Factorise <img src="https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%2011x" id="TexFormula1" title="x^{2} + 11x" alt="x^{2} + 11x" alig

9= 3 3_4- 2 7_8- b <br> B?

rosijanka [135]

Answer:

Step-by-step explanation:

9 - 3¾ - 2⅞ = 3⅜

He gave his grandmother 3⅜ pounds of apples.

4 0

3 years ago

Carl and Bob can demolish a building in 6 days, Anne and Bob can do it in 3, Anne and Carl in 5. How many days does it take all

nata0808 [166]

Answer:

59/20 days or 2.95 days

Step-by-step explanation:

Let Carl do the job in c days, Anne- in a, and Bob in b days

Then the portion of job they can do is 1/c, 1/a and 1/b

<u>As per given we have below equations:</u>

1/c + 1/b= 1/6
1/a + 1/b = 1/3
1/a + 1/c = 1/5

<u>Sum of all 3 equations gives us:</u>

2(1/a + 1/b + 1/c) = 1/6 + 1/3 + 1/5
2(1/a + 1/b + 1/c) = 5/30 + 10/30 + 6/30
2(1/a + 1/b + 1/c) = 21/30
2(1/a + 1/b + 1/c) = 7/10
1/a + 1/b + 1/c = 7/20

It means all three together can complete 7/20 of the job in one day

1 - 7/20 = 13/20

<u>As Anne and Bob can do 1/3 of the job in one day, they need time to complete the rest:</u>

13/20:1/3 = 39/20

<u>Add 1 day to this to find overall time:</u>

1 + 39 /20 = 59/20 days or 2.95 days

4 0

3 years ago

Evaluate the limit as x approaches 0 of (1 - x^(sin(x)))/(x*log(x))

e-lub [12.9K]

$sin~ x \approx x ~ ~\sf{as}~~ x \rightarrow 0$

We can replace sin x with x anywhere in the limit as long as x approaches 0.

Also,

$\large \lim_{ x \to 0 } ~ x^x = 1$

I will make the assumption that <span>log(x)=ln(x)</span><span>.

The limit result can be proven if the base of </span><span>log(x)</span><span> is 10.
</span>
$\large \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{x \log x } \\~\\ \large = \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{ \log( x^x) } \\~\\ \large = \lim_{x \to 0^{+}} \frac{1- x^{x} }{ \log( x^x) } ~~ \normalsize{\text{ substituting x for sin x } } \\~\\ \large = \frac{\lim_{x \to 0^{+}} (1) - \lim_{x \to 0^{+}} \left( x^{x}\right) }{ \log( \lim_{x \to 0^{+}}x^x) } = \frac{1-1}{\log(1)} = \frac{0}{0}$

We get the indeterminate form 0/0, so we have to use <span>Lhopitals rule

</span> $\large \lim_{x \to 0^{+}} \frac{1- x^{x} }{ \log( x^x) } =_{LH} \lim_{x \to 0^{+}} \frac{0 -x^x( 1 + \log (x)) }{1 + \log (x) } \\ = \large \lim_{x \to 0^{+}} (-x^x) = \large - \lim_{x \to 0^{+}} (x^x) = -1$
<span>
Therefore,

</span> $\large \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{x \log x } =\boxed{ -1}$ <span>
</span>

3 0

3 years ago

The tallest tree in the world is 379 feet tall. How tall will each of the trees be in the year 2030 if their models continue? Is

tresset_1 [31]

Models are patterns that are used to predict measurements and populations

<h3>How to model the tree</h3>

The question is incomplete, as the model and the dataset to model that growth of the tree are not given.

So, I will give a general explanation

If the model of the tree follows a linear model (e.g y = 2x + 3), then the model is not reasonable.

This is so because, population and growth cannot be measured by a linear model

However, if the growth of the trees follow an exponential model (e.g y = 2(3)^x), then the model is reasonable

Read more about mathematical models at:

brainly.com/question/24282972

3 0

2 years ago

At the end of 8 years, Anna paid $400 interest for a loan. If the simple annual interest rate was 4%, how much did Anna borrow?

TiliK225 [7]

Answer:

Step-by-step explanation:

Use the formula i = prt

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year,

then, solving our equation

P = 400 / ( 0.04 × 8 ) = 1250

P = $ 1,250.00

The principal required to

accumulate interest of $ 400.00

on a rate of 4% per year for 8 years is $ 1,250.00.

<h3><u>Brainliest Please!</u></h3>

4 0

3 years ago

Read 2 more answers