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3 years ago

Compare 6•10^8 with 3•10^6

Mathematics

1 answer:

Nina [5.8K]3 years ago

7 0

$6\cdot10^8=2\cdot10^2\cdot\underline{3\cdot10^6} \Longrightarrow 6\cdot10^8>3\cdot10^6$

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Limx→+∞ (x-(lnx)^2) =?

expeople1 [14]

$\lim_{x\to\infty}(x-\ln(x)^2) \\\lim_{x\to\infty}(x-2\ln(x)) \\\lim_{x\to\infty}\Big(x\Big(1-\dfrac{2\ln(x)}{x}\Big)\Big) \\\lim_{x\to\infty}x\cdot\lim_{x\to\infty}\Big(1-\dfrac{2\ln(x)}{x}\Big) \\\infty\cdot\Big(\lim_{x\to\infty}(1)-\lim_{x\to\infty}\Big(\dfrac{2\ln(x)}{x}\Big)\Big) \\\infty\cdot(1-2\lim_{x\to\infty}(1/x)) \\\infty\cdot(1-0) \\\infty\cdot1=\boxed{\infty}$

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3 0

3 years ago

1. 5 + (-8) =

seropon [69]

Answer:

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Step-by-step explanation:

7 0

3 years ago

Solve the system of inequalities to decide if the point (-3,2) is part of the solution; y<=-4x-3, +8y>=7

inna [77]

Answer:

$(x,y) = (-3,2)$ is a solution

Step-by-step explanation:

Given

$y \le -4x + 3$

$x + 8y \ge 7$

Required

Determine if $(x,y) = (-3,2)$ is a solution

$y \le -4x + 3$ becomes

$2 \le -4 * -3 + 3$

$2 \le 15$ --- this is true

$x + 8y \ge 7$

$-3+ 8 * 2 \ge 7$

$13 \ge 7$ --- this is also true

Hence,

$(x,y) = (-3,2)$ is a solution

6 0

3 years ago

What is the approximate age of a woman whose normal systolic pressure measures 125 mm Hg?

sashaice [31]

The approximate age of a woman whose normal systolic pressure measures 125 mm Hg is 31

The function is given as:

$P(A) = 0.006A^2 - 0.02A + 120$

When the normal systolic pressure is 125, it means that:

$P(A) = 125$

So, we have:

$125 = 0.006A^2 - 0.02A + 120$

Subtract 125 from both sides of the equation

$0= 0.006A^2 - 0.02A + 120 -125$

$0= 0.006A^2 - 0.02A - 5$

Rewrite the equation as:

$0.006A^2 - 0.02A - 5 = 0$

Using a graphing calculator, we have:

$A = \{30.58, -27.25\}$

But age cannot be negative.

So, we have:

$A = 30.58$

Approximate

$A =31$

Hence, the age of the woman is 31

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8 0

2 years ago

Read 2 more answers

√₂

snow_lady [41]

Answer:

$2000 was invested at 5% and $5000 was invested at 8%.

Step-by-step explanation:

Assuming the interest is simple interest.

<u>Simple Interest Formula</u>

I = Prt

where:

I = interest earned.
P = principal invested.
r = interest rate (in decimal form).
t = time (in years).

Given:

Total P = $7000
P₁ = principal invested at 5%
P₂ = principal invested at 8%
Total interest = $500
r₁ = 5% = 0.05
r₂ = 8% = 0.08
t = 1 year

Create two equations from the given information:

$\textsf{Equation 1}: \quad \sf P_1+P_2=7000$

$\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500$

Rewrite Equation 1 to make P₁ the subject:

$\implies \sf P_1=7000-P_2$

Substitute this into Equation 2 and solve for P₂:

$\implies \sf 0.05(7000-P_2)+0.08P_2=500$

$\implies \sf 350-0.05P_2+0.08P_2=500$

$\implies \sf 0.03P_2=150$

$\implies \sf P_2=\dfrac{150}{0.03}$

$\implies \sf P_2=5000$

Substitute the found value of P₂ into Equation 1 and solve for P₁:

$\implies \sf P_1+5000=7000$

$\implies \sf P_1=7000-5000$

$\implies \sf P_1 = 2000$

$2000 was invested at 5% and $5000 was invested at 8%.

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5 0

1 year ago