broth in which bacteria are growing, the bacteria population continues to grow for a

baherus [9]

Answer:

a) 1296 bacteria per hour

b) 0 bacteria per hour

c) -1296 bacteria per hour

Step-by-step explanation:

We are given the following information in the question:

The size of the population at time t is given by:

$b(t) = 9^6 + 6^4t-6^3t^2$

We differentiate the given function.

Thus, the growth rate is given by:

$\displaystyle\frac{db(t)}{dt} = \frac{d}{dt}(9^6 + 6^4t-6^3t^2)\\\\= 6^4-2(6^3)t$

a) Growth rates at t = 0 hours

$\displaystyle\frac{db(t)}{dt} \bigg|_{t=0}= 6^4-2(6^3)(0) = 1296\text{ bacteria per hour}$

b) Growth rates at t = 3 hours

$\displaystyle\frac{db(t)}{dt} \bigg|_{t=3}= 6^4-2(6^3)(3) = 0\text{ bacteria per hour}$

c) Growth rates at t = 6 hours

$\displaystyle\frac{db(t)}{dt} \bigg|_{t=6}= 6^4-2(6^3)(6) = -1296\text{ bacteria per hour}$

3 0

4 years ago

If the r-value, or correlation coefficient, of a data set is 0.854, what is the

Kruka [31]

Answer with explanation:
Coefficient of determination(r²), is defined as, how well the data values are associated with each other when Regression line is drawn. In regression analysis, the coefficient of determination measures , how well the regression predictions approximate the real data points, means it measures the closeness between two variables.The Value of r², lies between 0 to 1. If value of r²=1, it shows ,regression line that is data values are Perfectly associated with each other.
If ,r²=0, it means there is no variation between two variables.There is 0% variation between two variables.
→Coefficient of Variation=[Correlation coefficient]²
=r²
=(0.854)²
=0.854 × 0.854
=0.729316
=0.730(Approx)

7 0

2 years ago

PLS HELPPP ASAP MATH

HACTEHA [7]

Answer:

B. 2x + 4y

Step-by-step explanation:

If x = 4, and y = 7, let's substitute these values for x and y in the equations!

For A, the equation is 2xy. Substitute the values and you have 2(4)(7) which equals 56. This expression is incorrect since the expression doesn't equal 36.

For B, the equation is 2x + 4y. Substitute and you get the equation

2(4) + 4(7) → 8 + 28 = 36.

36 is your desired value, and you get that with the expression 2x + 4y.

6 0

3 years ago

Read 2 more answers

If the price is increasing at a rate of 2 dollars per month when the price is 10 dollars, find the rate of change of the demand.

densk [106]

Answer:

The demand reduces by $7.12 per month

Step-by-step explanation:

Given

$p\to price$

$x \to demand$

$2x^2+5xp+50p^2=24800.$

$p =10; \frac{dp}{dt} = 2$

Required

Determine the rate of change of demand

We have:

$2x^2+5xp+50p^2=24800.$

Differentiate with respect to time

$4x\frac{dx}{dt} + 5x\frac{dp}{dt} + 5p\frac{dx}{dt} + 100p\frac{dp}{dt} = 0$

Collect like terms

$4x\frac{dx}{dt} + 5p\frac{dx}{dt} = -5x\frac{dp}{dt} - 100p\frac{dp}{dt}$

Factorize

$\frac{dx}{dt}(4x + 5p) = -5(x + 20p)\frac{dp}{dt}$

Solve for dx/dt

$\frac{dx}{dt} = -\frac{5(x + 20p)}{4x + 5p}\cdot \frac{dp}{dt}$

Given that: $2x^2+5xp+50p^2=24800.$ and $p = 10$

Solve for x

$2x^2 + 5x * 10 + 50 * 10^2 = 24800$

$2x^2 + 50x + 5000 = 24800$

Equate to 0

$2x^2 + 50x + 5000 - 24800 =0$

$2x^2 + 50x -19800 =0$

Using a quadratic calculator, we have:

$x \approx -113\ and\ x\approx88$

Demand must be greater than 0;

So: $x=88$

So, we have: $x=88$ ; $p =10; \frac{dp}{dt} = 2$

The rate of change of demand is:

$\frac{dx}{dt} = -\frac{5(88 + 20*10)}{4*88 + 5*10} * 2$

$\frac{dx}{dt} = -\frac{5(288)}{402} * 2$

$\frac{dx}{dt} = -\frac{2880}{402}$

$\frac{dx}{dt} \approx -7.16$

This implies that the demand reduces by $7.12 per month

8 0

3 years ago

Solve the simultaneous equations 4x + 3y = 20 4x + 2y = 14

fiasKO [112]

Step-by-step explanation:

$\underline{ \underline{ \text{Given}}} :$

$\tt{4x + 3y = 20........... \text{ equation \: ( \: i \: )}}$
$\tt{4x + 2y = 14.......... \text{equation \: (ii)}}$

$\underline{ \text{USE \: ELIMINATION \: METHOD}} :$

Subtract equation ( ii ) from equation ( i ) :

Remember that the sign of each term of the second expression changes i.e equation ( i ) now becomes -4x -3y = -20

$\tt{ \cancel{4x }+ 2y = 14}$

$\tt{ \cancel{ - 4x} - 3y = - 20}$

__________________

$\tt{ - y = - 6}$

⟿ $\tt{ \boxed{ \tt{y = 6}}}$

Again , Substituting the value of y in equation ( ii ) :

⟿ $\tt{4x + 2 \times 6 = 14}$

⟿ $\tt{4x + 12 = 14}$

⟿ $\tt{4x = 2}$

⟿ $\boxed{ \tt{x = \frac{1}{2}}}$

$\red{ \boxed{ \boxed{ \tt{Our \: final \: answer : x = \frac{1}{2 } \: and \: y = 6}}}}$

Hope I helped ! ツ

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8 0

3 years ago